# Evaluation of Heat Transfer Performance of a Multi-Disc Sorption Bed Dedicated for Adsorption Cooling Technology

## Abstract

**:**

## 1. Adsorption Cooling Technology

#### 1.1. Environmental Demands

#### 1.2. Adsorption Chillers

_{2}, or ammonia. These working pairs in adsorption cooling technology are characterized by zero global warming potential (GPW) and ozone depletion potential (ODP) [14].

_{2}emissions and pollution [15], almost zero electricity consumption [6], no moving parts resulting in high reliability [16], simple control and maintenance [3]. Moreover, on the markets of the Middle and the Far East, adsorption technology is intensively developed because of the possibility of desalination of seawater along with the production of cooling energy [17]. But the widespread application of adsorption chillers is limited by the following shortcomings of adsorption cooling technology: low coefficient of performance [18], large weight and volume [16], intermittent cooling [14], high initial procurement cost [14], and exploitation under vacuum conditions [2].

#### 1.3. Design and Operation

#### 1.4. Literature Review

_{2}) characterized by high chemical resistance. The advantages of silica gel as adsorbent are also revealed in high adsorption/desorption rate, low regeneration heat, good long-term stability, and minimal hysteresis [45]. The analysis of the thermal behavior of devices using silica gel shows that their performance is very sensitive to heat and mass transfer rates inside the adsorbent beds [46]. According to [47], the lowest temperature needed to regenerate the adsorption chiller bed is required for the silica gel–water pair. Therefore, this sorption pair opens up a number of chiller’s possible applications because of the low temperature of the required heat source.

#### 1.5. The Main Aim of the Work

## 2. Research Object

#### 2.1. Multi-Disc Sorption Bed Design

#### 2.2. Inlet/Outlet Manifolds

#### 2.3. Lab-Scale Prototype

## 3. Research Methods

#### 3.1. Experimental Research

^{3}/s and the measurement accuracy of ±2% were used in order to determine the mass flow rate of both hot and cold water.

#### 3.2. Numerical Research

#### 3.2.1. CFD Tool

#### 3.2.2. Computational Domain and Discretization

^{®}meshing was implemented in order to maintain the layered elements on the boundary layers and fill the rest of the volume with high-quality polyhedral elements (Figure 9). Polyhedral cells consume less memory and computing time in comparison to tetrahedral elements. Moreover, they also have many neighbors, so gradients can be better approximated and layered polyhedral prisms can be applied on the boundaries to efficiently capture the boundary layer on no-slip walls. The mesh is fully conformal, which ensures that the nodes on both sides of the interface between fluid and solid regions match to each other. Such an approach assures no interpolation at the interface, which contributes to the reduction of computational time and ensures higher accuracy of the solution.

- ΔV
_{i}—volume of the ith cell; - N—total number of cells in the computational domain;

^{−2}was generated and then meshes of mean relative cell sizes decreased to 6.46 × 10

^{−2}and 4.72 × 10

^{−2}were prepared by scaling the initial mesh.

_{k}denotes the value of the variable important to the objective of the simulation study for the solution obtained with the kth mesh. The logarithmic mean temperature difference (LMTD) was selected as the above-mentioned variable.

#### 3.2.3. Boundary Conditions and Model Settings

_{MFR}ratios defined with Equation (8) and equal to 1.00, 1.33, and 1.66. The cold water inlet temperature was 294.1 K and hot water inlet temperature was 336.2 K. The above data was defined based on the experimental research.

- ${\dot{m}}_{HW}$—hot water mass flow rate (kg/s);
- ${\dot{m}}_{CW}$—cold water mass flow rate (kg/s);

#### 3.2.4. Sorption Modeling

## 4. Results and Discussion

#### 4.1. Heat Transfer Efficiency

- HW
_{in}—hot water inlet temperature (K); - HW
_{out}—hot water outlet temperature (K); - CW
_{in}—cold water inlet temperature (K); - CW
_{out}—cold water outlet temperature (K);

_{MFR}are presented in Table 3. The correction factor F is close to 1 for all analyzed R

_{MFR}ratios, which indicate the very good efficiency of the investigated innovative multi-disc construction.

_{MFR}

_{,}the temperatures also increased on both the hot and cold side of the sorption bed operating as a water–water heat exchanger. The lowest temperature was recorded by Probe 8 for all the analyzed R

_{MFR}ratios, although CFD results were 2.0% (R

_{MFR}= 1.00 and 1.33) or 2.1% (R

_{MFR}= 1.66) higher in comparison to experimental results. The highest temperature was recorded by Probe A for all the analyzed R

_{MFR}ratios. The relative difference between CFD and experimental results for Probe A ranged between 0.6% to 1.2%. The CFD and experimental results are qualitatively similar. The quantitative differences are presented in Figure 11 and range from 0.6% to 7.0%.

#### 4.2. Temperature Field in the Sorption Bed

_{HW}) in the sorption bed presented in Table 4. The ΔT

_{HW}is directly proportional to the heating power (HP) defined in Equation (11), which is one of the most important parameters of the adsorption chiller. Therefore, the increase in ΔT

_{HW}obtained through the analyzed cases leads to a 69% increase in HP for constant mass flow rate (${\dot{m}}_{HW}$) and specific heat (${c}_{p}$) of heating water.

#### 4.3. Weight and Dimension Factors

_{HX/S}) defined as the quotient of the total mass of the cylindrical heat transfer walls of the heat exchanger (m

_{HX}) to the total sorbent mass (m

_{S}). Lower values of R

_{HX/S}ratio are desirable in terms of the adsorption chiller performance and compact dimensions. Moreover, decreasing the fraction of heat exchanger mass in the total mass of the device leads to the growth of the COP because of supplying a greater portion of the thermal energy to the sorbent itself and not to the metal part of the sorption bed. Therefore, the d/a equal to 0.86 is the most advantageous design parameter value in the above context.

_{S}) is convenient to assess the degree of a dynamic perfection of the sorption bed as it is proportional to the specific power; the larger the ratio the higher power per unit adsorbent mass can be obtained [32].

## 5. Conclusions

_{HW}), logarithmic mean temperature difference (LMTD), heat exchanger mass to sorbent ratio (R

_{HX/S}), and heat transfer surface to sorbent mass ratio (S/m

_{s}).

## Funding

## Conflicts of Interest

## References

- Alsaman, A.; Askalany, A.; Ahmed, M.; Ali, E.; Harby, K.; Diab, M. Simulation model for silica gel-water adsorption cooling system powered by renewable energy. In Proceedings of the 3rd International Conference on Energy Engineering Faculty, of Energy Engineering, Aswan University, Aswan, Egypt, 28–30 December 2015. [Google Scholar]
- Elsheniti, M.B.; Hassab, M.A.; Attia, A.-E. Examination of effects of operating and geometric parameters on the performance of a two-bed adsorption chiller. Appl. Therm. Eng.
**2018**, 146, 674–687. [Google Scholar] [CrossRef] - Sultana, T. Effect of overall thermal conductance with different mass allocation on a two stage adsorption chiller employing re-heat scheme. Master’s Thesis, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, 2008. [Google Scholar]
- Khan, M.Z.I.; Alam, K.; Saha, B.B.; Hamamoto, Y.; Akisawa, A.; Kashiwagi, T. Parametric study of a two-stage adsorption chiller using re-heat—The effect of overall thermal conductance and adsorbent mass on system performance. Int. J. Therm. Sci.
**2006**, 45, 511–519. [Google Scholar] [CrossRef] - Saha, B.B.; Koyama, S.; Kashiwagi, T.; Akisawa, A.; Ng, K.C.; Chua, H.T. Waste heat driven dual-mode, multi-stage, multi-bed regenerative adsorption system. Int. J. Refrig.
**2003**, 26, 749–757. [Google Scholar] [CrossRef] - Sur, A.; Das, R.K. Review of technology used to improve heat and mass transfer characteristics of adsorption refrigeration system. Int. J. Air Cond. Refrig.
**2016**, 24, 1630003. [Google Scholar] [CrossRef] - Hassan, H.; Mohamad, A.; Alyousef, Y.; Al-Ansary, H. A review on the equations of state for the working pairs used in adsorption cooling systems. Renew. Sustain. Energy Rev.
**2015**, 45, 600–609. [Google Scholar] [CrossRef] - Voyiatzis, E.; Stefanakis, N.; Palyvos, J.; Papadopoulos, A. Computational study of a novel continuous solar adsorption chiller: Performance prediction and adsorbent selection. Int. J. Energy Res.
**2007**, 31, 931–946. [Google Scholar] [CrossRef] - Sztekler, K.; Kalawa, W.; Stefanski, S.; Krzywanski, J.; Grabowska, K.; Sosnowski, M.; Nowak, W. The influence of adsorption chillers on CHP power plants. MATEC Web Conf.
**2018**, 240, 05033. [Google Scholar] [CrossRef] - Sztekler, K.; Kalawa, W.; Nowak, W.; Stefanski, S.; Krzywanski, J.; Grabowska, K. Using the adsorption chillers for waste heat utilisation from the CCS installation. EPJ Web Conf.
**2018**, 180, 02106. [Google Scholar] [CrossRef] - Sztekler, K.; Kalawa, W.; Nowak, W.; Stefanski, S.; Krzywanski, J.; Grabowska, K. Using the adsorption chillers for utilisation of waste heat from rotary kilns. EPJ Web Conf.
**2018**, 180, 02105. [Google Scholar] [CrossRef] - Rezk, A.; Al-Dadah, R.; Mahmoud, S.; Elsayed, A. Effects of contact resistance and metal additives in finned-tube adsorbent beds on the performance of silica gel/water adsorption chiller. Appl. Therm. Eng.
**2013**, 53, 278–284. [Google Scholar] [CrossRef] - Saravanan, R.; Maiya, M.P. Thermodynamic comparison of water-based working fluid combinations for a vapour absorption refrigeration system. Appl. Therm. Eng.
**1998**, 18, 553–568. [Google Scholar] [CrossRef] - Kurniawan, A.; Rachmat, A. Others CFD Simulation of Silica Gel as an Adsorbent on Finned Tube Adsorbent Bed. E3S Web Conf.
**2018**, 67, 01014. [Google Scholar] [CrossRef] - Pyrka, P. Modelowanie trójzłożowej chłodziarki adsorpcyjnej. Zesz. Energetyczne
**2014**, 1, 205–216. [Google Scholar] - White, J. Literature review on adsorption cooling systems. Lat. Am. Caribb. J. Eng. Educ. 2013. Available online: https://www.researchgate.net/publication/289127089_LITERATURE_REVIEW_ON_ADSORPTION_COOLING_SYSTEMS (accessed on 8 December 2019).
- Shahzad, M.W.; Ybyraiymkul, D.; Burhan, M.; Oh, S.J.; Ng, K.C. An innovative pressure swing adsorption cycle. AIP Conf. Proc.
**2019**, 2062, 020057. [Google Scholar] - Grabowska, K.; Sosnowski, M.; Krzywanski, J.; Sztekler, K.; Kalawa, W.; Zylka, A.; Nowak, W. The Numerical Comparison of Heat Transfer in a Coated and Fixed Bed of an Adsorption Chiller. J. Therm. Sci.
**2018**, 27, 421–426. [Google Scholar] [CrossRef] - Xu, S.Z.; Wang, L.W.; Wang, R.Z. Thermodynamic analysis of single-stage and multi-stage adsorption refrigeration cycles with activated carbon–ammonia working pair. Energy Convers. Manag.
**2016**, 117, 31–42. [Google Scholar] [CrossRef] - Starace, G.; Fiorentino, M.; Meleleo, B.; Risolo, C. The hybrid method applied to the plate-finned tube evaporator geometry. Int. J. Refrig.
**2018**, 88, 67–77. [Google Scholar] [CrossRef] - Fiorentino, M.; Starace, G. The design of countercurrent evaporative condensers with the hybrid method. Appl. Therm. Eng.
**2018**, 130, 889–898. [Google Scholar] [CrossRef] - Elsheniti, M.B.; Elsamni, O.A.; Al-dadah Raya, K.; Mahmoud, S.; Elsayed, E.; Saleh, K. Adsorption refrigeration technologies. In Sustainable Air Conditioning Systems; BoD—Books on Demand: Norderstedt, Germany, 2018. [Google Scholar]
- Wu, W.-D.; Zhang, H.; Men, C. Performance of a modified zeolite 13X-water adsorptive cooling module powered by exhaust waste heat. Int. J. Therm. Sci.
**2011**, 50, 2042–2049. [Google Scholar] [CrossRef] - Sakoda, A.; Suzuki, M. Fundamental study on solar powered adsorption cooling system. J. Chem. Eng. Jpn.
**1984**, 17, 52–57. [Google Scholar] [CrossRef] [Green Version] - Sakoda, A.; Suzuki, M. Simultaneous Transport of Heat and Adsorbate in Closed Type Adsorption Cooling System Utilizing Solar Heat. J. Sol. Energy Eng. Trans. Asme. J. Sol. Energy Eng.
**1986**, 108, 239–245. [Google Scholar] [CrossRef] - Bahrehmand, H.; Khajehpour, M.; Bahrami, M. Finding optimal conductive additive content to enhance the performance of coated sorption beds: An experimental study. Appl. Therm. Eng.
**2018**, 143, 308–315. [Google Scholar] [CrossRef] - Kim, D.-S.; Chang, Y.-S.; Lee, D.-Y. Modelling of an adsorption chiller with adsorbent-coated heat exchangers: Feasibility of a polymer-water adsorption chiller. Energy
**2018**, 164, 1044–1061. [Google Scholar] [CrossRef] - Li, A.; Thu, K.; Ismail, A.B.; Shahzad, M.W.; Ng, K.C. Performance of adsorbent-embedded heat exchangers using binder-coating method. Int. J. Heat Mass Transf.
**2016**, 92, 149–157. [Google Scholar] [CrossRef] - Grabowska, K.; Krzywanski, J.; Nowak, W.; Wesolowska, M. Construction of an innovative adsorbent bed configuration in the adsorption chiller-Selection criteria for effective sorbent-glue pair. Energy
**2018**, 151, 317–323. [Google Scholar] [CrossRef] - Chang, K.-S.; Chen, M.-T.; Chung, T.-W. Effects of the thickness and particle size of silica gel on the heat and mass transfer performance of a silica gel-coated bed for air-conditioning adsorption systems. Appl. Therm. Eng.
**2005**, 25, 2330–2340. [Google Scholar] [CrossRef] - Grabowska, K.; Sosnowski, M.; Krzywanski, J.; Sztekler, K.; Kalawa, W.; Zylka, A.; Nowak, W. Analysis of heat transfer in a coated bed of an adsorption chiller. MATEC Web Conf.
**2018**, 240, 01010. [Google Scholar] [CrossRef] [Green Version] - Aristov, Y.I.; Glaznev, I.S.; Girnik, I.S. Optimization of adsorption dynamics in adsorptive chillers: Loose grains configuration. Energy
**2012**, 46, 484–492. [Google Scholar] [CrossRef] - Askalany, A.A.; Henninger, S.K.; Ghazy, M.; Saha, B.B. Effect of improving thermal conductivity of the adsorbent on performance of adsorption cooling system. Appl. Therm. Eng.
**2017**, 110, 695–702. [Google Scholar] [CrossRef] - Girnik, I.S.; Aristov, Y.I. Making adsorptive chillers more fast and efficient: The effect of bi-dispersed adsorbent bed. Appl. Therm. Eng.
**2016**, 106, 254–256. [Google Scholar] [CrossRef] - Demir, H.; Mobedi, M.; Ülkü, S. Effects of porosity on heat and mass transfer in a granular adsorbent bed. Int. Commun. Heat Mass Transf.
**2009**, 36, 372–377. [Google Scholar] [CrossRef] [Green Version] - Alam, K.C.A.; Saha, B.B.; Kang, Y.T.; Akisawa, A.; Kashiwagi, T. Heat exchanger design effect on the system performance of silica gel adsorption refrigeration systems. Int. J. Heat Mass Transf.
**2000**, 43, 4419–4431. [Google Scholar] [CrossRef] - Sosnowski, M.; Grabowska, K.; Krzywanski, J.; Nowak, W.; Sztekler, K.; Kalawa, W. The effect of heat exchanger geometry on adsorption chiller performance. J. Phys. Conf. Ser.
**2018**, 1101, 012037. [Google Scholar] [CrossRef] [Green Version] - Hong, S.; Ahn, S.; Kwon, O.; Chung, J. Optimization of a fin-tube type adsorption chiller by design of experiment. Int. J. Refrig.
**2015**, 49, 49–56. [Google Scholar] [CrossRef] - Ilis, G.G.; Demir, H.; Mobedi, M.; Saha, B.B. A new adsorbent bed design: Optimization of geometric parameters and metal additive for the performance improvement. Appl. Therm. Eng.
**2019**, 162, 114270. [Google Scholar] [CrossRef] - Gong, L.; Wang, R.; Xia, Z.; Chen, C. Design and performance prediction of a new generation adsorption chiller using composite adsorbent. Energy Convers. Manag.
**2011**, 52, 2345–2350. [Google Scholar] [CrossRef] - Rogala, Z. Adsorption chiller using flat-tube adsorbers—Performance assessment and optimization. Appl. Therm. Eng.
**2017**, 121, 431–442. [Google Scholar] [CrossRef] - Çağlar, A. The effect of fin design parameters on the heat transfer enhancement in the adsorbent bed of a thermal wave cycle. Appl. Therm. Eng.
**2016**, 104, 386–393. [Google Scholar] [CrossRef] - Pajdak, A.; Kudasik, M.; Skoczylas, N.; Wierzbicki, M.; Braga, L.T.P. Studies on the competitive sorption of CO2 and CH4 on hard coal. Int. J. Greenh. Gas Control
**2019**, 90, 102789. [Google Scholar] [CrossRef] - Pajdak, A.; Skoczylas, N.; Dębski, A.; Grzegorek, J.; Maziarz, W.; Kudasik, M. CO2 and CH4 sorption on carbon nanomaterials and coals—Comparative characteristics. J. Nat. Gas Sci. Eng.
**2019**, 72, 103003. [Google Scholar] [CrossRef] - Intini, M.; Goldsworthy, M.; White, S.; Joppolo, C.M. Experimental analysis and numerical modelling of an AQSOA zeolite desiccant wheel. Appl. Therm. Eng.
**2015**, 80, 20–30. [Google Scholar] [CrossRef] - Gurgel, J.; Andrade Filho, L.; Grenier, P.; Meunier, F. Thermal diffusivity and adsorption kinetics of silica-gel/water. Adsorption
**2001**, 7, 211–219. [Google Scholar] [CrossRef] - Demir, H.; Mobedi, M.; Ülkü, S. A review on adsorption heat pump: Problems and solutions. Renew. Sustain. Energy Rev.
**2008**, 12, 2381–2403. [Google Scholar] [CrossRef] [Green Version] - Krzywanski, J.; Grabowska, K.; Sosnowski, M.; Zylka, A.; Sztekler, K.; Kalawa, W.; Wójcik, T.; Nowak, W. Modeling of a re-heat two-stage adsorption chiller by AI approach. MATEC Web Conf.
**2018**, 240, 05014. [Google Scholar] [CrossRef] - Krzywanski, J.; Grabowska, K.; Herman, F.; Pyrka, P.; Sosnowski, M.; Prauzner, T.; Nowak, W. Optimization of a three-bed adsorption chiller by genetic algorithms and neural networks. Energy Convers. Manag.
**2017**, 153, 313–322. [Google Scholar] [CrossRef] - Krzywanski, J.; Grabowska, K.; Sosnowski, M.; Zylka, A.; Sztekler, K.; Kalawa, W.; Wojcik, T.; Nowak, W. An adaptive neuro-fuzzy model of a re-heat two-stage adsorption chiller. Therm. Sci.
**2019**, 23, 1053–1063. [Google Scholar] [CrossRef] [Green Version] - Papakokkinos, G.; Castro, J.; López, J.; Oliva, A. A generalized computational model for the simulation of adsorption packed bed reactors—Parametric study of five reactor geometries for cooling applications. Appl. Energy
**2019**, 235, 409–427. [Google Scholar] [CrossRef] - Sosnowski, M. Computational domain discretization in numerical analysis of forced convective heat transfer within packed beds of granular materials. Eng. Mech.
**2018**, 2018, 801–804. [Google Scholar] - Sosnowski, M.; Krzywanski, J.; Grabowska, K.; Gnatowska, R. Polyhedral meshing in numerical analysis of conjugate heat transfer. EPJ Web Conf.
**2018**, 180, 02096. [Google Scholar] [CrossRef] - Sosnowski, M. Computational domain discretization in numerical analysis of flow within granular materials. EPJ Web Conf.
**2018**, 180, 02095. [Google Scholar] [CrossRef] - Sosnowski, M.; Gnatowska, R.; Sobczyk, J.; Wodziak, W. Numerical modelling of flow field within a packed bed of granular material. J. Phys. Conf. Ser.
**2018**, 1101, 012036. [Google Scholar] [CrossRef] - Mitra, S.; Oh, S.T.; Saha, B.B.; Dutta, P.; Srinivasan, K. Simulation study of the adsorption dynamics of cylindrical silica gel particles. Heat Transf. Res.
**2015**, 46, 123–140. [Google Scholar] [CrossRef] - Khan, M.Z.I.; Alam, K.C.A.; Saha, B.B.; Akisawa, A.; Kashiwagi, T. Study on a re-heat two-stage adsorption chiller—The influence of thermal capacitance ratio, overall thermal conductance ratio and adsorbent mass on system performance. Appl. Therm. Eng.
**2007**, 27, 1677–1685. [Google Scholar] [CrossRef] - Wang, R.Z.; Xia, Z.Z.; Wang, L.W.; Lu, Z.S.; Li, S.L.; Li, T.X.; Wu, J.Y.; He, S. Heat transfer design in adsorption refrigeration systems for efficient use of low-grade thermal energy. Energy
**2011**, 36, 5425–5439. [Google Scholar] [CrossRef] - Antonellis, S.D.; Joppolo, C.M.; Molinaroli, L.; Pasini, A. Simulation and energy efficiency analysis of desiccant wheel systems for drying processes. Energy
**2012**, 37, 336–345. [Google Scholar] [CrossRef] - ANSYS. Fluent Mosaic Technology Automatically Combines Disparate Meshes with Polyhedral Elements for Fast, Accurate Flow Resolution; ANSYS: Canonsburg, PA, USA, 2018. [Google Scholar]
- Sosnowski, M.; Gnatowska, R.; Sobczyk, J.; Wodziak, W. Computational domain discretization for CFD analysis of flow in a granular packed bed. J. Theor. Appl. Mech.
**2019**, 57, 833–842. [Google Scholar] [CrossRef] - Sosnowski, M.; Gnatowska, R.; Grabowska, K.; Krzywański, J.; Jamrozik, A. Numerical Analysis of Flow in Building Arrangement: Computational Domain Discretization. Appl. Sci.
**2019**, 9, 941. [Google Scholar] [CrossRef] [Green Version] - Eça, L.; Hoekstra, M. A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. J. Comput. Phys.
**2014**, 262, 104–130. [Google Scholar] [CrossRef] - Sosnowski, M.; Krzywanski, J.; Scurek, R. A Fuzzy Logic Approach for the Reduction of Mesh-Induced Error in CFD Analysis: A Case Study of an Impinging Jet. Entropy
**2019**, 21, 1047. [Google Scholar] [CrossRef] [Green Version] - Celik, I.B.; Ghia, U.; Roache, P.J. Others Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J. Fluids Eng. Trans. ASME
**2008**, 130, 078001. [Google Scholar] - Kakac, S.; Liu, H.; Pramuanjaroenkij, A. Heat Exchangers: Selection, Rating, and Thermal Design; CRC Press: Boca Raton, FL, USA, 2012. [Google Scholar]

**Figure 1.**Basic, single-bed, single-stage adsorption cooling system: (

**a**) chiller design; (

**b**) Clapeyron diagram.

**Figure 2.**Sectional view of the investigated multi-disc sorption bed. (

**a**) disc-shaped sorbent packets; (

**b**) fixing net; (

**c**) heat exchanger main body.

**Figure 3.**Variants of investigated inlet/outlet manifolds. (

**a**–

**c**) represent three variants of the inlet/outlet manifold geometry.

**Figure 8.**The computational domain consisting of four subdomains. (

**a**) Multi-disc sorption bed; (

**b**) water; (

**c**) water vapor; (

**d**) sorbent.

**Figure 10.**The temperatures in the multi-disc sorption bed operating as a water–water heat exchanger obtained within the experimental research and computational fluid dynamics (CFD) analysis.

**Figure 11.**The relative difference between the temperatures in the multi-disc sorption bed operating as a water–water heat exchanger obtained in the experimental research and CFD analysis.

**Figure 12.**The temperature along the centerline of the sorption bed extending from the inlet (relative length = 0) to the outlet (relative length = 1).

h/a (-) | N (-) | LMTD (K) | H (-) | R (-) | ε (-) | ε_{i+1}/ε_{I} (-) | P (-) | e_{a} (%) | GCI (%) |
---|---|---|---|---|---|---|---|---|---|

4.7·10^{−}^{2} | 888 694 | 25.84 | 2.3603 | 1.3680 | −0.31 | converged | 2.867 | 1.20% | 1.03% |

6.5·10^{−}^{2} | 347 133 | 25.53 | 3.2289 | 1.3067 | −0.10 | ||||

8.4·10^{−}^{2} | 155 590 | 25.43 | 4.2192 | - | - |

Material | Density (kg·m^{−3}) | Specific Heat (J·kg^{−1}·K^{−1}) | Thermal Cond. (W·m^{−1}·K^{−1}) | Viscosity (kg·m^{−1}·s^{−1}) |
---|---|---|---|---|

water (liquid) | 998.2 | 4182 | 0.6 | 1.003·10^{−}^{3} |

water (vapor) | 0.5542 | f(T) | 0.0261 | 1.34·10^{−}^{5} |

silica gel | 800 | 924 | 0.18 | - |

copper | 8978 | 381 | 387.6 | - |

**Table 3.**The obtained logarithmic mean temperature difference (LMTD), P, R, F, and corrected LMTD values.

Analyzed Case | LMTD (K) | P (-) | R (-) | F (-) | F×LMTD (K) |
---|---|---|---|---|---|

R_{MFR} = 1.00; EXP | 27.19 | 0.306 | 1.000 | 0.975 | 26.51 |

R_{MFR} = 1.00; CFD | 25.84 | 0.326 | 1.017 | 0.970 | 25.07 |

R_{MFR} = 1.33; EXP | 27.47 | 0.340 | 0.776 | 0.985 | 27.06 |

R_{MFR} = 1.33; CFD | 26.70 | 0.361 | 0.742 | 0.985 | 26.30 |

R_{MFR} = 1.66; EXP | 28.23 | 0.363 | 0.588 | 0.985 | 27.80 |

R_{MFR} = 1.66; CFD | 27.16 | 0.384 | 0.598 | 0.980 | 26.62 |

**Table 4.**The hot water temperature (ΔT

_{HW}) for all d/a ratios and the relative increase in heating power (HP

_{%}) as well as hot water pressure drop (Δp

_{HW%}) in relation to the d/a = 0.54.

d/a (-) | 0.54 | 0.62 | 0.70 | 0.78 | 0.86 |
---|---|---|---|---|---|

ΔT_{HW} (K) | 1.71 | 2.10 | 2.24 | 2.52 | 2.89 |

HP_{%} (%) | 0 | 23 | 31 | 47 | 69 |

Δp_{HW%} (%) | 0 | 2 | 5 | 12 | 43 |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sosnowski, M.
Evaluation of Heat Transfer Performance of a Multi-Disc Sorption Bed Dedicated for Adsorption Cooling Technology. *Energies* **2019**, *12*, 4660.
https://doi.org/10.3390/en12244660

**AMA Style**

Sosnowski M.
Evaluation of Heat Transfer Performance of a Multi-Disc Sorption Bed Dedicated for Adsorption Cooling Technology. *Energies*. 2019; 12(24):4660.
https://doi.org/10.3390/en12244660

**Chicago/Turabian Style**

Sosnowski, Marcin.
2019. "Evaluation of Heat Transfer Performance of a Multi-Disc Sorption Bed Dedicated for Adsorption Cooling Technology" *Energies* 12, no. 24: 4660.
https://doi.org/10.3390/en12244660