Effect of Subducting Baffle Structure in Solar Air Heaters: A CFD Insight into Thermo-Hydraulic Performance

Abstract

Numerical analysis is an economically viable method for improving the performance of a thermal system without many trials. The numerical analysis reported in this paper serves to clarify the extent to which a newly designed subducting baffling structure impacts the performance of a solar air heater (SAH). The performance of different baffle shapes is evaluated through a two-dimensional Computational Fluid Dynamics (CFD) simulation in terms of the thermal (Nu), hydraulic (f), and thermo-hydraulic (THP) performances of the SAH. Moreover, the study is performed with different Reynolds numbers (Re) varying from 3000 to 18,000. The study investigates the parameters arm length (k), arm height (l), pitch (p), pitch angle (α), and arm angle (β) within the ranges of 40–60°, 140–160°, 0.03–0.07 m, 0.03–0.05 m, and 0.05–0.15 m, respectively. The results demonstrate that the assistance of a subducting baffle structure is more effective than a smooth arrangement. The SAH shows a maximum Nu and f of 101.23 and 0.97, respectively. The system with the best performance has revealed the highest THP of 0.798. The greatest intensification of heat transfer (Nu/Nu_s) and friction loss (f/f_s) are 2.58 and 87.76, respectively.

1. Introduction

In thermal applications, the demand for solar air heaters (SAHs) has increased, as they can deliver the necessary heat sustainably compared with fossil fuels. Thermal energy generation in SAHs occurs by directing the air to pass over an absorber plate that is exposed to solar energy. The conversion efficiency of thermal energy is influenced by various factors, i.e., the area of the absorber plate, airflow rate, and ambient conditions, and to a great extent it is determined by the configuration of the roughness on the absorber plate which can be a baffle, grooved, dimpled, wire mesh, chamfered ribs, helical, or have artificial roughness [1]. Essentially, the purpose of these configurations is to change the laminar sub-layer that is formed along the hot absorber surface by generating a significant disturbance in the flow pattern [2]. Experimental, theoretical, and numerical approaches have been used to analyze the performance of SAHs. Among these approaches, the numerical approach is more economical and facilitates an extensive knowledge of the physics associated with roughness [3]. This method has received increased attention in recent years within the context of SAHs. In cases where the secondary flow has only a small effect on the primary flow, a two-dimensional simulation is usually chosen in order to save computational time and costs [4]. While simulating the SAH, the use of the RNG k–ε model is said to give the results that are closest to the experimental and correlated ones [5]. Karpenko et al. [6] demonstrated the capability of CFD in analyzing complex hydrodynamic phenomena such as flow separation, pressure instability, and recirculation zones, reinforcing the applicability of CFD for thermo-hydraulic investigation in engineering systems.

Basically, the efficiency of SAH is judged by means of heat transfer, friction loss, as well as a combination of heat transfer and friction loss in terms of Nusselt number (Nu), friction factor (f), and thermo-hydraulic performance (THP) [7]. The heat and friction enhancement factors Nu/Nu_s and f/f_s, respectively, are used to compare the performance over the smooth duct [8]. Ikrame et al. used ≠-shaped baffles and identified that Nu was increased to 4.5-fold when the baffles were placed 0.071 m apart at an Re of 35,000 compared with the smooth SAH (SSAH) [9]. A comparison made between six different baffles showed that the sine wave baffle has the maximum Nu of 158 at Re of 15,000 and has the maximum Nu/Nu_s of 3.60 [10]. Staggered cuboid baffles have been analyzed for different positions of angle, pitch (p), height, length, and width. The optimal configuration has shown 4.34 times improvement in Nu when compared with an SSAH. This is reported due to the thorough mixing and formation of an effective vortex [11]. A triangular SAH with a perforated V-down pattern baffle has been numerically analyzed by Sachin and Muskan with a maximum Nu of 138 and a maximum Nu/Nu_s of 3.8 for a baffle height of 9 mm. At this geometry, greater turbulence is observed in the inter-baffle regions, and beyond 9 mm, baffles started blocking and reduced Nu [12]. Amit et al. experimented with the use of arched baffles fixed to the absorber plate in a counter-flow double pass SAH and identified the highest Nu of 62 at a Re of 10,000, which is a 17% increase in Nu compared with an SSAH [13]. To upgrade the impinging flow strength, fluid mixing, and boundary layer disturbance, twisted baffles have been introduced, and the results have shown that the Nu of twisted baffles can be increased by 1.48–4.72 times compared with that of normal baffles [14]. Ankush and Singal examined the synergistic impact of a perforated baffle together with semicircular tubes oriented perpendicularly to the airflow. The decrease in the viscous sub-layer resulting from enhanced fluid mixing is evidenced by a maximum Nu of 274.72, with a Nu/Nu_s ratio of 6.92 [15].

The ≠-shaped baffle recorded a minimum f/f_s of 3 when the baffles were placed 0.213 m apart at an Re of 15,000 [9]. The sine wave baffle recorded a minimum f/f_s of 2.7 at an Re of 18,000 [10]. Meanwhile, in the case of staggered cuboid baffles, the optimal configuration has a minimal f of 9.74 times the SSAH at an Re of 10,160. It is reported that the optimal baffle position that creates more turbulence leads to more Nu with high frictional loss [11]. The increase in baffle height increased the obstruction in the primary flow of the V-down pattern baffle in the triangular SAH, resulting in a corresponding maximum f and f/f_s of 0.046 and 5.13, respectively, when compared to an SSAH [12]. The inclusion of arched baffles has demonstrated minimum and maximum f/f_s values of 1.76 and 16.5, respectively, indicating that hydraulic loss (f) is substantial and Nu is higher [13]. The higher wall shear stress and significant turbulence result in substantial friction loss for twisted multiple V-baffles, which is 2.47 to 7.99 times greater than that of an SSAH [14]. A maximum f of 0.1707 and an f/f_s of 71.53 are observed in the combined configuration of a semicircular tube and perforated baffles. The cause of this is the formation of pressure drag and frictional drag forces, attributed to surface shear stress and pressure differentials, respectively, leading to recirculation flow behind the baffles [15].

The maximum THP for the ≠-shaped baffle of 2.12 is found at the baffle distance of 0.071 m and at an Re of 35,000 [9]. The sine wave baffle has given the maximum THP of 2.05 at an Re of 15,000 [10]. When staggered cuboid baffles are employed, the highest THP is recorded as 3.14 at an Re of 5080, and it is also stated that the THP diminishes as Re increases. So, it can be inferred that the maximum SAH performance can be realized at a low airflow rate [11]. The maximum thermal THP in the V-down pattern baffle is determined to be 2.54, suggesting that the installation of the baffle in an SAH is viable if it attains a high Nu with reduced pump power and a THP exceeding 1, regardless of Re [12]. However, in numerous instances, the THP falls below 1, indicating that the specific SAH exhibits a superior performance compared with the SSAH in terms of Nu and Nu/Nu_s. The study conducted by Menasria et al. on rectangular baffles in a continuous manner demonstrated a maximum THP of 0.857, along with an admirable Nu and Nu/Nu_s factor of 108 and 2.16, respectively, attributed to enhanced fluid mixing resulting from vigorous swirl motion and fluctuating disturbances within the viscous sub-layer. The reduction in THP is found to be solely attributable to the elevated f/f_s, which stands at 634 [16]. The optimal twisted V-shaped baffle configuration produced a maximum THP of 2.81, even at a lower f [14]. The maximum THP in the SAH with a semicircular tube and perforated baffle is found to be 2.51 at the lower Re of 3000. This is found to be lower at the cost of minimal f and high Nu [15].

This extensive review indicates that the baffle structure enhances the average Nu while concurrently reducing the f, due to the synergistic effects of ribs and channels [16]. However, the increase in pressure drop with baffle height must be acknowledged. According to the authors, the use of a subducting baffle in an SAH has not been previously reported. There are numerous potential benefits, in fact, the addition of a subducting baffle justifies further exploration for a variety of reasons. The subducting baffle can have the combined effect of ribs and baffles; thus, fluid mixing and heat transfer can be improved. The regular arrangement of subducting baffles may lead to even flow distribution, thus local hot spot formation can be prevented, turbulence can be strengthened, heat transfer can become uniform, and more heat transfer can be facilitated. Moreover, a full comprehension of heat transfer and fluid flow phenomena related to SAHs with a subducting baffle is necessary to the development of SAH design and efficiency. Due to this knowledge gap, a systematic and detailed analysis is performed in the current research to evaluate the performance of the subducting baffle-added SAH by investigating the flow and thermal behavior of the baffle. To achieve this aim, a two-dimensional numerical study is performed for an SAH with and without a subducting baffle. In the current research, besides changing the airflow rate, the geometry parameters such as arm length, arm height, pitch, pitch angle, and arm angle are also varied. The optimized parameters are determined for the best subducting baffle geometry to be proposed.

The main focus of this research is the evaluation of an SAH equipped with subducting baffles. The objectives of this study are outlined as follows:

• Designing an SAH with subducting baffles fixed at a particular distance from the absorber plate.
• Conducting fluid flow and thermal analysis through a two-dimensional CFD simulation.
• Determining the Nusselt number and friction factor for evaluating the thermal and hydraulic performance and THP of the SAH.
• Recognizing optimal design parameters using a device efficiency study over different geometries.
• Producing correlations for Nu and f by considering all the parameters under investigation.

2. Materials and Methods

The CFD analysis of the SAH followed a stepwise approach as described below:

• Creating an SAH design with the help of AutoCAD 2019 software by merging subducting baffles.
• Determining the range of the design and operational parameters of the subducting baffle configuration.
• Numerical simulations were carried out for the developed model under different design and operational parameters in Ansys Fluent.
• The Reynolds number, Nusselt number, and friction factor were evaluated to determine the thermal and hydraulic performance and THP.
• Displaying and discussing the Nusselt number, friction factor, THP, and the enhancement of the thermal and friction characteristics of the SAH concerning design and operational parameters.
• Identifying the best parameters through detailed performance analysis.

The CFD simulation serves as a proficient tool for examining and evaluating the impact of the design and operational parameters of SAHs [17]. Herein, the influence of different design and operational parameters on the SAH with the help of the subducting baffles is studied through CFD. The simulation involved geometry creation, meshing, writing the governing equation, boundary conditions application, and then simulation execution and results evaluation.

2.1. Geometry Design

The SAH with a subducting baffle configuration is designed in Ansys DesignModeler and analyzed in Ansys Fluent 2019 R3. The heater that is designed has three sections: inlet, test, and outlet. The inlet and outlet sections are made as per the ASHRAE standard [18]. The length of the test section is taken as L₂, which is enough to fit the sufficient number of baffles, and the inlet section L₁ is made greater than 5 × (W × H)^1/2 to make the flow fully developed, and the length of the exit L₃ is made more than half of the inlet. The L₁, L₂, and L₃ of the SAH for the present work are designed based on the standard procedure at 0.6 m, 1.5 m, and 0.4 m, respectively. Figure 1 represents the test section design. The geometry of the subducting baffle includes palm length (i), forearm length (j), arm length (k), arm height (l), palm and arm distance (g), pitch (p), pitch angle (α), and arm angle (β) and are depicted in Figure 1. A range of values for the design parameters k, l, p, α, and β is taken for the study, whereas the other design parameters i, j, and g are considered to be constant to reduce the problem complexity without losing the performance of the SAH, with the values 0.05 m for i and j and 0.09 m for g. The thickness of the baffle is taken as 0.002 m. The Re is taken as the operational parameter, and the range is fixed as 3000 ≥ Re ≤ 18,000. The range of the parameters and the values taken for the study are given in

Table 1. Range of investigating parameters and their absolute values.

S. No.	Parameters	Range	Values	Units
1.	Pitch angle (α)	40–60	40, 45, 50, 55, 60	Degree
2.	Arm angle (β)	140–160	140, 145, 150, 155, 160	Degree
3.	Arm length (k)	0.03–0.07	0.03, 0.04, 0.05, 0.06, 0.07	m
4.	Arm height (l)	0.03–0.05	0.03, 0.035, 0.04, 0.045, 0.05	m
5.	Pitch (p)	0.05–0.15	0.05, 0.075, 0.10, 0.125, 0.15	m
6.	Reynolds number (Re)	3000–18,000	3000, 6000, 9000, 12,000, 15,000, 18,000	-

.

2.2. Grid Generation

The fluid domain is subdivided into several smaller parts called subdomains or grids. This can be achieved by meshing the geometry with Ansys 2019 R3. The quality of the mesh should be good as it influences the computational time, the accuracy of the solution, and the convergence rate. Non-uniform meshing is performed to generate subdomains, and mesh refining was performed on the appropriate surfaces to increase the resolution of them. Surface refinement has been completed to ensure a smooth transition. The meshed portion in the smooth duct and especially in the absorber surface is shown enlarged in Figure 2. To observe the fluid flow activities, CFD was used, and the solver chosen was Fluent 2019 R3.

Grid Independence Test

A grid independence test is the main measure to determine the best grid setup. The best grid setup is considered to be reached when the numerical analysis results have very slight differences. The shape has been divided into parts starting from 12,750 elements with an element size of 5 × 10⁻⁶ m to 89,498 elements with a 15 × 10⁻⁷ m element size. The results of Nu and f for the influence of the number of grid elements are identified and are presented in Figure 3. The changes in the results of Nu and f are also indicated in

Table 2. Nu and f of smooth duct for different numbers of grid elements.

No. of Elements	Nu	% Deviation	f	% Deviation
12,750	50.55797	2.450662	0.0090094	9.906361
17,814	49.3486	2.338449	0.0100000	2.28379
27,750	48.22098	1.336599	0.0102337	1.548408
54,375	47.58496	0.397594	0.0103947	1.790481
89,498	47.39651	-	0.0105842	-

. It shows that the discretized geometry with 54,375 elements with an element size of 2 × 10⁻⁶ m showed less than 1% variation in Nu value and 5.4% variation in f value. Thus, for further analysis, the element size of 2 × 10⁻⁶ m has been chosen to perform non-uniform meshing along with surface refinement.

2.3. Governing Equations

The features of the fluid flow and heat transfer in a turbulent flow inside the SAH may be represented through mathematical expressions based on the governing equations of continuity, momentum, and energy. The main equations for the 2-D SAH model with an incompressible fluid, a turbulent fluid flow, and no radiation heat transfer are given as follows [19,20]:

Continuity equation:

$${\displaystyle \frac{\partial \left(\rho u_i\right)}{\partial x_i}}$$

(1)

Momentum equation:

$${\displaystyle \frac{\partial }{\partial x_i}}\left(\rho u_i{u}_j\right)+{\displaystyle \frac{\partial P}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_j}{\partial x_i}}\right)\right]+{\displaystyle \frac{\partial }{\partial x_j}}\left(-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(2)

Energy equation:

$${\displaystyle \frac{\partial }{\partial x_i}}\left(\rho u_{i}T\right)-{\displaystyle \frac{\partial }{\partial x_i}}\left[\left(\Gamma +{\Gamma }_t\right){\displaystyle \frac{\partial T}{\partial x_i}}\right]=0$$

(3)

where Pr, $\Gamma$, ${\Gamma }_t$, and T are the Prandtl number, molecular thermal diffusivity $\left({\displaystyle \frac{\mu }{Pr}}\right)$, turbulent thermal diffusivity $\left({\displaystyle \frac{{\mu }_t}{{Pr}_t}}\right)$, and the temperature of the air, respectively.

2.4. Boundary Conditions

The SAH domain represents a rectangular area on the x-y plane bounded by an inlet, an outlet, and walls. A velocity at the inlet, which was obtained from an Re range of 3000 to 18,000, is given to the SAH and changes from 0.24 m/s to 1.45 m/s. Air is the fluid medium while the absorber plate is made of aluminum solid medium. The properties of air and aluminum used for this study are listed in Table 3. The air inlet temperature is assumed to be 300 K. A turbulence intensity of 5% was specified at the inlet to represent a moderately developed duct flow, while the hydraulic diameter was determined based on the equivalent rectangular cross-section of the air passage as shown in Equation (8). These parameters were applied at the inlet boundary and used by ANSYS Fluent to initialize the turbulence quantities (k and ε). The pressure at the exit is set to the ambient pressure to give a consistent reference pressure for the flow calculation and to confirm that there is no pressure gradient at the exit [17]. A constant heat flux of 1000 W/m² is imposed on the absorber plate, which is the heating source in the SAH. Also, a no-slip condition is given to the fluid and solid mediums at the contact area to make sure that there is no relative motion between them [3].

The following is an expression for the boundary conditions:

At the bottom of the wall L₁ ≤ x ≤ L₁ + L₂, y = 0 (heating surface, excluding the surface below the arm, forearm, and palm),

$$q_w=1000\mathrm{W}/{\mathrm{m}}^2$$

(4)

At (0 ≤ x ≤ L₁), (L₁ + L₂ ≤ x ≤ L₃), y = 0,

$$q_w=0,\hspace{1em}{\displaystyle \frac{\partial T}{\partial y}}=0$$

(5)

At the upper wall (y = H), (0 ≤ x ≤ L₃),

$$q_w=0,\hspace{1em}{\displaystyle \frac{\partial T}{\partial y}}=0$$

(6)

At the duct entrance (x = 0, 0 ≤ y ≤ H),

$$u=u_{in},\mathrm{v}=0,\mathrm{T}=300\mathrm{K}$$

(7)

$$D={\displaystyle \frac{2\left(W\times H\right)}{\left(W+H\right)}},T_i={\displaystyle \frac{u^{\prime }}{U}}=0.05$$

(8)

At the duct exit (x = L₁ + L₂ + L₃, 0 ≤ y ≤ H),

$${\displaystyle \frac{\partial u}{\partial x}}=0,{\displaystyle \frac{\partial v}{\partial x}}=0,{\displaystyle \frac{\partial T}{\partial x}}=0{\mathrm{P}}_0=1.013\times {10}^{-5}\mathrm{Pa}$$

(9)

At the fluid–solid interface, no-slip is declared, hence, u = v = 0.

The continuity in heat transfer and temperature along the solid–fluid interface with no-slip condition is expressed as follows, according to ref. [21]:

$$\left.\begin{array}{c}{T}_{s|s-f}=T_{f|s-f}\\ k_f{\left({\displaystyle \frac{\partial T}{\partial \eta }}\right)}_{|f}=k_s{\left({\displaystyle \frac{\partial T}{\partial \eta }}\right)}_{|s}\\ u_{|s-f}=v_{|s-f}=0\end{array}\right\}$$

(10)

Table 3. Properties of fluid and solid domains.

Material	Density, ρ (kg/m3)	Specific Heat, cp (J/kg K)	Dynamic Viscosity, μ (Nm2)	Thermal Conductivity, k (W/m K)	Reference
Air	1.225	1006	1.78 × 10−5	0.024	[22]
Aluminum	2719	871	-	202.4	[23]

Table 3. Properties of fluid and solid domains.

Material	Density, ρ (kg/m3)	Specific Heat, cp (J/kg K)	Dynamic Viscosity, μ (Nm2)	Thermal Conductivity, k (W/m K)	Reference
Air	1.225	1006	1.78 × 10−5	0.024	[22]
Aluminum	2719	871	-	202.4	[23]

2.5. Assumptions for CFD Analysis

In order to simplify the problem and reduce computation time when evaluating heat transfer and fluid flow behavior, the assumptions listed below were taken in the CFD analysis [3,24].

• The present analysis uses a two-dimensional model; variations along the z-direction are neglected, as they are not critical for evaluating in-plane flow and heat transfer effects.
• The analysis utilizes a two-dimensional (2D) model, neglecting z-direction variations $\left({\displaystyle \raisebox{1ex}{$\partial $}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.}\approx 0\right)$. This assumption is valid as out-of-plane effects are non-critical for evaluating the primary in-plane flow and heat transfer characteristics.
• A steady-state airflow is assumed to be maintained inside the duct. This simplifies the representation of airflow dynamics and focuses on a stabilized flow pattern.
• No change in the physical and chemical properties of both domains at the working temperature. This simplifies the calculation and upholds consistency in analysis by maintaining the same material property throughout the analysis.
• The side walls and the absorber plate are considered to be adiabatic. This reduced the convergence time by eliminating the external heat loss from the SAH and concentrating only on the internal heat transfer.
• Negligible radiation heat transfer in the duct. This excludes the radiation heat transfer, which is negligible when compared with other heat transfer modes in the duct and hence simplifies the calculation.

2.6. Solution Method and Turbulence Model

Choosing an appropriate turbulence model for modeling the turbulence behavior of the fluid is a significant factor if you want to have accurate results. To obtain better convergence of the solution and to produce accurate and reliable results, the double precision and pressure-based solvers were used [4,8]. The k–ε turbulence model is preferred for this study because it provides a good balance between computational efficiency and accuracy for internal turbulent flows such as those in solar air heater ducts. The model effectively captures the turbulent kinetic energy and its dissipation rate, which are essential for predicting heat transfer enhancement caused by baffles.

Compared with the standard k–ε model, the RNG formulation incorporates an additional term that accounts for the effects of strain rate and streamline curvature, making it more suitable for predicting separated and recirculating flows induced by the baffle geometry. Furthermore, comparative validation with published results for ribbed channels confirmed that the RNG k–ε model predicts the Nusselt number and friction factor within ±6% of experimental data [25], thereby demonstrating its reliability for the present study. K and ɛ in this case refer to the kinetic energy and the turbulence dissipation rate. The convergence criteria for velocity, energy, and continuity are set to 10⁻⁸, 10⁻⁷, and 10⁻⁶, respectively. The general relation describing the renormalization group (RNG) turbulent model is taken from the work of Choudhury [24].

$${\displaystyle \frac{\partial \left(\rho k{u}_i\right)}{\partial x_i}}-{\displaystyle \frac{\partial }{\partial x_i}}\left({\alpha }_k{\mu }_{eff}{\displaystyle \frac{\partial k}{\partial x_j}}\right)=G_k-\rho \epsilon$$

(11)

$${\displaystyle \frac{\partial \left(\rho \epsilon u_i\right)}{\partial x_i}}={\displaystyle \frac{\partial }{\partial x_i}}\left({\alpha }_{\epsilon }{\mu }_{eff}{\displaystyle \frac{\partial k}{\partial x_i}}\right)+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}{G}_k-\left(C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+R_{\epsilon }\right)$$

(12)

where µ_eff and G_k are the effective turbulent viscosity and turbulent kinetic energy generation, respectively. α_k, and α_ε are the inverse of the effective turbulent Prandtl number for k and ε. α_k, α_ε, C_1s, and C_2s are the constants with values of 1.39, 1.39, 1.42, and 1.68, respectively, and G_k is the production term and is expressed as

$$G_k={\tau }_{ij}{S}_{ij}=\left(-\rho \overline{u_i{u}_j}\right)S_{ij}$$

(13)

$$G_k=0.5\left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_i}{\partial x_j}}\right)$$

(14)

$${\mu }_{eff}=\mu +\rho C_{\mu }\times {\displaystyle \frac{k^2}{\epsilon }}$$

(15)

where C_µ is a constant with a value of 0.085.

2.7. Post Processing of Results

From the simulation results, the performance of the SAH, according to values such as Nu, f, and THP, is determined using the standard relations as given below.

The Reynolds number (Re) is given by the following, according to ref. [26]:

$$Re={\displaystyle \frac{\rho vD}{\mu }}$$

(16)

where $\rho$ is the air density (kg/m³), v is the air velocity (m/s), D is the hydraulic diameter (m), and µ is the dynamic viscosity (Nm²).

The convective heat transfer (h) is calculated from the following, according to ref. [8]:

$$h={\displaystyle \frac{\dot{m}\times c_p\times \left(T_{out}-T_{in}\right)}{A_c\times \left(T_p-T_{in}\right)}}$$

(17)

where $\dot{m}$ is the mass flow rate of air (kg/s), c_p is the specific heat capacity of air (kJ/kg K), A_c is the area of absorber plate (m²), and T_out, T_in, T_p, and T_m are the temperature of air at outlet, inlet, plate, and bulk mean temperature of flow (K), respectively.

The bulk mean temperature of the fluid is determined from the following, according to ref. [27]:

$$T_m={\displaystyle \frac{T_{out}-T_{in}}{2}}$$

(18)

Nu denotes the heat transfer between the fluid and the hot solid surface by correlating the convective heat transfer and the conductive heat transfer at the boundary, and is calculated using ref. [28] as follows:

$$Nu={\displaystyle \frac{hD}{k}}$$

(19)

where k is the thermal conductivity of air (W/mK).

The thermo-hydraulic diameter (D) of the collector is determined using the following relation [29]:

$$D={\displaystyle \frac{2\left(W\times H\right)}{\left(W+H\right)}}$$

(20)

where W and H are the width and height of the collector (m).

The friction factor (f) in the collector is evaluated using the following, according to ref. [30]:

$$f={\displaystyle \frac{∆PD}{2\rho L_2{v}^2}}$$

(21)

where ΔP is the pressure drop in the collector (N/m²).

The thermo-hydraulic performance of the air heater is calculated from the following, according to ref. [31]:

$$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{o}-\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{u}\mathrm{l}\mathrm{i}\mathrm{c}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}={\displaystyle \frac{\left(\raisebox{1ex}{$Nu$}\!\left/ \!\raisebox{-1ex}{${Nu}_s$}\right.\right)}{\sqrt[3]{\left(\raisebox{1ex}{$f$}\!\left/ \!\raisebox{-1ex}{$f_s$}\right.\right)}}}$$

(22)

where Nu_s and f_s denote the Nusselt number and friction factor for the collector without baffles, and the Nu and f denote the same for SAH under study.

2.8. Validation of CFD Results

The measured values of Nu and f for the smooth duct were compared with those obtained from the Dittus–Boelter and Gnielinski equations, respectively. The Nu evaluation in smooth SAH is performed by the Dittus–Boelter method and is given as follows, according to ref. [32]:

$${Nu}_s=0.023{Re}^{0.8}{Pr}^{0.4}$$

(23)

The f of the smooth SAH is found using the Gnielinski equation and is expressed as follows, according to ref. [33]:

$$f={\left(1.58ln\left(Re\right)-3.82\right)}^{-2}$$

(24)

3. Results and Discussion

3.1. Validating the Computational Results

A comparison and validation of Nu and f from the computation and empirical correlations developed by Dittus–Boelter and Gnielinski were completed to check the CFD results’ reliability. Figure 4 presents the values obtained from the numerical calculations and correlations. The CFD results show a slight difference from the correlation for both Nu and f for the smooth duct, thus confirming the CFD’s reliability in predicting Nu and f. It means that the CFD results are close to the empirical correlation. Nevertheless, the CFD results for SAHs with subducting baffles exhibit a considerable difference in both Nu and f due to more factors influencing it. Such a difference has also been acknowledged in the cited literature [17].

3.2. Effect of Pitch Angle (α)

The effect of α in the subducting structure on the performance of the SAH is examined, while keeping the other study parameters constant at β = 150°, k = 0.05, l = 0.04, and p = 0.10.

3.2.1. Effect of α on Thermal Performance

Figure 5a–e clearly show that the fluid flow characteristics have been influenced by the change in α. The palm feature has generated three vortex regions beneath the palm, with the vortex size being minimal near the palm corner and increasing as it approaches the heating surface between the palm and forearm. Furthermore, the size of the vortex region is increased by the increase in α, which in turn increases the intensity of turbulence and the area of contact in the region between the palm and the forearm. Additionally, the vortex near the palm corner is reduced. This has enabled a rise in the rate of convective heat transfer between the hot surface and the air. Therefore, the Nu increases as α increases from 40° to 55°, as illustrated in Figure 6a. However, the Nu experiences a decrease at a higher α, specifically beyond 55°, and is anticipated to continue to decrease as α continues to rise. This might be explained by the fact that at a higher α the size of the hot surface on the base between the palm and forearm becomes almost the same, and most of the vortex region is formed below the forearm and arm areas that are not heated. The variation in Nu with Re at different α shows that Nu increases with Re at all α. The increase in turbulence due to an increase in Re impinges the thermal boundary layer and enhances heat transfer. The maximum Nu is obtained at 55°, which means that this pitch angle is the most effective one to achieve the highest thermal performance.

3.2.2. Effect of α on Hydraulic Performance

The hydraulic performance variation with different α was analyzed. Increasing α from 40° to 60° results in an increase in f, as can be seen in Figure 6b. This means that the flow in the main stream is limited to some extent by the increase in α. With increasing α, most of the air is guided through a narrowed region above the forearm, so that the flow of air between the palm and the forearm is reduced. Thus, the nozzle effect is observed between the forearm and glass, as indicated by the rise in fluid velocity at the exit. This can be observed by comparing Figure 5a–e. Therefore, the limitation in the airflow causes a higher pressure drop and f. It can be seen from Figure 6b that f is decreasing along with Re. At higher Re, the flow is fully turbulent, thus the skin friction is reduced and the f is lowered [17]. There is a slight decrease in f at 50°, which may be due to the symmetrical flow separation occurring in the upstream and downstream flow. So, the lowest α (40°) can be chosen for the best f.

3.2.3. Effect of α on Thermo-Hydraulic Performance

From Figure 6c, it is observed that the THP of the SAH is significantly influenced by α. The THP increases with an increase in α from 40° to 50°. In this range, Nu increases, and the f also increases. However, the heat transfer dominates the friction, leading to higher THP. Beyond an α of 50°, the THP tends to decline. The reason for this is mainly the constantly rising f and decreasing heat transfer Nu. Re is only responsible for the decrease in THP according to the observations. The main reason for flow separation due to turbulence, which causes the fluid flow pattern to be more disturbed, is turbulence where convective heat transfer is hindered, but also f is dominating rather than Nu. Hence, to obtain the highest THP, a value of 50° for α is chosen.

3.3. Effect of Arm Angle (β)

The influence of the arm angle (β) of the subducting baffle on the SAH performance was studied. The other parameters were kept constant: α = 50°, k = 0.05 m, l = 0.04 m, and p = 0.10 m.

3.3.1. Effect of β on Thermal Performance

The vortex region developed over the forearm and arm is large, as evidenced by the velocity profile for the lower β at 140° in Figure 7a. As a result, the fluid mixing layer between the hot solid and the cold fluid has been disturbed and the heat transfer has been enhanced. The vortex zone is shown to shrink and almost disappear in the case of β being changed to 145°, 150°, 155°, and 160° as in Figure 7b, Figure 7c, Figure 7d and Figure 7e, respectively. Similarly, the variation in β over the arm surface leads to flow separation and reattachment that are controlled. The turbulence intensity in the arm and forearm, which are exposed to heat flux, decreases with the reduction in the vortex size. This causes the Nu to be reduced as the convective heat transfer between the air and the hot surface decreases. Figure 8a shows that increasing β significantly decreases the Nu of the SAH. It is found that Nu increases with Re for all the β values considered. So, to obtain the highest Nu or maximum heat transfer, the lower β, 140°, has to be selected if β is used.

3.3.2. Effect of β on Hydraulic Performance

Figure 8b shows the results regarding the impact of β on f. An increase in β is observed to diminish the overall friction in the SAH, consequently leading to a reduction in the f. The lower β is a parameter that raises the forearm; thus, the flow of the upper fluid stream is restricted and the air is allowed to pass between the palm and forearm thereby increasing the fluid–wall friction and the pressure drop. By increasing β, the forearm and arm are brought into a nearly straight line, thus the upper stream flow becomes unobstructed and the fluid flow pattern is slightly influenced. This has substantially reduced the effect of fluid flow disturbance and turbulence. It has been found that f decreases with an increase in Re for all the β values considered. Hence, a β of 160° should be selected in order to have the minimal f.

3.3.3. Effect of β on Thermo-Hydraulic Performance

It is evident from Figure 8c that with the increase in β, the THP of the SAH is decreased. The reason is that with the increase in β, the turbulence and flow characteristics are reduced, and therefore both the Nu and f associated with THP tend to decrease. In addition, it is also observed that the increase in Re causes the decrease in the THP of the SAH, owing to the domination of f over Nu at higher Re. Thus, to obtain the maximum THP in the SAH, the β value of 140° is favored.

3.4. Effect of Arm Length (k)

The influence of k in the subducting baffle design on the performance of the SAH is analyzed, maintaining the other study parameters constant at α = 50°, β = 140°, l = 0.04 m, and p = 0.10 m. In the study of the influence of k on SAH performance, the number of subducting baffles is six for k ≤ 0.06 m, while the number of baffles is limited to five when k ≥ 0.07 m due to spatial constraints within the heater.

3.4.1. Effect of k on Thermal Performance

The disturbance of the fluid flow patterns on the heating surface is beneficial for heat transfer optimization. The parameter k was observed to significantly alter the flow characteristics from Figure 9a–e. However, it has a small effect on changing the thermal performance of the SAH as shown in Figure 10a. The vortex on the arm, affected by the β, is making a very small area of contact between the air and the arm when k is low, which becomes larger as k increases. The alteration in contact area minimally influences heat transfer enhancement up to a k value of 0.06 m, as illustrated in Figure 9a. An additional increase in k diminishes the number of baffle structures, resulting in no observable effect beyond a k value of 0.06 m. In addition, the rise in k covers the area beneath the arm, resulting in no alteration of the heating surface area. Therefore, a k of 0.06 m is necessary to achieve an optimal thermal performance.

3.4.2. Effect of k on Hydraulic Performance

Figure 9a–e indicate that k significantly influences the friction between air and the plate. The formation of a vortex beneath the arm and the enhancement of surface contact between the air and the plate over the arm are clearly observable. This may explain the minor increase in f until the k value reaches 0.06 m. As k increases further, the number of baffles decreases from six to five, resulting in a significant reduction in friction caused by the baffles, which leads to a decline in the f value after a k value of 0.06 m.

3.4.3. Effect of k on Thermo-Hydraulic Performance

The rise in k increased the surface contact between the air and the arm, while simultaneously decreasing the area on the bottom plate. Therefore, there is no alteration in the thermal absorption area. This does not disrupt the fluid flow abruptly. Also, the increase in k has enabled the coverage of the vortex region induced by the effect of β. This effect has shown a marginal increase in Nu up to a k value of 0.06 m, as seen in Figure 10c. However, the rise in k has expanded the turbulence zone over the arm, concurrently increasing friction loss, thereby diminishing hydraulic performance, as evidenced by the increase in f up to k = 0.06 m. At k = 0.07 m, the friction loss decreases while the Nu remains constant, similar to that at k = 0.06 m. Therefore, to achieve a superior thermal and minimal hydraulic performance, specifically a high thermo-hydraulic performance, a k value of 0.07 m has been chosen. As a result, the number of baffles is reduced to five for further analysis.

3.5. Effect of Arm Height (l)

The effect of changing the distance between the base plate and the arm (l) on the performance of the SAH has been evaluated. Other parameters were kept constant at α = 50°, β = 140°, k = 0.07 m, and p = 0.10 m. Figure 11a–e represent the velocity profile for different l values, and Figure 12a–c show the thermal performance, hydraulic performance, and THP of the SAH, respectively, for various l values.

3.5.1. Effect of l on Thermal Performance

In Figure 12a, Nu decreases as the l increases from 0.03 m to 0.035 m, after which it rises with further increases in l. When the l is slightly increased, the flow pattern becomes marginally disrupted; however, the majority of air passes over the forearm, with only a minor volume being redirected beneath it, as evidenced by the development of a vortex below the palm and forearm. Consequently, the heat transfer diminishes, leading to a decrease in Nu. An increase in l beyond 0.035 m augments airflow beneath the forearm by restricting the air above it. As illustrated in Figure 11b–e, it tends to produce elongated vortices marked by extended flow separation and reattachment near the arm. This has augmented the heat transfer from the arm. The simultaneous formation of vortices beneath the palm significantly disrupts the laminar sub-layer, facilitating layer mixing, thereby enhancing heat transfer and resulting in an increase in Nu. The increase in airflow in relation to Re intensifies the disturbance of the thermal boundary layer near the hot surface, resulting in elevated heat transfer and consequently an increase in the Nu with rising Re. Therefore, an arm length of 0.05 m is necessary to achieve optimal heat transfer in the SAH.

3.5.2. Effect of l on Hydraulic Performance

From Figure 12b, it is generally observed that the f increases with an increase in l, and it decreases with an increase in Re. As l increases, the upper fluid stream flow is obstructed, as evidenced by Figure 11a–e, resulting in an increased pressure drop across the series of baffles. Thus, f increases with an increase in l, indicating that the SAH exhibits a superior hydraulic performance at elevated l values. According to Re, an increase in Re results in a decrease in f. This is because, in comparison to low flow rates, a higher Re maintains more airflow, which results in less friction due to the lower skin friction. However, at a higher Re and l exceeding 0.04 m, the f surpasses that observed at a low Re, indicating the generation of substantial turbulence that impedes fluid flow. Therefore, a value of l = 0.03 m is preferable for a low hydraulic performance.

3.5.3. Effect of l on Thermo-Hydraulic Performance

Figure 12c indicates that the THP of the SAH marginally increases with an increase in l. However, as l increases from 0.03 m to 0.035 m, a decrease in THP is noted, followed by a gradual increase until l reaches 0.05 m. At an l of 0.035 m, the resistance to airflow predominates over heat transfer, resulting in the observed dip. After 0.035 m, the THP increased, indicating that for every rise in l, proper mixing is promoted along with improved heat transfer with minimal friction loss. The increase in airflow at a higher Re reduces the thermal performance of the SAH due to the predominance of friction loss across the baffle structure. Therefore, in the case of l, 0.05 m is chosen to achieve the maximum THP in the SAH.

3.6. Effect of Pitch (p)

The performance of the SAH concerning changes in p is examined while maintaining the other parameters constant at α = 50°, β = 140°, k = 0.07 m, and l = 0.05 m. As p represents the distance between baffles, an increase in p diminishes the number of baffles due to the constrained space within the SAH. At a p of 0.05 m, there are seven baffles; at 0.075 m, there are six baffles; and at 0.1 m, 0.125 m, and 0.15 m, there are five baffles each.

3.6.1. Effect of p on Thermal Performance

Figure 12a displays the fluctuation in Nu in relation to different values of p. The change in p has a minimal impact on the thermal performance of the SAH, although it slightly reduces as p increases. This happens because when the p is altered, the configuration of the subducting baffle remains unchanged due to the preceding step, leading to simply a shift in the baffle’s position. As a result, turbulence generation remains unchanged, and the fluid flows uniformly across the baffles and the base plate. This is clearly evident from Figure 13a–e. As p approaches 0.05 m, closeness and a higher number of baffles generate higher turbulence intensity, resulting in an elevated Nu. A slight decrease in Nu is noted at 0.075 m l for all Re, which is potentially attributable to the reduction in interaction between the air and the heated surface. In general, the reduction in the number of baffles has led to a reduction in turbulence, resulting in inadequate mixing. Therefore, the overall decrease in Nu is observed as p increases. The same effect was observed in the previous literature [3]. In the case of Re, it is noted that increased airflow correlates with a higher Nu. This results from the enhanced flow disruption and turbulence induced by the enhanced airflow rate. The maximum Nu occurs at a p equal to 0.05 m, indicating the optimal p for attaining an optimal thermal performance.

3.6.2. Effect of p on Hydraulic Performance

The impact of p on hydraulic performance has been examined in Figure 14b. The friction between the air and the internal surface of the SAH diminishes as the p increases. There is a significant decline in f at a p of 0.075 m, which clearly indicates a reduction in the number of baffles. Subsequently, with an additional increase in p, the friction loss experiences a minor elevation. This signifies that the elevated pitch has induced turbulence in the fluid flow and has barely hindered the flow. In the case of Re, a higher Re (18,000) leads to reduced friction loss, thereby diminishing hydraulic performance relative to another Re. Therefore, a p of 0.1 m is required when optimal f is considered.

3.6.3. Effect of p on Thermo-Hydraulic Performance

Figure 14c depicts a correlation between the THP and p. This indicates that p has a more favorable effect on heat transfer between the air and the hot surface than the friction loss occurring between them. At a higher p, the fluid exhibits considerable turbulence, resulting in reduced f, while simultaneously enhancing heat transfer, as evidenced by increased Nu. Also, the Nu dominated over the friction loss. In the case of Re, the increased flow rate diminished turbulence and enhanced flow passage due to the baffles being positioned at greater intervals. Thus, an elevated p (0.15 m) is necessary, signifying an optimal configuration of baffles within the confined space to achieve enhanced THP in this SAH.

The comprehensive analysis indicates that the subducting baffle has modified the flow characteristics, thereby enhancing the thermal and thermo-hydraulic performance with minimal friction loss. Therefore, the optimal parameters for the baffle geometry identified from each analysis are α = 50, β = 150°, k = 0.05, l = 0.04, and p = 0.10.

3.7. Effect of Reynolds Number

The change in airflow changes the flow characteristics, thus different flow patterns that are influenced by heat transfer and pressure drop may result. Hence it is very important to find out how the airflow rate influences the SAH. The airflow rate in terms of Re has been studied for optimal parameters and is explained in detail below.

3.7.1. Effect of Reynolds Number on Nu

The influence of the Re on the Nu of the SAH is studied, the impinging parameters α, β, k, l, and p are considered, and the outcomes are depicted in Figure 15a–e, correspondingly. Most of the time, it is found that the Re has a positive effect on the heat transfer, which means that the Re causes more turbulence and mixing of the fluid, thus the heat exchange between air and the hot surface is intensified. It is clear from Figure 15a that the greater the α, the greater the Nu in all Re cases. Whereas in the case of β in Figure 15b, the Nu decreases when the Re increases for all cases of β. The rise in β enhances the unobstructed movement of upstream air without significantly affecting the flow pattern. From Figure 15c, the increase in k has made a different flow pattern with respect to Re, hence unusual heat transfer has been observed. l generated positive effects on Nu for all the Re values. Overall, all modified absorber plates with subducting baffles have demonstrated a superior thermal performance compared with the smooth duct.

3.7.2. Effect of Reynolds Number on f

It is observed that the variation in f with respect to Re is not similar when compared with each parameter, as seen in Figure 16a–e. However, overall, the decrease in friction with an increase in Re is observed. In the case of α, the f tends to increase with an increase in Re, whereas the lower α has an adverse effect. This results from enhanced flow disruption and turbulence. In the case of p, the friction loss increases until an Re of 15,000. This is likely attributable to the intensified flow disruption, which has impacted the overall flow pattern. However, after an Re of 15,000, the effect is reversed, indicating a decrease in f rather than an increase. This is clearly attributable to the fully developed turbulent flow, which enhances mixing, reduces skin friction, and results in a lower f.

3.7.3. Effect of Reynolds Number on THP

The impact of the Re on the THP of the SAH has been analyzed through numerical results, as illustrated in Figure 17a–e. The Re negatively affects THP; specifically, an increase in the Re results in a decrease in THP across all examined parameters. The elevated THP at a lower Re, specifically at 3000, signifies a predominance of heat transfer over friction loss, whereas at a higher Re, increased turbulence leads to flow separation, disrupts the flow pattern, and amplifies shear stress generation. This hindered heat transfer efficiency, ultimately leading to a decreased overall performance of the SAH. Therefore, to enhance SAH performance, an appropriate Re must be chosen to significantly increase Nu while minimally affecting f.

In the above discussions, it is found that changing the study parameters palm length (i), forearm length (j), arm length (k), arm height (l), pitch (p), pitch angle (α), and arm angle (β) results in a maximum THP of 0.798 when i = 0.05 m, j = 0.05 m, k = 0.07 m, l = 0.05 m, p = 0.15 m, α = 50°, and β = 155° at Re = 3000. However, the maximum values of Nu and f are 101.23 and 0.97, respectively, at the optimized parameter values.

3.8. Development of Correlations

From the interpretations, it is found that the parameters Nu and f are functions of α, β, k, l, and p. Therefore, these heat transfer and frictional parameters can be characterized by the functional relationship mentioned below.

$$Nu=\mathrm{f}\left(\alpha ,\beta ,k,l,p\right)$$

(25)

$$f=\mathrm{f}\left(\alpha ,\beta ,k,l,p\right)$$

(26)

A regression analysis is conducted according to the standard methodology to determine the correlation of Nu and f based on the simulated results.

The correlation between Nu and f is derived using linear regression on logarithmically transformed data. Hence, the relation between Nu and Re can be expressed as

$$Nu=C_0{Re}^n$$

(27)

where C₀ is the intercept and n is the slope.

Taking the natural logarithm of both sides to linearize the relationship gives

$$\mathrm{l}\mathrm{n}\left(Nu\right)=\mathrm{l}\mathrm{n}\left(C_0\right)+n\mathrm{l}\mathrm{n}\left(Re\right)$$

(28)

Equation (28) can be written as

$$ln\left(Nu\right)=C_1+nln\left(Re\right)$$

(29)

where C₁ = ln(C₀).

From the intercept C₁, we can calculate C₀ as

$$C_0=e^{C_1}$$

(30)

We then plot the Nu corresponding to the Re from the simulation on the log scale. A regression analysis has been carried out to find the n and C₁. From the result, Equation (27) can be written as

$$Nu=C_0·{Re}^{0.5914}$$

(31)

The coefficient C₀ depends on the other dependent parameters α, β, k, l, and p. Hence, the next plot of lnC₀ against lnα is plotted, and using the regression analysis, the following equation is derived.

$$Nu=C_1·{Re}^{0.5914}·{\alpha }^{-0.008}$$

(32)

The coefficient C₁ depends on the other dependent parameters β, k, l, and p. Hence, the next plot of lnC₁ against lnβ is plotted. The subsequent equation is derived through regression analysis.

$$Nu=C_2·{Re}^{0.5914}·{\alpha }^{-0.008}·{\beta }^{-0.0010}$$

(33)

Likewise, the procedure is followed to add the other independent parameters k, l, and p in the regression equation of Nu, and the concluding coefficient C₅ is determined as 0.2851. The final regression equation for Nu for the SAH with a subducting baffle is derived as

$$Nu=C_5·{Re}^{0.5914}·{\alpha }^{-0.008}·{\beta }^{-0.0010}·k^{0.0004}·l^{-0.0002}·p^{0.0002}$$

(34)

The procedure followed for deriving the correlation for Nu is also applied to derive the correlation for f, and the final relation is given below. The coefficient C₅ of f is determined as 0.2920.

$$f=C_5·{Re}^{0.0840}·{\alpha }^{0.0143}·{\beta }^{0.0074}·k^{-0.0034}·l^{0.0028}·p^{-0.0024}$$

(35)

The final correlations show that the powers of parameters α, β, k, l, and p are almost zero, indicating their negligible contribution to heat transfer and friction loss. Nevertheless, the single parameters have significantly influenced Nu and f when changed only. The values of Nu and f calculated by the simulations and predicted through the developed correlations are very close to each other, and their comparison is presented in Figure 18a,b. It is found that more than 99% of the data points lie within the deviation limit of ± 11% for Nu and f. Thus, the established correlations may be employed to ascertain the values of Nu and f at the proper level of accuracy.

3.9. Comparison with Previous Studies

After the numerical analysis, it is also very important to confirm the results obtained by means of an experiment or comparable studies [34,35]. However, validation through experimental investigation was not possible since the goal was to predict the operation of the SAH with new subducting baffles. Hence, the validation was made by comparing the numerical findings of similar research. The table compares the present study’s results with those of other studies concerning heat transfer enhancement (Nu/Nu_s), friction factor enhancement (f/f_s), and THP. The roughness configuration in the SAH changes from one study to another and it includes ribs, baffles, winglets, and impinging jets with different geometries. As previously mentioned, the THP for a configuration with a transverse rib was 1.042 [3], for honeycomb-shaped roughness was 1.7 [16], for V-shaped perforated baffles was 1.3 [36], for an inclined winglet was 1.35 [37], and a maximum of 3.34 was achieved for ‘S’-shaped ribs [38]. Therefore, the SAH’s performance is dependent upon its configuration and geometry, and it can only be compared within a specific range of values. However, these configurations show a high f/f_s of 1.8–3.2 and a maximum Nu/Nu_s in the range of 1.52–2.2. Additionally,

Table 4. Comparison of numerical outcomes in relation to prior research.

Researcher	Geometry of Roughness	Nu/Nus	f/fs	THP
Bensasi et al. [39]	Rectangular baffle	-	-	0.53–0.75
Madhukeshwara Nanjundappa [40]	Cubical roughness	-	-	0.67
Jacek and Magdalena [41]	Multiple-fin array	-	-	0.411
Sameer Ali Alsibiani [42]	Rectangular pattern	2.5–4.8	20–160	0.48–1.62
Raisan et al. [18]	Trapezoidal ribs	1.1–2.1	14.3–17.5	0.49–0.85
Menasria et al. [35]	Rectangular baffle	1.62–3.72	14–634	0.30–0.85
Prasad et al. [3]	Transverse ribs	1.15–1.55	1.4–7.67	0.72–1.04
Present study	Subducting baffle	1.36–2.58	14.33–87.76	0.42–0.798

shows the results of Nu/Nu_s, f/f_s, and THP of numerous other basic configurations that have improved heat transfer at a minimal friction factor. Menasria et al. [16] achieved a maximum Nu/Nu_s of 3.72 with an f/f_s of 634 by employing the baffle configuration. However, their maximum THP is only 0.85. The maximum f/f_s is 7.67 when simple ribs are employed; however, the maximum Nu/Nu_s is a mere 1.55. In contrast to this, the proposed subducting baffle showed a satisfactory heat transfer performance, with a maximum Nu/Nu_s of 2.58 at a reasonable f/f_s and THP of 87.76 and 0.798, respectively.

4. Conclusions

A 2D numerical analysis is conducted for an SAH that features a novel subducting baffle setup. The arm is fixed at a specific distance from the absorber plate using thin metal strips, and the palm is attached by a rivet to investigate the enhancement of thermal and flow behavior. In this study, the palm arm length (k), arm height (l), pitch (p), pitch angle (α), and arm angle (β) are adjusted from 0.03 m to 0.07 m, 0.03 m to 0.05 m, 0.05 m to 0.15 m, 40° to 60°, and 104° to 160°, respectively. The palm length (i) and forearm length (j) remain constant at 0.05 m. The THP evaluates the overall performance of the SAH by evaluating the heat transfer in terms of the Nusselt number (Nu), friction loss in terms of the friction factor (f), and the thermal and friction enhancement factors Nu/Nu_s and f/f_s, respectively. The Nu, f, and THP values were found to be 25.57 to 101.32, 0.266 to 0.97, and 0.42 to 0.798, respectively, within the range of Re (3000–18,000) considered in the study. The numerically obtained data are also used to derive the correlation for determining Nu and f. The following is a comprehensive list of the key insights from the current study.

• The fluid flow characteristics of the SAH have changed due to the addition of a subducting baffle. Collectively, it contributed to improved heat transfer compared with the smooth absorber plate by promoting turbulence, disrupting the boundary layer, and facilitating control flow separation. This is clear because, in comparison to the smooth configuration, the Nu showed a 2.13-fold increase.
• The number of baffles in the SAH has decreased as a result of the increase in k and p. The Nu enhancement is not significantly affected by the increase in k, as it maintains the absorber area; however, it decreases the f. Nevertheless, the turbulence effect is diminished as a result of the reduction in the number of baffles due to the increase in p, which results in a reduction in Nu.
• The SAH has achieved the maximum Nu of 101.32 at k = 0.07 m, l = 0.05 m, p = 0.15 m, α = 60°, and β = 155° at Re = 18,000 while the maximum f was achieved at k = 0.07 m, l = 0.05 m, p = 0.05 m, α = 50°, and β = 155° at Re = 15,000. To consider the optimal conditions, the geometry of the SAH having a maximum THP of 0.798 at i = 0.05 m, j = 0.05 m, k = 0.07 m, l = 0.05 m, p = 0.15 m, α = 50°, and β = 155° at Re = 3000 is selected.
• When p (0.05 m) and R (3000) are at their lowest, the maximum thermal enhancement (Nu/Nu_s) of 2.58 is observed, while k and l are at their highest in the study range. Conversely, the friction enhancement (f/f_s) of 87.76 is observed when the Re is at its maximum (18,000). The rate of increment in Nu/Nu_s is greater than that of f/f_s. As a result of the greater increase in f/f_s, the THP tends to decrease.

5. Future Research

The following areas of research are identified for enhancing and analyzing the SAH deeply as an extension of the present work.

• Reversal of airflow: In the current configuration, there is an additional option to operate with air in the reverse direction. This could also offer a substantial improvement in terms of thermal and pressure drop. Nevertheless, the thermal and flow characteristics must be identified by conducting a comprehensive analysis of the effect of geometry in the reverse direction.
• Experimental analysis: To investigate the geometry’s response to the changing natural environment, experimental analysis must be conducted with the optimal geometry of the current novel configuration. It is essential to validate the performance under real-world conditions in order to guarantee its reliability.
• Environmental and economic analysis: For economic and environmental reasons, the SAH must be analyzed to determine its impact on clean energy initiatives and sustainability, justifying investment and policy support.