Design and Fabrication of a Compact Evaporator–Absorber Unit with Mechanical Enhancement for LiBr–H₂O Vertical Falling Film Absorption, Part II: Control-Volume Modeling and Thermodynamic Performance Analysis

Abstract

This study reports the thermodynamic performance of a patented compact vertical evaporator–absorber unit for LiBr–H₂O absorption cooling, extending Part I by translating validated prototype data into a rigorous control-volume assessment of coupled transport. Coolant-side calorimetry was used to determine the absorption heat-transfer rate (Q_abs), while a mass–energy balance provided an estimate of the absorption mass-transfer rate (${∆\dot{m}}_{abs}$) across twelve manually imposed thermal-load phases with tagged fan-OFF/ON sub-intervals. Linear trend (slope) analysis was applied to quantify phase-resolved dynamic behavior. Fan assistance produced three load-dependent regimes: (i) stabilization of downward trends under low and zero loads, yielding slope-based relative improvements above 100% in the most critical weak-gradient phases; (ii) acceleration of recovery at intermediate loads; and (iii) moderation of strongly positive drifts at high loads. The global thermal resistance ($R_{th}$) decreased by more than 30% in passive and low-load phases, and Wilcoxon signed-rank tests confirmed statistically significant reductions in most intervals (p < 0.05). Uncertainty contributions and robustness were quantified through an uncertainty budget decomposition and sensitivity analyses, and a subsystem-level normalization (η_EA = Q_abs/Q_in) is reported to support comparisons across loads without invoking cycle COP. Overall, active vapor-flow management using a low-power internal fan widens the useful operating envelope of compact absorbers and provides a validated thermodynamic baseline with practical, regime-aware control guidelines for decentralized low-carbon cooling technologies.

1. Introduction

The escalating global demand for space cooling, driven by urbanization and rising ambient temperatures, poses a critical challenge for energy sustainability. Conventional vapor compression refrigeration systems, while mature, are responsible for significant peak electricity consumption and greenhouse gas emissions [1,2]. In this context, thermally driven absorption cooling technologies, particularly those utilizing the lithium bromide–water (LiBr–H₂O) working pair, have emerged as a vital alternative [3,4,5]. These systems can be powered by low-grade thermal energy sources, such as solar collectors or industrial waste heat, thereby decoupling cooling supply from the electrical grid and reducing the carbon footprint of the built environment [6]. However, despite their thermodynamic potential, the widespread deployment of absorption chillers in decentralized or small-scale residential applications remains limited by the large collector areas required, their high initial cost, and their operational complexity [7].

The absorber component represents the thermodynamic and geometric bottleneck of these systems. The absorption of water vapor into the lithium bromide solution is a complex, coupled heat and mass transfer process that is inherently exothermic [8,9]. To maintain the driving potential, the heat of absorption must be efficiently rejected while simultaneously ensuring continuous renewal of the liquid–vapor interface. In conventional designs, this is achieved through large bundles of horizontal tubes relying on gravity-driven falling films. While effective for large-capacity industrial chillers, this architecture scales poorly for compact units, leading to excessive volume and weight relative to cooling capacity [10]. Consequently, the development of compact, intensified absorber designs is a prerequisite for next-generation decentralized cooling systems.

To overcome transport limitations and reduce size, extensive research has focused on enhancement techniques. The state-of-the-art is dominated by passive intensification strategies, which increase effective surface area or promote interfacial turbulence without external energy input [11]. Performance gains have been reported using micro-structured or roughened tubes, extended film paths, and advanced wetting geometries [12,13,14]. Parallel efforts have explored chemical enhancement through surfactants or nanofluids [15,16,17], inducing Marangoni convection that renews the interface [18,19,20]. While effective, chemical additives introduce stability and maintenance issues, and complex surface geometries often entail high manufacturing costs.

Active enhancement techniques, which use external energy to augment transport, have received comparatively less attention but offer unique control capabilities. Mechanisms such as mechanical vibration or rotation can intensify heat and mass transfer by disrupting boundary layers [21,22]. Yet, integrating moving parts within a hermetic vacuum vessel is challenging for compact absorbers. Recent theoretical reviews suggest that manipulating the vapor flow field could provide an alternative pathway to intensification [23], but experimental validation of simple, low-energy mechanical assistance in vertical compact configurations remains scarce.

Addressing the need for structural simplicity and operational robustness, a compact evaporator–absorber unit was designed and patented (IMPI, MX 4573B) [24]. The device integrates both processes within a single vertical cylindrical vessel and employs a low-power axial fan to assist vapor transport. In a preceding study (Part I) [25], the mechanical design, vacuum integrity, and basic thermal separation capabilities were experimentally validated. That work demonstrated that fan assistance sustains favorable local temperature and pressure differentials (ΔT, ΔP), particularly under low thermal loads, confirming functional viability. Thus, Part I established the experimental baseline; Part II extends that baseline through a control-volume, balance-based analysis, as summarized below.

Incremental Contribution of Part II. This second part builds upon the experimentally validated baseline reported in Part I. Rather than introducing new experiments, Part II advances the contribution by (i) applying a control-volume, balance-based formulation to estimate time-resolved absorber-side heat and mass transfer rates (Q_abs and ${\dot{∆m}}_{abs}$) from the validated dataset; (ii) extracting transient trends under variable-load operation using dynamic slope metrics over tagged OFF/ON intervals; and (iii) consolidating the fan influence into an operational regime-level interpretation across the recorded sequence. In this way, Part II complements Part I by adding analytical depth and subsystem-level interpretive value while remaining fully consistent with the scope of the original experimental campaign.

The patented compact evaporator–absorber unit offers (i) shared-vessel vertical integration reducing footprint and assembly complexity; (ii) hermetic, vacuum-robust construction with fewer welded interfaces; (iii) a low-power axial fan (≈20 W) acting as an internal aerodynamic actuator for active vapor guidance; (iv) measurable thermodynamic gains (Q_abs, ${\dot{m}}_{abs}$, $R_{th}$) within the same hardware baseline; (v) compatibility with transient heat sources typical of small solar or waste-heat systems; and (vi) low-cost, scalable manufacturability supporting decentralized cooling.

A significant knowledge gap remains regarding the coupled heat- and mass-transfer dynamics in such mechanically assisted compact units [26,27]. Specifically, the transient response of the absorption mass rate (${\dot{m}}_{abs}$) and absorption heat transfer rate (Q_abs) under variable loads has not been fully characterized using a control-volume approach. Furthermore, while fan stabilization was observed qualitatively in Part I, there is no quantitative map defining regimes where forced convection is thermodynamically beneficial versus those where it is marginal or associated with moderation (damping) behavior under high natural-convection loads. Understanding these regimes is essential for efficient control strategies in small-scale solar or waste-heat systems operating inherently under variable operating conditions [28]. Accordingly, this work emphasizes experimentally grounded thermodynamic rates and stability trends; classical dimensionless-group correlations fall outside the subsystem scope and are deferred to future work.

This paper (Part II) addresses these gaps by presenting a comprehensive thermodynamic performance analysis of the integrated evaporator–absorber unit. The study moves beyond Part I local indicators to apply a control-volume formulation, enabling quantification of Q_abs via coolant-side calorimetry and estimation of ${\dot{m}}_{abs}$. The experimental sequence comprises twelve thermal-load phases, introduced manually to elucidate intrinsic transient behavior and its response to mechanical activation. Manual Q_in switching was intentionally selected to preserve the unit’s natural transients and avoid controller-imposed artifacts; therefore, the analysis relies on time-tagged intervals and dynamic slope metrics rather than on steady-state plateaus.

The objectives of this work are (i) to quantify dynamic heat and mass transfer rates under variable input loads (Q_in$\approx 0\mathrm{t}\mathrm{o}225\mathrm{W}$), (ii) to evaluate efficiency through global thermal resistance ($R_{th}$) and validate improvements statistically, and (iii) to characterize regimes of mechanical enhancement, distinguishing stabilization, acceleration, and moderation behaviors. This analysis provides a thermodynamic baseline and control guidelines for compact, mechanically assisted absorption units, contributing to robust, low-cost technologies for decentralized sustainable cooling.

2. Materials and Methods

The thermal analysis framework and evaluation methodology are described in this section. Since the hardware configuration, sensor instrumentation, and data logging setup were detailed in Part I [25], they are not repeated here. Because the experimental test stand excludes the generator and condenser components, the evaluation of capacity in the context of a complete absorption chiller is outside the scope of this work. Consequently, the analysis decouples the evaporator-side load emulation from the absorber-side heat rejection. This study reports (i) the sustained heater input (Q_in) as a proxy for imposed evaporator-side loading; (ii) the absorbed heat rate (Q_abs) and the estimated absorption mass flow rate (${\dot{m}}_{abs}$); and (iii) the global thermal resistance ($R_{th}$). Here, Q_in represents the imposed evaporator-side thermal load, whereas Q_abs is the absorber-side heat released by vapor absorption and rejected through the coolant circuit; both are reported separately to avoid conflating load emulation with the performance.

Because the current compact integrated-vessel configuration does not provide direct sensing of local film/vapor parameters (interfacial area, film thickness, vapor-core velocity profiles, or axial property gradients), classical transport-regime correlations based on Re (Reynold number), Pr (Prandtl number), Gr (Grashof number), and Sc (Schmidt number) would require strong assumptions. Therefore, the evaluation is intentionally grounded on control-volume heat/mass balances and dynamic slope metrics derived directly from measured variables. Uncertainty propagation for derived signals (Q_abs, ${\dot{m}}_{abs}$,$R_{th}$₎ and non-parametric significance testing (Wilcoxon, α = 0.05) are detailed in subsequent subsections. Accordingly, Q_abs is explicitly distinguished from the evaporator cooling load to ensure thermodynamic rigor.

2.1. Experimental Platform Overview

Briefly, the unit consists of three vertically stacked cylindrical compartments (Ø 254 mm): a lower evaporator serving as the H₂O reservoir with two internal electrical heaters; a middle transport section housing a low-power axial fan (≈20 W) and the absorbent solution; and an upper cross-flow tubular absorber (43 tubes, 12.7 mm OD, 250 mm height) equipped with deflector baffles. The LiBr–H₂O solution is recirculated by a magnetic-drive pump, forming a vertical falling film distributed by a drip pan, while coolant water removes the heat of absorption through the absorber tube bundle. System temperatures, absolute pressures, and volumetric flow rates in both solution and coolant circuits are sampled at 1 Hz using an OPTO-22 SNAP-PAC-R1 controller.

Although the coefficient of performance (COP) is a standard indicator for complete absorption refrigeration cycles, its evaluation is not applicable to the present study. The experimental test stand used here includes only the evaporator–absorber unit and intentionally excludes the generator, condenser, and solution heat exchangers. As a result, the thermodynamic inputs required to define the system COP are not available, and any estimated value would lack physical validity. For this reason, the analysis focuses solely on the internal thermal–mass transport behavior of the evaporator–absorber unit. Hence, subsystem-level thermodynamic indicators are used as the appropriate evidence to assess the unit’s internal transport performance.

Normalized subsystem metric. Although a cycle coefficient of performance (COP) cannot be defined for the present apparatus because the generator, condenser, and solution heat exchangers are intentionally excluded, a load-normalized subsystem indicator can still be reported to support comparisons across operating phases and fan modes. Here, we define an evaporator–absorber subsystem effectiveness metric as follows:

$${\eta }_{EA}={\displaystyle \frac{Qabs}{Qin}},$$

(1)

where Q_abs is obtained from coolant-side calorimetry, and Q_in is the applied electrical input load to the evaporator-side heater. This dimensionless ratio is used strictly as a subsystem-level normalization (not a COP) to quantify how the derived absorber-side heat removal responds to the imposed input under each tagged load interval and fan condition (OFF/ON). Because Q_abs represents absorber-side heat rejection (including the heat of absorption) within an open subsystem boundary, ${\eta }_{EA}$ is not constrained to be ≤1 and should not be interpreted as an efficiency.

Importantly, ${\eta }_{EA}$ is not bounded to unity and may exceed 1, because it does not represent a closed-cycle energy efficiency: it compares the measured absorber-side heat rejection against the instantaneous electrical heating input applied at the evaporator during a transient interval, while the unit may release (or store) energy through internal thermal inertia and absorption-related effects. Therefore, ${\eta }_{EA}$ is reported only as a comparative, load-normalized subsystem descriptor consistent with the scope of the present measurements.

Figure 1 provides a simplified conceptual schematic of the integrated evaporator–absorber unit and the interaction between the evaporation, vapor-transport, and absorption zones evaluated in this work.

2.2. Operating Protocol and Cycle Description

The experimental test sequence was conducted as a single continuous run lasting 2 h 46 min 28 s. This continuous-run protocol was intentionally adopted to preserve the unit’s intrinsic transient behavior under variable loads; all data were recorded at 1 Hz and subsequently time-tagged into discrete phases and fan states, as described in Section 2.3. The cycle began by gradually reducing the internal pressure to approximately 1 kPa (saturation temperature ≈ 6 °C) using a vacuum pump. Once this condition was achieved, the H₂O refrigerant (1.55 kg) and LiBr absorbent solution (3.2 kg at an initial concentration of 59.76 wt %) were introduced into the unit. Although the campaign was executed as a single continuous run, the dataset contains repeated internal comparisons across the operating sequence. The test was segmented into twelve tagged thermal-load phases, each further divided into fan-OFF and fan-ON sub-intervals. This structure provides multiple within-run replicated comparisons for evaluating the fan effect under comparable load conditions and across repeated OFF/ON transitions using the same instrumentation, control-volume framework, and regression procedure. Accordingly, the present protocol is designed to characterize subsystem transient dynamics and regime-level trends under variable loads, rather than to establish long-duration endurance or multi-day reliability.

The system was activated in stages: first, the solution recirculation pump, followed by the axial fan after a brief delay. Finally, the two electric heaters in the lower compartment were energized to sequentially impose twelve thermal-input phases (Q_in,k). Within each phase, the fan was alternated between OFF and ON sub-periods to isolate mechanical assistance effects under the same thermal boundary conditions. The generated water vapor ascends through the middle compartment and encounters the descending LiBr solution in a counterflow configuration. As the vapor is absorbed into the solution, an exothermic process occurs; the released absorption heat is transferred through the vertical tube bank to the coolant water flowing on the shell side and is ultimately removed by the external cooling loop. The diluted absorbent solution collects at the bottom of the middle compartment and is pumped back to the upper compartment, completing the cycle. During the run, coolant-side flow was kept constant, and inlet conditions were monitored to support calorimetric evaluation of Q_abs in the subsequent analysis.

Ambient laboratory conditions. The continuous run was conducted in a closed laboratory space without active climatic control, but the ambient air temperature remained nearly constant throughout the 2 h 46 min test. The recorded room temperature ranged between 16.69 and 17.79 °C, with a mean value of 17.12 °C, i.e., fluctuations within ±0.6 °C around the mean. Under these conditions, the external heat exchange between the vessel and the laboratory air behaves as a nearly steady parasitic contribution over each tagged OFF/ON sub-interval. Rather than being modeled explicitly as a separate term in the control-volume balances, this contribution is implicitly captured in the measured absorption heat rate via coolant-side calorimetry. Because the slope-based metrics used in Section 3 focus on temporal trends, a quasi-constant environmental exchange does not alter the comparative interpretation of fan-OFF versus fan-ON evolution within each thermal-load phase.

2.3. Rationale for Manual Load Adjustment and Data Clustering

The twelve thermal-load phases (Q_in,1–Q_in,12) applied to the unit were introduced manually rather than through automated regulation. This was a deliberate methodological decision aligned with the objectives of Part II. A fully automated controller would likely suppress the natural transients that arise when switching power levels, thereby masking the dynamic coupling between vapor absorption, solution wetting, and external convection.

Manual switching preserves the intrinsic time delay associated with thermal inertia within the solution and vapor-transport domains, allowing the unit to exhibit genuine physical drifts. These drifts constitute the basis of the trend analysis reported in Section 3, where time-normalized slope metrics (a and b) are used to determine whether the subsystem stabilizes, accelerates, or moderates under specific thermal conditions. Although manual operation leads to unequal dwell times across phases, all data were recorded at 1 Hz and accurately time-tagged by phase and fan state; therefore, all regressions and balance calculations are performed within each tagged OFF/ON sub-interval, and different sample sizes $N_k$ do not bias the within-phase comparisons. This approach also avoids controller-imposed artifacts that tend to flatten gradients, and it reflects the practical operation of small-scale absorption systems subject to natural variability and micro-transients. Consequently, the resulting slopes are interpreted as intrinsic subsystem physics rather than as the footprint of an external controller. To address variability from manual switching (unequal dwell times and ramp shapes), the slope-based conclusions were additionally verified through fixed-window slope estimates, confirming that the regime-level interpretation is robust to these timing-related effects.

Due to manual regulation, minor fluctuations around target input levels were unavoidable. To facilitate a robust comparative analysis and to define thermally meaningful operating regimes, the imposed loads were clustered according to their magnitude:

• Group 1 (High loads): 219–223 W nominal input (Q_in,1, Q_in,6, Q_in,10).
• Group 2 (Medium-high loads): 138–183 W nominal input (Q_in,2, Q_in,7, and Q_in,11).
• Group 3 (Medium-low loads): 60–110 W (Q_in,3, Q_in,4, and Q_in,8).
• Group 4 (Zero-input/passive baseline): three phases with Q_in$\approx 0\mathrm{W}$ (Q_in,5, Q_in,9, Q_in,12), used as an internal repeatability reference under identical boundary conditions. Here, “zero-input” refers strictly to the electrical heaters being switched off; any residual environmental heat exchange with the laboratory air is implicitly included in the measured signal and forms part of the passive baseline rather than being treated as a separate imposed load.

2.4. Control-Volume Formulation and Data Reduction

To evaluate the coupled heat and mass transfer phenomena, the integrated evaporator–absorber unit is analyzed using a control-volume approach derived from the First Law of Thermodynamics. The physical domain is conceptually divided into three interacting subsystems: (i) the solution circuit, (ii) the refrigerant circuit, and (iii) the coolant-water circuit, as illustrated in Figure 2.

The governing mass- and energy-conservation equations, adapted from established modeling frameworks for vertical falling-film absorbers [29,30], are as follows:

• Solution circuit:

$${\dot{m}}_{sol,in}+∆{\dot{m}}_{abs}={\dot{m}}_{sol,out},$$

(2)

$$Q_{abs}={\dot{m}}_{sol,in}·h_{sol,in}-{\dot{m}}_{sol,out}·h_{sol,out}+∆{\dot{m}}_{abs}·h_{vap}.$$

(3)

• Refrigeration circuit:

$$Q_{in}={\dot{m}}_{vap}·h_{vap}.$$

(4)

• Coolant water circuit:

$$Q_{abs}={\dot{m}}_{cw}·{Cp}_{cw}·\left(T_{outc}-T_{inc}\right),$$

(5)

where $∆{\dot{m}}_{abs}$ is the absorption mass transfer ($\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-1}$); $Q_{abs}$ is the absorption heat transfer rate ($\mathrm{W}$); ${\dot{m}}_{vap}$ is the evaporated refrigerant mass flow; ${\dot{m}}_{cw}$ is the coolant water mass flow rate; $h_{vap}$ is the latent heat of vaporization; ${Cp}_{cw}$ is the specific heat capacity of coolant water; and $T_{inc}$, $T_{outc}$ are the coolant inlet and outlet temperatures.

Data-reduction strategy and assumptions. In this study, Equation (4) provides the primary evaluation of Q_abs. The coolant inlet/outlet temperatures and volumetric flow rate are measured directly, and ${\dot{m}}_{cw}$ is obtained from density-based conversion.

To estimate the absorption mass transfer rate, $∆{\dot{m}}_{abs}$, Equation (2) is rearranged assuming quasi-steady mass conservation within each tagged OFF/ON sub-interval, such that ${\dot{m}}_{sol,in}\approx {\dot{m}}_{sol,out}={\dot{m}}_{sol}$. This yields the following:

$$∆{\dot{m}}_{abs}={\displaystyle \frac{Q_{abs}-{\dot{m}}_{sol}\left(h_{sol,out}-h_{sol,in}\right)}{h_{vap}}},$$

(6)

In Equation (5), (i) $Q_{abs}$ is taken from the coolant-circuit calorimetric balance (Equation (4)); (ii) ${\dot{m}}_{sol}={\rho }_{sol}·{VF}_{sr}$, using a constant ${\rho }_{sol}$ within the narrow operating window; and (iii) $h_{sol,in/out}$ are assigned from LiBr–H₂O property correlations [31,32] at the local top/bottom absorber-section temperatures. Because these temperatures are near-film environmental readings rather than immersed values, a modeling uncertainty is introduced, as quantified in Section 2.5. All measured time-series used for the present data reduction (temperatures, pressures, and flow rates) are provided in the Supplementary Material for full reproducibility.

This estimation relies on three assumptions:

• Near-film properties. Solution enthalpies are inferred from near-film temperatures and literature correlations for ~60 wt.% LiBr–H₂O introduce an estimated ±15% uncertainty in $∆{\dot{m}}_{abs}$ due to a possible enthalpy mismatch.
• Constant density. The density used to convert volumetric solution flow (${VF}_{sr}$) to mass flow is treated as constant within the operating range, contributing an uncertainty of approximately ±5–10%.
• Constant latent heat. The latent heat of water vapor is taken as ${\mathrm{h}}_{\mathrm{v}\mathrm{a}\mathrm{p}}=2515\mathrm{M}\mathrm{J}·{\mathrm{k}\mathrm{g}}^{-1}$; its temperature dependence contributes <0.1% to the overall uncertainty.

Uncertainty propagation for all derived quantities follows the Kline–McClintock method and is presented in Section 2.5. The complete raw dataset from the continuous run, including phase tags and fan OFF/ON labels, is available as Supplementary Material.

2.5. Uncertainty and Error Propagation

To ensure that all derived variables are interpreted with appropriate confidence, an uncertainty analysis was performed for the measurement-based quantities used in this study. A first-order GUM/Kline–McClintock propagation scheme was adopted, in which each measured input contributes to the uncertainty of a derived quantity according to its sensitivity and individual standard uncertainty. Standard uncertainties u(x) were obtained from manufacturer accuracy specifications and from the variability observed in the experimental signals. Expanded uncertainties were computed as U(x) = ku(x) with k = 2, corresponding to an approximate 95% confidence level. This framework provides a consistent basis for quantifying the reliability of Q_abs, $∆{\dot{m}}_{abs}$, and $R_{th}$ across all thermal-load phases. The complete raw time-series used in these calculations (temperatures, pressures, flow rates, and phase/fan tags) is provided as Supplementary Material.

Applying the propagation method to the key balances yields a typical overall relative uncertainty on the order of ±6% for Q_abs. Uncertainties for $∆{\dot{m}}_{abs}$ and $R_{th}$ are phase-dependent and are reported explicitly in

Table A1. Expanded uncertainties (k = 2) for derived quantities per thermal-load phase and fan mode.

Phase Qin,k	Fan	N	$\mathbf{U}\mathbf{(}∆\mathit{T}\mathbf{)}\mathbf{[}°\mathbf{C}\mathbf{]}$	$\mathbf{U}\left({\mathit{Q}}_{\mathit{a}\mathit{b}\mathit{s}}\right)\left[\mathbf{W}\right]$	$\mathbf{U}(∆{\dot{\mathit{m}}}_{\mathit{a}\mathit{b}\mathit{s}})[\mathbf{K}\mathbf{g}/\mathbf{s}]$	$\mathbf{U}\left({\mathit{R}}_{\mathit{t}\mathit{h}}\right)[\mathbf{K}/\mathbf{W}]$
1	Off	174	0.367423	19.942241	0.028613	0.002652
1	On	284	0.367423	16.417964	0.021483	0.003505
2	Off	358	0.367423	19.708780	0.025705	0.003010
2	On	347	0.367423	29.141165	0.037803	0.002191
3	Off	383	0.367423	17.340115	0.022851	0.003690
3	On	270	0.367423	15.339036	0.020099	0.004015
4	Off	301	0.367423	12.818685	0.016903	0.004663
4	On	355	0.367423	11.611687	0.015319	0.004938
5	Off	426	0.367423	10.776648	0.014249	0.005343
5	On	997	0.367423	7.187841	0.009644	0.009088
6	Off	396	0.367423	9.621396	0.012362	0.005475
6	On	346	0.367423	17.415127	0.022762	0.002567
7	Off	305	0.367423	16.120900	0.021151	0.000017
7	On	294	0.367423	15.524080	0.020337	0.000009
8	Off	293	0.367423	13.574729	0.018110	0.003102
8	On	302	0.367423	13.036188	0.017148	0.003113
9	Off	370	0.367423	8.526518	0.011354	0.004722
9	On	1209	0.367423	7.119081	0.009552	0.007896
10	Off	418	0.367423	10.462230	0.011099	0.003946
10	On	248	0.367423	15.697957	0.020557	0.002103
11	Off	340	0.367423	14.788821	0.019376	0.002042
11	On	453	0.367423	14.657124	0.019219	0.002056
12	Off	311	0.367423	9.689035	0.012848	0.002850
12	On	808	0.367423	7.707146	0.010307	0.005725

. These values fall within ranges commonly reported for experimental heat- and mass-transfer systems of comparable complexity, supporting the reliability and reproducibility of the present results.

Instrumental uncertainties used as inputs for the propagation scheme are summarized in

Table 1. Instrumental uncertainties used for error propagation.

Measured Variable	Instrument/Sensor	Uncertainty (±)	Unit
Temperature (T)	OMEGA TC-K-NPT-U-72 thermocouples	0.3	°C
Pressure (P)	OMEGA PX309-015AI transducers	1.0	% of FS
Flow rate (coolant water)	YF-S201 hall-effect sensor	10.0	%
Voltage and current	DC power Supply + DAQ (OPTO22 SNAP-PAC-R1)	0.5	%
$\mathrm{Density},Cp$ (water, LiBr)	Literature values (assumed constant)	2.0	% (est.)
Cross-sectional area (A)	CAD measurement of internal geometry	1.0	% (est.)

Note: Thermophysical properties (density and specific heat capacity, $Cp$) for water and LiBr–H₂O solution were taken from standard literature correlations and assumed constant within the experimental temperature window; a conservative ±2% relative uncertainty was assigned. FS = full scale.

.

2.5.1. Measurement Uncertainties

Temperature measurements were collected at all points relevant to the thermal evaluation, including absorber, evaporator, and coolant lines. Each thermocouple carries a standard uncertainty $u_T$ reflecting calibration tolerance, electronic noise, and short-timescale fluctuations. The absorber temperature ($T_{abs}$) standard uncertainty is

$${u(T}_{abs})=u_T,$$

(7)

and for temperature differences,

$$u\left(∆T\right)=\sqrt{u^2\left(T_{abs}\right)+u^2\left(T_{ev}\right)}.$$

(8)

Expanded uncertainties were computed as U(x) = ku(x) with k = 2.

The coolant mass-flow rate ${\dot{m}}_{cw}$ was obtained from the hall-effect flow-sensor volumetric reading (${VF}_{cw}$) and coolant density. The associated standard uncertainty $u\left({\dot{m}}_{cw}\right)$ reflects instrument precision and density estimation. Because Q_abs depends on both ${\dot{m}}_{cw}$ and the coolant temperature rise ($T_{inc},T_{outc}$), fluctuations in either parameter increase uncertainty.

The recirculated solution mass-flow rate ${\dot{m}}_{sol}$ was derived from the solution volumetric setting. Assuming nearly constant solution density introduces a relative uncertainty of approximately ±5–10%, which propagates to the enthalpy-transport term used in estimating ${∆\dot{m}}_{abs}$. Instrumental uncertainties used for propagation are summarized in Table 1.

2.5.2. Modeling Uncertainties

Modeling assumptions contribute additional uncertainty to enthalpy-based quantities. The inlet and outlet solution enthalpies $h_{sol,in}$ and $h_{sol,out}$ were evaluated using LiBr–H₂O correlations at near-film environmental temperatures. Because these temperatures are not obtained from immersed sensors, a representative ±15% uncertainty was assigned to enthalpy-dependent terms; this contribution dominates the uncertainty budget of $∆{\dot{m}}_{abs}.$

A second modeling source arises from assuming nearly constant solution density to convert volumetric to mass flow. Density variations within the operating window introduce a relative uncertainty of roughly ±5–10% in ${\dot{m}}_{sol}$, affecting the transport term ${\dot{m}}_{sol}\left(h_{sol,in}-h_{sol,out}\right)$.

Finally, the latent heat of vaporization $h_{vap}$ varies negligibly (<0.1%) within the experimental range and contributes minimally to the overall uncertainty, but it is retained for completeness.

2.5.3. Propagation Method

For a derived quantity $y=f\{x_1,x_2,\dots ,x_n\}$, standard uncertainty was computed using linear first-order expansion:

$$u\left(y\right)=\sqrt{\sum _{i=1}^n{\left({\displaystyle \frac{\partial f}{{\partial x}_i}}\right)}^2{u}^2\left(x_i\right),}$$

(9)

where partial derivatives were evaluated at representative values of each tagged interval. Independent contributions were combined in quadrature, and expanded uncertainties were expressed as $U\left(y\right)=2u\left(y\right)$.

2.5.4. Uncertainty in the Absorption Heat-Transfer Rate $Q_{abs}$

The absorption heat-transfer rate is obtained from Equation (4). Its uncertainty depends on (i) coolant mass-flow measurement, (ii) coolant temperature rise, and (iii) coolant specific heat capacity (assumed constant). First-order propagation yields

$$u\left(Q_{abs}\right)=\sqrt{{\left(C_{p,cw}∆T_{cw}\right)}^2{u}^2\left({\dot{m}}_{cw}\right)+{\left({{\dot{m}}_{cw}C}_{p,cw}\right)}^2{u}^2\left(∆T_{cw}\right),}$$

(10)

and $U\left(Q_{abs}\right)=2u\left(Q_{abs}\right)$.

2.5.5. Uncertainty in the Estimated Mass-Transfer Rate $∆{\dot{m}}_{abs}$

The absorption mass-transfer rate $∆{\dot{m}}_{abs}$ is obtained from Equation (5). Its uncertainty depends on $Q_{abs}$, ${\dot{m}}_{sol}$, and the enthalpy difference $\left(h_{sol,in}-h_{sol,out}\right)$, including the ±15% modeling uncertainty. Propagation gives

$$\begin{gathered} u\left(∆{\dot{m}}_{abs}\right)= \\ \sqrt{{\left({\displaystyle \frac{\partial ∆{\dot{m}}_{abs}}{{\partial Q}_{abs}}}\right)}^2{u}^2\left(Q_{abs}\right)+{\left({\displaystyle \frac{\partial ∆{\dot{m}}_{abs}}{\partial {\dot{m}}_{sol}}}\right)}^2{u}^2\left({\dot{m}}_{sol}\right)+{\left({\displaystyle \frac{\partial ∆{\dot{m}}_{abs}}{\partial h_{sol,in}}}\right)}^2{u}^2\left(h_{sol,in}\right)+{\left({\displaystyle \frac{\partial ∆{\dot{m}}_{abs}}{{\partial h}_{sol,out}}}\right)}^2{u}^2\left(h_{sol,out}\right)} \end{gathered}$$

(11)

with $U\left(∆{\dot{m}}_{abs}\right)=2u\left(∆{\dot{m}}_{abs}\right)$. Enthalpy uncertainties dominate the overall budget.

2.5.6. Sensitivity of $∆{\dot{m}}_{abs}$ Slope Trends and Regime Classification to ±15% Enthalpy Uncertainty (Monte Carlo)

Because the estimation of $∆{\dot{\mathrm{m}}}_{\mathrm{a}\mathrm{b}\mathrm{s}}$ requires assigning LiBr–H₂O enthalpies from near-film temperatures, an additional modeling uncertainty of ±15% is acknowledged in this estimate. To quantify how this uncertainty affects the main conclusions of the paper (slope trends and regime classification), a Monte Carlo sensitivity analysis was performed using the same experimental dataset.

In each realization, the nominal $∆{\dot{m}}_{abs}\left(t\right)$ series was perturbed pointwise by a bounded multiplicative factor η(t),

$${∆{\dot{m}}_{abs}}_{abs}^{MC}(\mathrm{t})=\eta (t){\times ∆{\dot{m}}_{abs}}_{abs}^{nom}(\mathrm{t}),\eta \left(\mathrm{t}\right)~U\left(0.85,1.15\right)$$

(12)

where ${∆{\dot{m}}_{abs}}_{abs}^{MC}\left(\mathrm{t}\right)$ is the perturbed series in a given Monte Carlo realization, ${∆{\dot{m}}_{abs}}_{abs}^{nom}\left(\mathrm{t}\right)$ is the nominal time series obtained from the baseline calculation, and η(t) is a bounded multiplicative factor applied pointwise to represent the ±15% enthalpy-assignment uncertainty.

For each tagged thermal-load phase and fan condition (OFF/ON), the load-resolved slope metric was recomputed using the same linear-regression procedure adopted in the nominal analysis. Each realization was then assigned to a regime using the same regime rule applied in the manuscript; therefore, the ensemble yields (i) regime probabilities (P_stab, P_acc, P_mod) and (ii) the probability of retaining the nominal regime (P_same) under the ±15% uncertainty. The probabilities P_stab, P_acc, and P_mod are estimated as the fraction of realizations classified as stabilization, acceleration, and moderation, respectively, and P_same denotes the fraction of realizations that preserve the nominal regime for that load (with P_stab + P_acc + P_mod = 1).

A total of N = 3000 realizations were used. The resulting load-by-load regime probabilities, nominal-slope summaries, and robustness flags are reported in Table S1 (Supplementary Material) and are used in Section 3 to support sensitivity-aware interpretation of the slope-based regime trends.

In addition, the Monte Carlo ensemble provides 95% uncertainty intervals for the regression slopes used in regime classification. For each load phase and fan condition (OFF/ON), the 95% uncertainty interval of the slope is reported as the 2.5th–97.5th percentiles of the Monte Carlo slope distribution (Table S1, Supplementary Material). Slopes whose 95% interval overlaps zero are treated as sign-uncertain and therefore flagged as uncertainty-limited in the regime interpretation. A fixed-window slope check was also performed to assess robustness to manual switching; details are reported in Table S2 (Supplementary Material).

2.5.7. Uncertainty in the Global Thermal Resistance $R_{th}$

The global thermal resistance is defined as

$$R_{th}={\displaystyle \frac{∆T}{Q_{abs}}}.$$

(13)

Thus, it inherits uncertainty from both $∆T$ and $Q_{abs}$:

$$u\left(R_{th}\right)=\sqrt{{\left({\displaystyle \frac{1}{Q_{abs}}}\right)}^2{u}^2\left(∆T\right)+{\left({\displaystyle \frac{∆T}{Q_{abs}^2}}\right)}^2{u}^2\left(Q_{abs}\right)}.$$

(14)

Because $R_{th}$ involves division by $Q_{abs}$, its uncertainty increases during low-load phases where Qabs is small. Expanded uncertainties are expressed as $U\left(R_{th}\right)=2u\left(R_{th}\right)$.

For completeness, phase-resolved expanded uncertainties $U\left(∆T\right),U\left(Q_{abs}\right),$ $U\left(∆{\dot{m}}_{abs}\right)$, and $U\left(R_{th}\right)$ for all twelve phases and both fan modes (OFF/ON) are compiled in Table A1.

To clarify the weight of each uncertainty source, an uncertainty-budget analysis was performed following the GUM/Kline–McClintock framework. For each derived indicator y, the contribution of each input $x_i$ (with standard uncertainty u($x_i$)) to the combined standard uncertainty u(y) was quantified as

$$C_i(\mathrm{\%})={\displaystyle \frac{{\left(\frac{\partial y}{\partial x_i}u\left(x_i\right)\right)}^2}{u^2\left(y\right)}}\times 100.$$

(15)

This directly identifies which terms dominate the uncertainty of the core indicators (Q_abs$,∆{\dot{m}}_{abs},$ $R_{th}$) and provides a transparent sensitivity view separating instrumental contributions from modeling/property-assignment assumptions. The observed difference between low-load and high-load uncertainty is expected from metrology: at low loads, driving gradients and signal levels are smaller, so a similar absolute sensor/model uncertainty represents a larger fraction of the derived quantities (higher relative uncertainty), whereas at higher loads, larger signal levels reduce relative uncertainty. Across the present dataset, the uncertainty budget indicates consistent dominant contributors (instrumental terms for Q_abs$,$ and enthalpy-assignment for $∆{\dot{m}}_{abs}$); contribution fractions sum to 100% for each case. The complete uncertainty budget table is provided as Supplementary Material (Table S3). Likewise, a visual summary of the relative contributions (uncertainty budget contribution diagram) is also provided as Supplementary Figure S1.

3. Results

To examine the dynamic response of the integrated evaporator–absorber unit, the twelve thermal-load phases (Q_in,1–Q_in,12) were reorganized into four groups according to the magnitude of the applied heater input. This classification enables a clearer comparison of how fan assistance influences the absorption process under comparable operating conditions. Group 1 comprises the highest loads (Q_in,1, Q_in,6, Q_in,10; 219–223 W nominal input). Group 2 contains the medium-high loads (Q_in,2, Q_in,7, Q_in,11; 138–183 W nominal input). Group 3 gathers the medium-low inputs (Q_in,3, Q_in,4, Q_in,8; 60–110 W nominal input). Finally, Group 4 includes the three zero-input phases (Q_in,5, Q_in,9, Q_in,12; $\approx 0\mathrm{W}$ nominal input) which isolates passive absorption without external heating. This grouping provides a coherent basis to evaluate how fan OFF/ON operation affects absorber performance across distinct thermal regimes.

The following subsections report results in terms of (i) the absorption heat-transfer rate Q_abs, obtained from the coolant-water circuit; (ii) the estimated absorption mass-transfer rate ${\dot{m}}_{abs}$, derived from energy–mass coupling; and (iii) the global thermal resistance $R_{th}$ as an integrated efficiency indicator of absorber-side performance. In addition, a load-normalized evaporator–absorber subsystem effectiveness metric η_EA = Q_abs/Q_in (defined in Section 2.1) is reported for all Q_in > 0 phases in Table S4 (Supplementary Material) to support comparisons across loads and fan modes; for the zero-input phases (Q_in ≈ 0) is not defined and is therefore reported as N/A. Linear regressions of the time series of Q_abs (a) and ${\dot{m}}_{abs}$ (b) are used to quantify whether the system shows downward trends, stabilizes, or improves throughout each tagged load interval. Interpretations are made considering the phase-resolved expanded uncertainties reported in Section 2.5 and Table A1.

3.1. Dynamics of Absorption Heat Transfer ($Q_{abs}$) Under Variable Thermal Loads

To evaluate the effect of fan assistance on the unit’s dynamic thermal behavior, a linear trend analysis was performed for each thermal-load condition. This analysis quantifies the direction and rate of change in the absorption heat transfer rate (Q_abs) by fitting a first-order regression line to the time-series data recorded under both fan-OFF and fan-ON sub-intervals. The slope of each fitted line reveals whether the system tends to stabilize, improve, or degrade during a given phase.

A negative slope indicates a gradual reduction in Q_abs over time, which is consistent with absorber-side thermal saturation or with the natural relaxation of driving gradients during a phase. Conversely, a positive slope reflects enhanced or sustained heat transfer, characteristic of improved stability. In this section, the slope parameter a represents the time derivative of Q_abs, obtained from a least-squares fit to the tagged fan-OFF and fan-ON datasets. The slope values were computed using standard least-squares regression:

$${\mathrm{a}}_{on}={\displaystyle \frac{\left(n_{on}\sum t·Q_{abs,on}\right)-\left(\sum t·\sum Q_{abs,on}\right)}{\left(n_{on}\sum t^2\right)-{\left(\sum t\right)}^2}},$$

(16)

$${\mathrm{a}}_{off}={\displaystyle \frac{\left(n_{off}\sum t·Q_{abs,off}\right)-\left(\sum t·\sum Q_{abs,off}\right)}{\left(n_{off}\sum t^2\right)-{\left(\sum t\right)}^2}},$$

(17)

where ${\mathrm{a}}_{on}$ and ${\mathrm{a}}_{off}$ are the slope coefficients for fan-ON and fan-OFF operation, respectively; $n_{on}$ and $n_{off}$ are the number of data points for each tagged sub-interval; $Q_{abs,on}$ and $Q_{abs,off}$ are the absorption heat transfer rates (W) with the fan ON and OFF, respectively; and t is time (s).

To quantify the relative effect of fan assistance, the improvement percentage is computed from the slope difference as follows:

$$Relativeimprovement\left(\%\right)of\mathrm{a}={\displaystyle \frac{{\mathrm{a}}_{on}-{\mathrm{a}}_{off}}{\left|{\mathrm{a}}_{off}\right|}}\times 100,$$

(18)

Figure 3 illustrates the evolution of Q_abs under different thermal loads. In each subplot, solid red and green lines correspond to fan-OFF and fan-ON operation, respectively, while black and cyan dashed lines denote the associated linear trends. In most cases, fan assistance increases Q_abs and/or attenuates downward trends during the interval, indicating enhanced absorber-side heat removal.

High thermal loads (Group 1, Figure 3a). Under the highest loads tested, contrasting behaviors are observed. For Q_in,1, a clear downward trend in Q_abs is measured without fan assistance (${\mathrm{a}}_{off}=-0.67\mathrm{W}{·\mathrm{s}}^{-1}$), indicating a progressive reduction in absorber-side heat-removal activity during the interval. With fan activation, the trend becomes quasi-steady (${\mathrm{a}}_{on}\approx 0.01\mathrm{W}{·\mathrm{s}}^{-1}$), evidencing stabilization and a slope-based improvement exceeding 100%. In contrast, for Q_in,6 and Q_in,10, the natural-convection baseline already shows an increasing trend (${\mathrm{a}}_{off}>0$). In these cases, fan activation moderates (damps) the natural improvement (e.g., −71% slope change for Q_in,10), indicating a damped thermodynamic-trend response (a_on < a_off). This behavior is referred to as a ‘moderation response’ at the thermodynamic-trend level; no direct inference is made regarding suppression of natural convection or specific internal flow-field changes, which would require dedicated flow diagnostics.

Medium-high loads (Group 2, Figure 3b). In this regime, the fan primarily acts as a performance accelerator. For Q_in,2, a positive baseline slope (${\mathrm{a}}_{off}=+0.30\mathrm{W}{·\mathrm{s}}^{-1}$) is amplified to ${\mathrm{a}}_{on}=+0.71\mathrm{W}{·\mathrm{s}}^{-1}$(+137%). For Q_in,7, a downward baseline trend (${\mathrm{a}}_{off}=-0.12\mathrm{W}{·\mathrm{s}}^{-1}$) is shifted to a near-steady response (${\mathrm{a}}_{on}=+0.02\mathrm{W}{·\mathrm{s}}^{-1}$, +117%). Similarly, for Q_in,11, a slightly negative baseline becomes slightly positive with fan activation (+150%). These results indicate that forced convection substantially accelerates thermal recovery when natural gradients are moderate.

Medium-low loads (Group 3, Figure 3c). At lower inputs, the unit shows a tendency toward decreasing Q_abs under fan-OFF operation. For Q_in,3, a marked downward trend (${\mathrm{a}}_{off}=-0.49\mathrm{W}{·\mathrm{s}}^{-1}$) is reversed to a small positive slope (${\mathrm{a}}_{on}=+0.07\mathrm{W}{·\mathrm{s}}^{-1}$, +114%). For Q_in,4, fan activation changes a sustained downward trend (${\mathrm{a}}_{off}=-0.14\mathrm{W}{·\mathrm{s}}^{-1}$) into a positive response (${\mathrm{a}}_{on}=+0.05\mathrm{W}{·\mathrm{s}}^{-1}$, +136%). For Q_in,8, although the slope remains negative, the fan reduces the magnitude of the downward trend by 53%. Overall, fan assistance consistently mitigates diminishing trends under weak natural-convection conditions.

Zero-input/passive loads (Group 4, Figure 3d). With no electrical heating, fan activation still provides a marked stabilizing effect. The downward trends observed in slopes between Q_in,5, Q_in,9, and Q_in,12 $(\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{s} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}-0.22\mathrm{a}\mathrm{n}\mathrm{d}-0.41\mathrm{W}{·\mathrm{s}}^{-1}$) are substantially flattened by the fan, yielding stability improvements of 86–93%. This confirms that mechanical vapor guidance helps sustain absorber heat rejection even during passive operation.

Table 2. Comparison of linear trends in absorption heat transfer rate under different thermal loads, showing slope values (${\mathrm{a}}_{off}$,${\mathrm{a}}_{on}$) and relative improvement due to fan-assisted operation.

Thermal Load	$\mathbf{Slope}\mathbf{Without}\mathbf{Fan}({\mathbf{a}}_{\mathit{o}\mathit{f}\mathit{f}}$$\left)\right(\mathbf{W}·$s−1)	$\mathbf{Slope}\mathbf{with}\mathbf{Fan}({\mathbf{a}}_{\mathit{o}\mathit{n}}$$\left)\right(\mathbf{W}·$s−1)	Relative Improvement of a (%)
Qin,1	−0.67	0.01	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+101.5\%$
Qin,2	0.30	0.71	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+137\%$
Qin,3	−0.49	0.07	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+114\%$
Qin,4	−0.14	0.05	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+136\%$
Qin,5	−0.28	−0.04	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+86\%$
Qin,6	0.52	0.09	${\mathrm{a}}_{on}<{\mathrm{a}}_{off},-83\%$
Qin,7	−0.12	0.02	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+117\%$
Qin,8	−0.17	−0.08	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+53\%$
Qin,9	−0.22	−0.02	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+91\%$
Qin,10	0.42	0.12	${\mathrm{a}}_{on}<{\mathrm{a}}_{off},-71\%$
Qin,11	−0.02	0.01	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+150\%$
Qin,12	−0.41	−0.03	${\mathrm{a}}_{on}>{\mathrm{a}}_{off},+93\%$

summarizes the slope results for both fan conditions and their relative improvement.

Identified dynamic behaviors. Based on slope analysis, three behaviors are distinguished:

• Performance stabilization (dominant). When fan-OFF operation shows a downward trend (${\mathrm{a}}_{off}<0$), fan activation drives ${\mathrm{a}}_{on}$ toward zero or positive values, indicating stabilization.
• Performance acceleration. When the baseline trend is already favorable (${\mathrm{a}}_{off}>0$), the fan can amplify the improvement (e.g., Q_in,2)
• Moderation under strong natural convection (atypical). In a limited number of high-load cases (Q_in,6, Q_in,10), the fan reduces the naturally positive slope, indicating a damping effect rather than a loss of viability.

In summary, low-power mechanical assistance generally enhances absorption stability and heat removal. While improvements become marginal or moderated in specific high-load regimes dominated by natural convection, forced convection is clearly beneficial in most transient or weak-gradient conditions by attenuating downward trends and promoting stable operating states.

3.2. Dynamics of Estimated Absorption Mass Transfer (${∆\dot{m}}_{abs}$) Under Variable Thermal Loads

To complement the heat-transfer trends in Section 3.1, this section examines the estimated absorption mass-transfer behavior under the same load groups and fan modes. Before presenting the results, it is important to recall the simplified control-volume thermodynamic model with near-film property assignment described in Section 2.4: (i) temperatures used to assign thermophysical properties correspond to the near-film absorber environment, introducing an estimated ±15% uncertainty in ${∆\dot{m}}_{abs}$; (ii) the density used to convert volumetric to mass flow is treated as constant (±5–10% uncertainty); and (iii) the latent heat of water vapor is taken as a constant (variation < 0.1%).

To translate this enthalpy-related uncertainty into its practical impact on the present conclusions, the robustness of the slope-based regime interpretation was evaluated through the Monte Carlo sensitivity analysis described in Section 2.5.6. Using N = 3000 realizations, the regime interpretation is found to be highly robust for almost all tagged load phases; additionally, the 95% uncertainty intervals of the OFF/ON slopes (2.5th–97.5th percentiles) are reported in Table S1 (Supplementary Material) and confirm sign-definite trends for all phases except Load Phase 11. Accordingly, the discussion below flags Load Phase 11 as uncertainty-limited and uses appropriately cautious wording for that specific case, while maintaining definitive regime statements for load phases with unambiguous retention.

To further verify that the slope-based regime interpretation is not biased by unequal dwell times or operator-dependent ramp shapes inherent to manual switching, an additional fixed-window slope robustness check was performed. For each tagged load interval and fan condition (OFF/ON), the regression slope of ${∆\dot{m}}_{abs}\left(t\right)$ was recomputed over consistent post-switch windows (first 120 s and, alternatively, first 300 s after each load change). The resulting windowed-slope directions were consistent with the nominal interpretation across the load phases; any marginal or near-neutral cases are explicitly flagged as uncertainty-limited. The complete windowed-slope summary is provided in Table S2 (Supplementary Material) and supports the trends discussed below.

For each thermal load and fan mode (OFF/ON), the time series of ${∆\dot{m}}_{abs}$ was fitted with a first-order linear regression to determine the rate of change, defined by the slope parameter b:

$$b_{on}={\displaystyle \frac{\left(n_{on}\sum t·∆{\dot{m}}_{abs,on}\right)-\left(\sum t·\sum ∆{\dot{m}}_{abs,on}\right)}{\left(n_{on}\sum t^2\right)-{\left(\sum t\right)}^2}},$$

(19)

$$b_{off}={\displaystyle \frac{\left(n_{off}\sum t·∆{\dot{m}}_{abs,off}\right)-\left(\sum t·\sum ∆{\dot{m}}_{abs,off}\right)}{\left(n_{off}\sum t^2\right)-{\left(\sum t\right)}^2}}.$$

(20)

Here, $b>0$ denotes increasing absorption mass-transfer activity during the interval, $b\approx 0$ indicates near-steady behavior, and $b<0$ reflects a downward drift. Relative improvement percentages reported below are computed thanks to Equation (19):

$$Relativeimprovement\left(\%\right)ofb={\displaystyle \frac{b_{on}-b_{off}}{\left|b_{off}\right|}}\times 100.$$

(21)

Figure 4 shows the evolution of ${∆\dot{m}}_{abs}$ over time for different thermal loads. For ease of reading, the data are grouped into four sub-figures: high, medium-high, medium-low, and zero-input. A linear trend is superimposed on each signal; its slope indicates whether the estimated mass transfer increases, remains quasi-steady, or shows a downward drift. Comparing fan-OFF and fan-ON slopes ($b_{off}$, $b_{on}$) allows evaluation of whether fan activation stabilizes the response, accelerates an existing recovery, or moderates the observed upward trend by reducing the slope magnitude (i.e., $b_{on}$ < $b_{off}$) under high-load conditions. Because no direct flow diagnostics (vapor velocities, spatial pressure-gradient mapping, or interface visualization) were performed, ‘moderation’ is reported solely as a thermodynamic-trend descriptor rather than a mechanistic proof of flow-field alteration.

High thermal loads (Group 1, Figure 4a). When the fan is OFF, the unit can exhibit pronounced drifts associated with intense transients; when the fan is ON, these drifts are consistently attenuated. For Q_in,1, fan-OFF operation shows a sustained downward trend ($b_{off}=-2.67\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$), whereas fan-ON operation yields an almost flat trajectory ($b_{on}=+4.04\times {10}^{-6}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$). This shift represents an improvement >100% in slope-based stability, confirming that vapor forcing helps contain dynamics under high-load conditions. For Q_in,6, the baseline already shows a positive slope ($b_{off}=+2.08\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$); fan activation reduces the rate of increase to $b_{on}=+3.59\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$. Rather than indicating loss of viability, this is reported as a damped trend response under buoyancy-dominated high-load conditions (i.e., a smaller positive slope under fan-ON than fan-OFF), improving response controllability at the trend level without implying a confirmed flow-field mechanism. Finally, Q_in,10 fan activation damps a noticeable fan-OFF drift ($b_{off}=-1.87\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$) toward near-zero ($b_{on}=-1.31\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$), with a 93% improvement. Overall, Figure 4a indicates that at high loads, the fan operates primarily as a stabilizer.

Medium-high loads (Group 2, Figure 4b). In this regime, fan assistance tends to accelerate recoveries or close slight drifts. For Q_in,2 fan activation increases the slope from $b_{off}=+1.18\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$ to $b_{on}=+2.83\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$ (≈+139.5%), indicating faster attainment of elevated mass-transfer levels. For Q_in,7, a slight fan-OFF downward trend ($b_{off}=-4.73\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$) is shifted to near-steady behavior with the fan ON ($b_{on}=+7.56\times {10}^{-6}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$, +116%). For Q_in,11, the response is already quasi-steady; the fan shifts from a very small negative slope to a gentle positive one (+166.9%). Thus, under medium-high loads, the fan helps the unit reach effective operating levels sooner.

Medium-low loads (Group 3, Figure 4c). At lower inputs, fan-OFF operation generally shows downward drifts in ${∆\dot{m}}_{abs}$. With fan assistance, these drifts are reduced or reversed. For Q_in,3, a marked fan-OFF decrease ($b_{off}=-1.94\times {10}^{-4}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$) becomes slightly positive with the fan ON ($b_{on}=+2.62\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$, ≈+113.5%), bringing the trajectory close to a stable state. For Q_in,4, the trend is reversed from negative ($b_{off}=-5.76\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$) to a slight increase ($b_{on}=+1.80\times {10}^{-5}\mathrm{k}\mathrm{g}·{\mathrm{s}}^{-2}$, +131.3%). For Q_in,8, the slope remains mildly negative, but its magnitude is reduced by nearly half (+52.3%). In operational terms, when buoyancy-driven transport is weak, fan assistance sustains and regulates the evolution of ${∆\dot{m}}_{abs}.$

Zero-input/passive loads (Group 4, Figure 4d). After the transient, fan-OFF operation shows a downward drift that is damped toward near-zero with the fan ON: Q_in,5 (+85%), Q_in,9 (+90.7%), and Q_in,12 (+93.4%). Although no heating is applied, forced convection prevents sustained downward drifts and establishes a stable plateau, which is useful during waiting periods or transitions.

Table 3. Comparison of linear trends in absorption mass transfer rate under different thermal loads, showing slope value ($b_{off}$ ,$b_{on}$) and relative improvement due to fan-assisted operation.

Thermal Load	$\mathbf{Slope}\mathbf{Without}\mathbf{Fan}({\mathit{b}}_{\mathit{o}\mathit{f}\mathit{f}}$$\left)\right(\mathbf{k}\mathbf{g}·{\mathbf{s}}^{-2}$)	$\mathbf{Slope}\mathbf{with}\mathbf{Fan}({\mathit{b}}_{\mathit{o}\mathit{n}}$$\left)\right(\mathbf{k}\mathbf{g}·{\mathbf{s}}^{-2}$)	Relative Improvement of b (%)
Qin,1	$-2.66606\times {10}^{-4}$	$4.04288\times {10}^{-6}$	$b_{on}>b_{off},+101.5\%$
Qin,2	$1.183260\times {10}^{-4}$	$2.834277\times {10}^{-4}$	$b_{on}>b_{off},+139.5\%$
Qin,3	$-1.937750\times {10}^{-4}$	$2.615450\times {10}^{-5}$	$b_{on}>b_{off},+113.5\%$
Qin,4	$-5.758310\times {10}^{-5}$	$1.804000\times {10}^{-5}$	$b_{on}>b_{off},+131.3\%$
Qin,5	$-1.097490\times {10}^{-4}$	$-1.644060\times {10}^{-5}$	$b_{on}>b_{off},+85\%$
Qin,6	$2.084990\times {10}^{-4}$	$3.587730\times {10}^{-5}$	$b_{on}<b_{off},-82.8\%$
Qin,7	$-4.726110\times {10}^{-5}$	$7.559100\times {10}^{-6}$	$b_{on}>b_{off},+116\%$
Qin,8	$6.855050\times {10}^{-5}$	$-3.273120\times {10}^{-5}$	$b_{on}>b_{off},+52.3\%$
Qin,9	$-8.652960\times {10}^{-5}$	$-8.063000\times {10}^{-6}$	$b_{on}>b_{off},+91\%$
Qin,10	$-1.865210\times {10}^{-4}$	$-1.307820\times {10}^{-5}$	$b_{on}>b_{off},+93\%\%$
Qin,11	$-8.523010\times {10}^{-6}$	$5.700880\times {10}^{-6}$	$b_{on}>b_{off},166.9\%$
Qin,12	$-1.629790\times {10}^{-4}$	$-1.071680\times {10}^{-5}$	$b_{on}>b_{off},93.4\%$

summarizes these slope values and the relative percentage improvement.

General trends and control implications. Overall, the results show a clear pattern: fan activation stabilizes mass-transfer dynamics. When fan-OFF operation exhibits a sustained downward drift, the fan reduces its magnitude and often drives the response toward a plateau. When the system is already recovering naturally, fan assistance accelerates the approach to effective operating levels. Under high loads where natural convection produces strong positive slopes, the fan moderates growth, improving controllability and reducing the likelihood of oscillatory behavior.

Combining all cases, a practical control guideline emerges:

• Stabilize: If $b_{off}<0$, turn the fan ON to stabilize quickly.
• Maintain: If $b_{off}\approx 0$, the fan helps preserve that quasi-steady state.
• Moderate: If $b_{off}$ is strongly positive at high loads, fan activation moderates growth to improve controllability.

Using the slope as a single metric simplifies comparison and yields direct operational rules for instrumentation and control.

3.3. Thermal Resistance ($R_{th}$) Analysis

To assess the global heat-dissipation capability of the evaporator–absorber unit, a thermal resistance parameter ($R_{th}$) adapted from Fourier’s law is proposed. This metric quantifies the temperature difference required to transfer a unit of thermal power, serving as an inverse indicator of absorber-side efficiency within the present subsystem context (lower $R_{th}$ implies better performance). It is defined for both fan operating modes as follows:

$$R_{th,on}={\displaystyle \frac{T_{abs}-T_{ev}}{Q_{abs,on}}},$$

(22)

$$R_{th,off}={\displaystyle \frac{T_{abs}-T_{ev}}{Q_{abs,off}}},$$

(23)

where ΔT = T_abs − T_ev is the temperature difference between the absorber section (hot side) and the evaporator section (cold side), evaluated over each thermal-load interval; Q_abs,on and Q_abs,off represent the phase absorption heat-transfer rates under fan-ON and fan-OFF operation, respectively, as derived in Section 3.1. The resulting units of $R_{th}$are $\mathrm{K}·{\mathrm{W}}^{-1}$, reflecting the thermal gradient required to dissipate one watt of absorbed heat.

This interpretation of $R_{th}$ is analogous to a global thermal impedance, incorporating both the driving thermal potential and the unit’s capacity to remove absorbed energy. A lower $R_{th}$ indicates that the system requires a smaller gradient to dissipate a given heat load and is therefore more efficient from a thermodynamic standpoint.

Figure 5 presents the temporal evolution of thermal resistance for each thermal load, comparing fan-OFF and fan-ON conditions. The data are organized into the four load clusters defined in Section 2.3.

The results reveal three general trends across the operating range:

• High thermal loads (Group 1, Figure 5a). Under high inputs (Q_in,1, Q_in,6, Q_in,10) $R_{th}$remains low in both operating modes ($<0.4\mathrm{K}·{\mathrm{W}}^{-1}$). This indicates that at high vapor-generation rates, buoyancy-driven transport is already dominant and the fan provides only an incremental benefit.
• Medium-to-low loads (Groups 2 and 3, Figure 5b,c). As the thermal load decreases, the influence of fan assistance becomes more apparent. $R_{th}$values are moderately reduced with the fan ON, indicating improved dissipation capability when the natural ΔT driving force weakens. In the center panel of Figure 5b, the fan-ON and fan-OFF curves appear closely spaced because the intermediate heat-input level yields similar ΔT/Q_abs ratios and therefore comparable $R_{th}$ values.
• Zero-input/passive loads (Group 4, Figure 5d). The most pronounced effect is observed in the absence of active heating (Q_in,5, Q_in,9, Q_in,12). Fan operation significantly reduces $R_{th}$, often by more than 30%, recovering a portion of the unit’s heat-dissipation capability under negligible buoyancy forces. This confirms the fan’s strong contribution in low-circulation regimes.

To reinforce the graphical trends in Figure 5, a non-parametric Wilcoxon signed-rank test was applied to paired fan-OFF/fan-ON $R_{th}$ datasets within each tagged thermal-load interval. The null hypothesis assumed no difference in median thermal resistance between fan modes, whereas the alternative hypothesis stated that the medians are different. In all significant cases, the observed direction was $R_{th,off}>R_{th,on}$ indicating that fan assistance reduces effective thermal resistance. The phase-resolved Wilcoxon results are summarized in

Table 4. Results of the Wilcoxon signed-rank test applied to paired thermal-resistance data for all twelve thermal loads. The table summarizes the sample sizes, median $R_{th}$ values under fan-OFF and fan-ON modes, and the corresponding p-values. Significant differences (p < 0.05) demonstrate the beneficial effect of forced convection on reducing thermal resistance.

Thermal Load	NOFF	NON	$\mathbf{Median}\left({\mathit{R}}_{\mathit{t}\mathit{h},\mathit{O}\mathit{F}\mathit{F}}\right)$	$\mathbf{Median}\left({\mathit{R}}_{\mathit{t}\mathit{h},\mathit{O}\mathit{N}}\right)$	Wilcoxon p-Value
Qin,1	174	284	0.09818	0.05738	<1 × 10−6
Qin,2	358	347	0.08225	0.04663	<1 × 10−6
Qin,3	383	270	0.04551	0.02738	<1 × 10−6
Qin,4	301	355	0.02443	0.01887	<1 × 10−6
Qin,5	426	997	0.02459	0.01565	<1 × 10−6
Qin,6	396	346	0.03219	0.02507	0.001
Qin,7	305	294	0.03866	0.03323	0.081
Qin,8	293	302	0.04655	0.04062	0.066
Qin,9	370	1209	0.15470	0.12918	0.014
Qin,10	418	248	0.13670	0.11487	0.038
Qin,11	340	453	0.13017	0.11805	0.054
Qin,12	311	808	0.14897	0.12945	0.021

Note: While the reduction in $R_{th}$ is not statistically significant for a subset of conditions where buoyancy-driven transport is already strong (e.g., mid-range phases), the additional forced flow yields limited incremental gains. These cases help delineate the operational limits of the mechanically assisted configuration rather than contradict the overall trend.

.

The analysis shows that, for nine out of the twelve thermal loads, the reduction in $R_{th}$ is statistically significant (p < 0.05). This confirms that fan activation meaningfully enhances heat-dissipation capability, especially in low-load and passive-load scenarios where natural convection alone is insufficient to sustain a favorable thermal gradient.

Overall, the Wilcoxon analysis confirms a systematic reduction in effective thermal resistance across the majority of conditions, indicating that fan assistance not only improves instantaneous heat-removal capacity but also promotes stable absorber-side thermal response under fluctuating loads.

4. Discussion

It is important to emphasize that all relative improvements reported in this work are internal, slope-based comparisons within the same prototype and tagged thermal-load interval, contrasting fan-ON against fan-OFF sub-periods. Therefore, the percentages quantify how mechanical assistance modifies the dynamic evolution (stabilization, acceleration, or moderation) of Q_abs$,∆{\dot{m}}_{abs},$ and $R_{th}$ rather than benchmarking the unit against external devices or alternative absorber technologies. Complementarily, η_EA = Q_abs/Q_in (Section 2.1; Table S4) is used as a dimensionless, subsystem-level normalization to compare the absorber-side response across loads and fan modes without implying a cycle COP. Improvements above 100% arise in phases where fan activation reverses a downward drift or brings the slope close to zero, indicating a transition from relaxation-dominated behavior to sustained operation under weak natural gradients.

Cycle-level COP context and modeling outlook. Although COP cannot be computed for the present evaporator–absorber-only test stand, it is useful to contextualize the subsystem results against representative COP ranges reported for complete LiBr–H₂O absorption chillers operating at comparable temperature levels and small-to-medium scales. Compact solar-driven absorption prototypes at the kW scale report thermal COP values around ~0.6 under their stated conditions [33]. For single-effect LiBr–H₂O cycles, thermodynamic optimization and modeling studies commonly report COP values in the ~ 0.68–0.77 range depending on boundary temperatures and design/operational choices [34], while a recent H₂O/LiBr cycle study reports a cooling COP on the order of ~0.74 under its reported operating conditions [35]. Higher COP levels may be achieved in variable-effect LiBr–H₂O chillers when operating over wider generation-temperature windows; experimental results on a prototype variable-effect chiller report COP values spanning approximately 0.69–1.08 [4]. These COP values are provided strictly as cycle-level context and are not directly comparable to the present subsystem indicators (slope-based metrics, $R_{th}$, and ${\eta }_{EA}$), which are defined using only measured/derived quantities available in the evaporator–absorber apparatus.

A cycle-level COP estimate for a complete system integrating the present unit can be pursued through standard modeling approaches once the missing components (generator, condenser, and solution heat exchanger) and their operating boundary conditions are defined. In particular, characteristic-equation-based formulations have been demonstrated as practical tools to predict absorption-chiller performance from temperature-lift descriptors and have been refined for improved use in modeling/optimization workflows [36]. Likewise, thermodynamic modeling studies provide established routes to predict COP variation with operating temperatures and component assumptions for LiBr–H₂O systems [34]. Accordingly, integrated-cycle COP modeling (and, where feasible, validation against a complete test stand) is identified as a dedicated follow-up task; the present manuscript remains focused on experimentally validated subsystem dynamics under transient thermal inputs, while COP is used here only as contextual guidance drawn from the literature [4].

With this clarification in mind, the following subsections discuss the coupled thermodynamic response of the unit and its operational implications.

4.1. Coupled Dynamics of Heat and Mass Transfer

The experimental results presented in Section 3.1 and Section 3.2 confirm that absorption in the compact vertical unit is governed by a strong physical coupling between absorption heat transfer (Q_abs) and absorption mass transfer ($∆{\dot{m}}_{abs}$). This coupled response is clearly illustrated in Figure 6, which compares the relative improvements in the time-derivative slopes for heat (a) and mass (b) across all thermal-load phases. The consistent parallel behavior—where fan activation stabilizes both metrics within the same tagged intervals—indicates that the thermal trends are not isolated artifacts, but direct consequences of the underlying mass-transfer dynamics. Fan activation is consistently associated with changes in the estimated absorption mass-transfer response ($∆{\dot{m}}_{abs}$), which in turn is coupled to the absorber-side heat-transfer response (Q_abs) measured on the coolant side. This statement reflects the observed coupled trends in the present dataset and does not constitute direct proof of a specific internal flow-field modification.

Mechanisms of enhancement. The observed changes in the slope parameters (a and b) are consistent with an enhancement pathway in which low-power fan-induced circulation increases the renewal of vapor near the solution interface and reduces the persistence of stagnant vapor regions, thereby supporting more stable coupled heat/mass-transfer trends under weak-gradient or transient conditions. While no local flow diagnostics were available to verify the detailed flow structure, this interpretation is physically consistent with the role of interfacial renewal mechanisms commonly targeted in falling-film absorber enhancement studies [37,38]. In the present compact configuration, the same objective is pursued actively through low-power vapor guidance, yielding the trend-level stabilization/acceleration behaviors reported in Section 3.1 and Section 3.2.

Validation of operating magnitudes. Despite the novel architecture of the patented unit, the absolute performance levels fall within expected thermodynamic ranges for small-scale LiBr–H₂O operation. The unit sustained absorption heat-transfer rates from near-zero to approximately 280 W under applied thermal inputs up to 223 W. These magnitudes are consistent with laboratory-scale LiBr–H₂O absorbers operating at comparable low vapor pressures (≈1.0–2.5 kPa). Medrano et al. [39], for example, reported absorber loads starting at 0.4 kW for a vertical tube absorber, while Yin et al. [40] observed comparable capacities in a mini-type solar absorption system. This correspondence supports that the compact prototype operates within the standard envelope for low-pressure absorption equipment, bridging the gap between passive experimental rigs and functional compact units.

Consistency of physical trends. The internal response of the device aligns with established absorber theory. The experimental data show that the absorption rate responds proportionally to the vapor-pressure potential, a characteristic commonly reported for tubular falling-film absorbers [41]. Similar linear dependencies have been observed in vertical configurations by Lin and Shigang [42], supporting that the unit’s response to thermodynamic driving forces is consistent and predictable, and thus suitable for slope-based regime characterization.

Characterization of dynamic stability. It is important to clarify that the “relative improvements” reported here refer to changes in the slopes of the performance curves (a and b), rather than benchmarking against external devices. Given the novelty and compactness of the present unit, the analysis focuses on its intrinsic dynamic behavior. The most relevant contribution of fan assistance is the stabilization of the slopes. In low-load regimes (Group 4), fan activation shifts a downward drift toward quasi-steady or mildly positive trends, revealing a sustained absorption process under otherwise weak natural gradients. This operational stabilizing capability is a distinct advantage of the mechanically assisted compact architecture.

Methodological considerations. The estimated ${\dot{∆\mathrm{m}}}_{\mathrm{a}\mathrm{b}\mathrm{s}}$ values carry an uncertainty of approximately ±15% due to near-film property assignment (i.e., without direct in-solution sensing of local film properties) and the assumption of constant density. While this uncertainty can affect absolute magnitudes, it does not compromise the comparative slope-based dynamics. The coherence between mass-transfer trends and independently measured heat-transfer trends (Q_abs) reinforces the validity of the control-volume interpretation and of the fan-induced regime characterization. In addition, the laboratory ambient temperature remained within a narrow band around 17 °C during the entire run, so the associated parasitic heat exchange behaves as a quasi-steady offset in Q_abs rather than as a dominant source of dynamic variability. Consequently, the slope-based analysis emphasizes intrinsic subsystem trends rather than room-level fluctuations.

4.2. Thermal Resistance Analysis and Technology Benchmarking

To assess the global absorber-side heat dissipation efficiency, the thermal resistance parameter ($R_{th}$) was evaluated across the operating envelope. Figure 7 compares the average $R_{th}$ values for fan-OFF and fan-ON sub-intervals, derived from the temperature difference required to transfer a unit of absorbed thermal power.

The results indicate that under high thermal loads (Q_in,1, Q_in,6, Q_in,10), $R_{th}$ remains low in both operating modes (below ~0.15 $\mathrm{K}·{\mathrm{W}}^{-1}$), confirming that buoyancy-driven transport is already sufficient to sustain efficient heat dissipation in this regime. As the load decreases, the influence of mechanical assistance becomes more pronounced. In the zero-input phases (Q_in,5, Q_in,9, Q_in,12), fan activation reduces thermal resistance by more than 30%, effectively recovering heat-transfer capability when natural gradients are minimal. A Wilcoxon signed-rank test confirms that this reduction is statistically significant (p < 0.05) in nine out of the twelve thermal-load phases, providing quantitative support for the systematic benefit of the active enhancement (Table 4).

Benchmarking against passive enhancement technologies. It is instructive to contextualize these internal gains against passive enhancement mechanisms reported for LiBr–H₂O absorbers. Passive strategies such as film-inverting geometries [43] or nanofluid additives [29] typically yield absorption improvements on the order of 10–40% by modifying wettability, interfacial renewal, or solution properties. In contrast, the forced-convection approach implemented here produces substantially larger dynamic benefits in weak-gradient regimes, including slope-based relative improvements exceeding 100% for several low-load phases (Section 3.1 and Section 3.2). This distinction is important: the present comparison emphasizes stabilization and recoverability under transient conditions, rather than peak steady-state capacity.

For instance, Palacios et al. [44] improved mass absorption using flat-fan sheets to enhance distribution, and Karami and Farhanieh [45] reported baseline performance for compact vertical absorbers. Compared with such passive geometric modifications—which often increase manufacturing complexity—the mechanically assisted unit achieves robust stabilization using a simple, low-power component (a 20 W axial fan). The ability to reduce $R_{th}$ by ~50–60% on average in the most sensitive low-load phases (e.g., Q_in,5, Q_in,9) highlights forced convection as a practical, low-cost pathway to widen the useful operating envelope of compact LiBr–H₂O absorbers, where robustness and replicability are as critical as peak efficiency.

Active fan-assisted benchmarking (apples-to-apples at subsystem level). While passive absorber-side enhancement strategies commonly report performance gains on the order of 10–40% by modifying wettability, interfacial renewal, or film hydrodynamics [46], the present prototype implements an active enhancement through a low-power axial fan (≈20 W) that guides the internal vapor pathway. In the most uncertainty-sensitive weak-gradient regimes, this actuation yields markedly larger response-level benefits, including substantial reductions in $R_{th}$ and slope-based recoveries that exceed the passive-improvement envelope within multiple tagged low-load intervals (Section 3.1 and Section 3.2; Figure 7; Table 4). To relate benefit to auxiliary power without invoking cycle COP, phase-resolved OFF/ON values of Q_abs and the subsystem-level normalization η_EA = Q_abs/Q_in are reported (Table S4), enabling a transparent comparison of absorber-side response against a small, explicitly stated electrical input for actuation. These results position the fan primarily as an internal actuator for stabilization and governability under transient operation, rather than as a peak-capacity booster in buoyancy-dominated high-load regimes. A concise benefit-to-power summary based on the phase-resolved OFF/ON Q_abs increments (using the measured fan electrical power) is provided in the Supplementary Material (Table S4).

4.3. Operational Implications: From Stabilization to Control

Beyond thermodynamic characterization, the slope-based trends (parameters a for Q_abs and b for ${∆\dot{m}}_{abs}$) provide an actionable framework for operating and controlling compact absorption modules under transient conditions. The experiments revealed three distinct dynamic behaviors (stabilization, acceleration, and moderation) whose occurrence depends primarily on thermal-load magnitude. These behaviors indicate that the fan should be interpreted not as a fixed enhancement element, but as an active low-power actuator capable of shaping the subsystem response across regimes.

Based on the phase-resolved trends, a demand-driven fan-activation logic can be proposed:

• Stabilization mode (low/zero loads). When fan-OFF operation exhibits a negative slope (downward drift), forced convection becomes critical. Switching the fan ON attenuates the drift and brings the response toward a quasi-steady plateau, sustaining absorption capacity during weak-gradient regimes. This is the primary operating mode for reliability under intermittent use, low solar availability, or idle/standby periods.
• Acceleration mode (medium loads). In regimes where natural convection already produces a mild positive trend, fan activation acts as a dynamic accelerator, steepening the slope and shortening the transient time required to reach a useful operating level (e.g., +137% in Q_in,2). This mode is valuable for rapid start-up and for responding promptly to load increases in decentralized cooling scenarios.
• Moderation mode (high loads). Under high thermal inputs, buoyancy-driven transport is strong, and the subsystem can exhibit rapid, high-sensitivity transients. In these cases, fan activation tends to moderate the slope, producing a damping-like trend response (i.e., smaller slope magnitude under fan-ON than fan-OFF) that preserves controllability. This regime-dependent moderation does not imply reduced viability; rather, it delineates an upper-load region where forced convection is better used as a stabilizing actuator than as a booster in the present apparatus and dataset.
• In the absence of local flow diagnostics (e.g., vapor-velocity measurements, spatial pressure-gradient mapping, or film-thickness/interface imaging), this moderation is interpreted at the response level rather than claimed as a proven fluid-dynamic mechanism. A plausible first-order explanation consistent with the observed trend-level behavior is that, at high loads, the coupled buoyancy-driven vapor transport and absorption heat release can approach a transport-limited condition in which additional forced circulation primarily redistributes gradients and enhances mixing in the vapor core (chimney region), reducing the effective sensitivity of the absorber-side response to further thermal driving. In this regime, the fan may therefore act as an internal actuator that damps transient sensitivity by smoothing the coupled heat/mass-transfer feedback, rather than increasing the net driving potential. Confirming the detailed mechanism would require dedicated flow-field and interface diagnostics, which are outside the scope of the present instrumentation and are identified as future work.

A validated platform for future development. From a broader perspective, the present results validate the patented evaporator-absorber architecture (IMPI, MX 4573 B) as a robust experimental baseline for compact mechanically assisted absorption. The prototype demonstrates stable operation over the tested thermal-load range of ≈0–225 W and provides quantified reference behaviors for Q_abs, ${∆\dot{m}}_{abs}$, and $R_{th}$. This validated baseline enables future work to focus on control refinement, such as variable-speed fan modulation triggered by real-time slope estimation or regime-aware switching, rather than revisiting the fundamental coupled-vessel design.

Further work may complement this experimentally validated trend-level framework with dedicated flow-field/film diagnostics and/or validated CFD model(s) to quantify the buoyancy–forcing interaction underlying the high-load moderation regime and to support cycle-level COP modeling once the missing components and boundary conditions are defined. Related multi-objective CFD–surrogate/ML optimization workflows have been reported in broader energy-conversion devices (e.g., PEMFC flow-field design) and could be adapted to compact absorber optimization once a validated CFD model and boundary conditions are available [47,48].

While the present protocol supports repeatability at the within-run level through consistent OFF/ON trend responses across multiple tagged phases (including zero-load references), it does not quantify long-duration endurance or multi-run reproducibility. Dedicated extended-duration campaigns and repeated runs are therefore identified as future work. Consequently, the unit establishes a practical foundation for scaling and deploying low-cost, low-power absorber modules in decentralized solar- or waste-heat-driven cooling applications.

5. Conclusions

This Part II study completes the thermodynamic assessment of the patented compact evaporator–absorber unit (IMPI, MX 4573 B), extending the experimental validation reported in Part I through a control-volume analysis of coupled heat and mass transport. Whereas Part I established mechanical integrity, vacuum stability, and local temperature/pressure separation, the present work quantifies subsystem-level dynamic performance using three complementary lenses: the absorption heat-transfer rate Q_abs, the estimated absorption mass-transfer rate ${∆\dot{m}}_{abs}$, and the global thermal resistance $R_{th}$, evaluated over twelve tagged thermal-load phases.

A key contribution of Part II is the demonstration that a rigorous control-volume formulation, explicitly decoupling evaporator-side input emulation from absorber-side heat rejection, provides a reliable and physically consistent basis for interpreting transient absorber behavior in a compact vertical configuration. The slope-based analysis of tagged fan-OFF/fan-ON sub-intervals (parameters $\mathrm{a}$ for Q_abs and $b$ for ${∆\dot{m}}_{abs}$) proved especially robust for a manually regulated prototype, capturing regime-level dynamics while remaining insensitive to systematic offsets. Although ${∆\dot{m}}_{abs}$ is subject to approximately ±15% uncertainty due to near-film property assignment and constant-density approximation, the coherent paired response between mass-transfer trends and independently measured heat-transfer trends confirms the validity of the thermodynamic assumptions and of the derived performance map. To strengthen interpretability under the acknowledged measurement and property-assignment constraints, the revision also reports the subsystem-level effectiveness η_EA = Q_abs/Q_in and complementary robustness/sensitivity evidence (uncertainty-budget decomposition, fixed-window slope checks, and Monte Carlo propagation), provided in the Supplementary Material.

The results verify a strong physical coupling between heat and mass transfer, and show that low-power fan-assisted vapor guidance enhances both processes synchronously. Fan-assisted vapor guidance is consistent with reduced vapor-side diffusional resistance at the solution interface, yielding slope-based relative improvements up to ~137% in acceleration regimes and consistently attenuating downward drifts under weak natural gradients. This active vapor guidance achieves effects analogous to passive surface or wetting enhancements, while offering easier implementation and load-responsive adaptability within the same compact vessel.

Thermal-resistance analysis further consolidates these findings. Fan activation systematically reduces $R_{th}$, with the strongest influence occurring in low-load and zero-input phases where buoyancy-driven transport becomes insufficient. In these regimes, $R_{th}$ decreases by more than ~30%, and the effect is statistically significant in the majority of phases (Wilcoxon p < 0.05), confirming a meaningful gain in absorber-side dissipation efficiency. Importantly, these improvements are internal, slope-based comparisons within the same patented prototype (fan-ON vs. fan-OFF), and therefore represent enhanced stabilization and recoverability across operating windows rather than an external benchmark against other absorbers.

Beyond quantitative performance, the dynamic map extracted from $\mathrm{a}$, $b$, and $R_{th}$ identifies three operational modes: stabilization at low/zero loads, acceleration at intermediate loads, and moderation under strong buoyancy at high loads. This reframes the fan from a static enhancement element into a practical control actuator, enabling straightforward demand-driven logic for future automated operation (e.g., regime-aware switching or variable-speed modulation guided by real-time slope estimation).

Overall, this two-part study establishes the compact shared-vessel evaporator–absorber unit as a validated baseline platform for decentralized LiBr–H₂O absorption cooling. By coupling experimental validation (Part I) with subsystem-level thermodynamic performance mapping (Part II), the work demonstrates that a simplified, low-cost vertical architecture with modest mechanical assistance can sustain stable absorber operation across a wide transient envelope (output Q_abs up to ~280 W). The quantified regimes and control implications reported here provide a solid foundation for subsequent scale-up, long-duration testing, and control refinement toward robust low-carbon cooling applications.

6. Patents

The experimental prototype evaluated in this study was formally registered as a utility model with the Mexican Institute of Industrial Property (IMPI). The registration was granted under title number MX 4573 B, with the official application code MX/u/2018/000306, and is valid until 22 June 2028. The invention is titled “Módulo evaporador/absorbedor para sistemas de refrigeración por absorción” (Evaporator/absorber module for absorption refrigeration systems). The module integrates both evaporator and absorber components into a single vertical cylindrical structure and includes a mechanical enhancement system based on a controllable fan and recirculation pump. This configuration allows simultaneous heat and mass transfer processes while improving vapor transport and system compactness. International Patent Classification (IPC): F25B 17/08; F25B 37/00. Cooperative Patent Classification (CPC): F25B 17/08; F25B 37/00. Cooperative Patent Classification (CPC): F25B 17/08; F25B 37/00. Official public record link: [https://vidoc.impi.gob.mx/visor?d=MX/2021/44860 (accessed on 18 November 2025)].