Mathematical Modeling of the Heat Generated through an Evaporator-Absorber Accompanied by Thermal Storage for the Solar Energy Applications

Abstract:

An evaporator-absorber geometry allows the absorption of incident solar radiation andconverts it into thermal energy useful for the evaporation of a working fluid. The evaporator-absorberworks with two fluids: a heat transfer fluid transmitting heat to a working fluid, which, circulatesalong the thermal circuit composed of an evaporator, a turbine, a condenser and a pump. The aim ofthis research work is to analyze the heat transfer through the evaporator-absorber and to extract themathematical equations model the heat exchange process between the component elements of theevaporator-absorber: a serpentine tube, a working fluid and a cylindrical tube. In this case, theworking fluid is water, and the heat transfer fluid is air, which is heated by the thermal energyconverted from solar energy. The mathematical equations describing the heat transfer are extractedby using the nodal method and discretized by the finite difference method. Afterwards, the presentwork estimates the outlet temperature of each element of the evaporator-absorber and studies thestorage capacity of the cylindrical tube. Then, the water temperature distribution on the geometry ofthe evaporator and the required quantity of water and the number of spires to have a high outlettemperature of the water vapor are determined. As a result, the mathematical modeling estimated thatthe outlet temperature of the serpentine tube is higher than the outlet temperature of the water.Additionally, the temperature of the storage tube maintains its increase throughout the day. Thequality of the heat transfer in the serpentine tube is improved by placing the tube in a vertical positionand by adopting a lower volume of water compared to the maximum volume, which is supported bythis tube.

• Periodical: International Journal of Engineering Research in Africa (Volume 64)
• Pages: 71-92
• DOI: https://doi.org/10.4028/p-3m6c59
• Online since: June 2023
• Authors: Firyal Latrache*, Zakia Hammouch, Karima Lamnaouar, Benaissa Bellach, Mohammed Ghammouri
• Keywords: Absorber-Evaporator, Heat Transfer, Mathematical Modeling, Nodal Method, Thermal Storage

References

[1] H.V. Asselt, Governing fossil fuel production in the age of climate disruption: Towards an international law of 'leaving it in the ground', Earth System Governance. 9 (2021) 100118.

DOI: 10.1016/j.esg.2021.100118

[2] J. Li, L. Yang, Back side of the coin: How does non-fossil energy diffusion result in less efficient fossil-based technologies, Environmental Impact Assessment Review. 96 (2022) 106848.

DOI: 10.1016/j.eiar.2022.106848

[3] O.B. Adekoya, J. K. Olabode, S. K. Rafi, Renewable energy consumption, carbon emissions and human development: Empirical comparison of the trajectories of world regions, Renewable Energy. 179 (2021) 1836-1848.

DOI: 10.1016/j.renene.2021.08.019

[4] G. Hu, Z. Xu, G. Wang, B. Zeng, Y. Liu, Y. Lei, Forecasting energy consumption of long-distance oil products pipeline based on improved fruit fly optimization algorithm and support vector regression, Energy. 224 (2021) 120153.

DOI: 10.1016/j.energy.2021.120153

[5] Y. Kasseh, A. Touzani, S. El Majaty, What public lighting governance model should be deployed in Moroccan cities for sustainable and efficient energy management?, Materials Today: Proceedings. 72 (2023) 3244-3252.

DOI: 10.1016/j.matpr.2022.07.123

[6] S.P. Tembhare, D. P. Barai, B. A. Bhanvase, Performance evaluation of nanofluids in solar thermal and solar photovoltaic systems: A comprehensive review, Renewable and Sustainable Energy Reviews. 153 (2022) 111738.

DOI: 10.1016/j.rser.2021.111738

[7] F. M. D. Nascimento, J. C. M. Siluk, P. D. Rigo, F. S. Savian, Approach to measure the potential for electricity consumer adoption of photovoltaic technology from the perspective of distribution system operators: A mobile application, Journal of Cleaner Production. 380 (2022) 134940.

DOI: 10.1016/j.jclepro.2022.134940

[8] R. K. Kumar, N. V. V. K. Chaitanya, S. K. Natarajan, Solar thermal energy technologies and its applications for process heating and power generation – A review, Journal of Cleaner Production. 282 (2021) 125296.

DOI: 10.1016/j.jclepro.2020.125296

[9] M. Jankowski, A new indicator for minimizing size of an ORC power plant based on heat exchanger and turbine design parameters, Applied Thermal Engineering. 201 (2022) 117750.

DOI: 10.1016/j.applthermaleng.2021.117750

[10] A. S. Alsagri, Design and dynamic simulation of a photovoltaic thermal-organic Rankine cycle considering heat transfer between components, Energy Conversion and Management. 225 (2020) 113435.

DOI: 10.1016/j.enconman.2020.113435

[11] M. N. Hossain, K. Ghosh, N. K. Manna, Integrated thermal modeling, analysis, and sequential design of heat exchanger surfaces of a natural circulation RDF boiler including evaporator tubes, Applied Thermal Engineering. 211 (2022) 118455.

DOI: 10.1016/j.applthermaleng.2022.118455

[12] G. E. Song, J. L. D. Y. Lee, A method to reduce the flow depth of a plate heat exchanger without a loss of heat transfer performance, International Journal of Heat and Mass Transfer. 55 (2012) 2992-2998.

DOI: 10.1016/j.ijheatmasstransfer.2012.02.027

[13] O. Douadi, R. Ravi, M. Faqir, E. Essadiqi, A conceptual framework for waste heat recovery from compression ignition engines: Technologies, working fluids & heat exchangers, Energy Conversion and Management: X. 16 (2022) 100309.

DOI: 10.1016/j.ecmx.2022.100309

[14] Chenjiyu Liang, Yuan Wang, Xianting Li, Energy-efficient air conditioning system using a three-fluid heat exchanger for simultaneous temperature and humidity control, Energy Conversion and Management, Volume 270, 15 October 2022, 116236.

DOI: 10.1016/j.enconman.2022.116236

[15] S. Yeasmin, Zahurul Islam, A.K. Azad, Eare M. Morshed Alam, M.M. Rahman, M.F. Karim, Thermal performance of a hollow cylinder with low conductive materials in a lid-driven square cavity with partially cooled vertical wall, Thermal Science and Engineering Progress, Volume 35, 1 October 2022, 101454.

DOI: 10.1016/j.tsep.2022.101454

[16] C. Wu, H. Yang, X. He, C. Hu, L. Yang, H. Li, Principle, development, application design and prospect of fluidized bed heat exchange technology: Comprehensive review, Renewable and Sustainable Energy Reviews. 157 (2022) 112023.

DOI: 10.1016/j.rser.2021.112023

[17] Y. Wu, H. Geng, G. Hao, D. Li, Experimental study on heat exchange efficiency of rock bed heat storage system based on broken rock mass, Energy Reports. 8 (2022) 12456-12465.

DOI: 10.1016/j.egyr.2022.08.274

[18] X. Chang, N. Watanabe, H. Nagai, H. Nagano, Visualization of thermos-fluid behavior of loop heat pipe with two evaporators and one condenser under various orientation with even heat loads, International Journal of Heat and Mass Transfer. 198 (2022) 123397.

DOI: 10.1016/j.ijheatmasstransfer.2022.123397

[19] A. Häberle, D. Krüger, Chapter 18 - Concentrating solar technologies for industrial process heat, Concentrating Solar Power Technology (Second Edition) Principles, Developments, and Applications, Woodhead Publishing Series in Energy, 2021, pp.659-675.

DOI: 10.1016/b978-0-12-819970-1.00011-6

[20] A. A. Lokhande, D. R. Waghole, S. A. Dayane, Heat transfer augmentation in shell and tube heat exchangers using copper oxide nanofluid with modified geometry: A numerical investigation, Materials Today: Proceedings. 72 (2023) 1240-1245.

DOI: 10.1016/j.matpr.2022.09.290

[21] M. Sheng, Y. Yang, X. Bin, S. Zhao, C. Pan, F. Nawaz, W. Que, Recent advanced self-propelling salt-blocking technologies for passive solar-driven interfacial evaporation desalination systems, Nano Energy. 89 (2021) 106468.

DOI: 10.1016/j.nanoen.2021.106468

[22] B. Schönfeld, U. Westedt, K. G. Wagner, Vacuum drum drying – A novel solvent-evaporation based technology to manufacture amorphous solid dispersions in comparison to spray drying and hot melt extrusion, International Journal of Pharmaceutics. 596 (2021) 120233.

DOI: 10.1016/j.ijpharm.2021.120233

[23] H. Zhong, L. Zeng, J. Long, K. Xia, H. Lu, A. Yongga, Anti-frosting operation and regulation technology of air-water dual-source heat pump evaporator, Energy. 254 (2022) 124393.

DOI: 10.1016/j.energy.2022.124393

[24] P. R. Gupta, A. K. Tiwari, Z. Said, Solar organic Rankine cycle and its poly-generation applications – A review, Sustainable Energy Technologies and Assessments. 49 (2022) 101732.

DOI: 10.1016/j.seta.2021.101732

[25] Ashwni, A. F. Sherwani, Advanced exergy analysis of renewable heat source driven ORC-VCR system, Materials Today: Proceedings. 56 (2022) 3687-3691.

DOI: 10.1016/j.matpr.2021.12.440

[26] J. Yang, Computational fluid dynamics studies on the induction period of crude oil fouling in a heat exchanger tube, International Journal of Heat and Mass Transfer. 159 (2020) 120129.

DOI: 10.1016/j.ijheatmasstransfer.2020.120129

[27] P. Promvonge, S. Skullong, Enhanced thermal performance in tubular heat exchanger contained with V-shaped baffles, Applied Thermal Engineering. 185 (2021) 116307.

DOI: 10.1016/j.applthermaleng.2020.116307

[28] O. Arsenyeva, O. Matsegora, P. Kapustenko, A. Yuzbashyan, J. J. Klemeš, The water fouling development in plate heat exchangers with plates of different corrugations geometry, Thermal Science and Engineering Progress. 32 (2022) 101310.

DOI: 10.1016/j.tsep.2022.101310

[29] C. Cunault, Y. Coquinot, C. H. Burton, S. Picard, A. M. Pourcher, Characteristics and composition of fouling caused by pig slurry in a tubular heat exchanger – Recommended cleaning systems, Journal of Environmental Management. 117 (2013) 17-31.

DOI: 10.1016/j.jenvman.2012.12.017

[30] W. Li, P. Hrnjak, Effect of single-phase flow maldistribution on the thermal performance of brazed plate heat exchangers, Applied Thermal Engineering. 219 (2023) 119465.

DOI: 10.1016/j.applthermaleng.2022.119465

[31] Z. Yi, Y. Xu, X. Chen, Numerical study on heat transfer characteristics of supercritical CO2 in a vertical heating serpentine micro-tube, Applied Thermal Engineering. 212 (2022) 118609.

DOI: 10.1016/j.applthermaleng.2022.118609

[32] P. N. Shrirao, M. K. Chaudhary, A. N. Patil, Performance evaluation of heat transfer characteristics of heat exchanger in longitudinal fluid flow with serpentine tubes of constant pitch, Materials Today: Proceedings. 72 (2023) 864-869.

DOI: 10.1016/j.matpr.2022.09.082

[33] V. T. Rao, Y. R. Sekhar, A. K. Pandey, Z. Said, D. M. R. Prasad, M. S. Hossain, J. Selvaraj, Thermal analysis of hybrid photovoltaic-thermal water collector modified with latent heat thermal energy storage and two side serpentine absorber design, Journal of Energy Storage. 56 (2022) 105968.

DOI: 10.1016/j.est.2022.105968

[34] M. A. Ebadian, G. Yang, E. Bigzadeh, J. F. Walker, T. J. Abraham, Mathematical modeling of liquid waste evaporation from the Melton Valley storage tanks using heat and mass transfer in a bubble chain, Nuclear Engineering and Design. 128 (1991) 305-315.

DOI: 10.1016/0029-5493(91)90168-h

[35] W. Zalewski, Mathematical model of heat and mass transfer processes in evaporative condensers, International Journal of Refrigeration. 16 (1993) 23-30.

DOI: 10.1016/0140-7007(93)90017-3

[36] C. L. Han, J. J. Ren, W. P. Dong, M. S.  Bi, Numerical investigation of supercritical LNG convective heat transfer in a horizontal serpentine tube, Cryogenics. 78 (2016) 1-13.

DOI: 10.1016/j.cryogenics.2016.05.005

[37] A. Mahamoudou, N.  Le Pierrès, J.  Ramousse, Review of coupled heat and mass transfer studies in falling film absorbers: Modeling, experimental and thermodynamic approaches, International Journal of Refrigeration. 136 (2022) 229-244.

DOI: 10.1016/j.ijrefrig.2022.01.024

[38] H. S. Mora, S. Q. García, M. A. P. Labarrios, R. I. C. Ramírez, Alejandro Torres-Aldaco, Dynamic mathematical heat transfer model for two-phase flow in solar collectors, Case Studies in Thermal Engineering. 40 (2022) 102594.

DOI: 10.1016/j.csite.2022.102594

[39] V. T. Rao, Y. R. Sekhar, A. K. Pandey, Z. Said, D. M. R. Prasad, M. S. Hossain, J. Selvaraj, Thermal analysis of hybrid photovoltaic-thermal water collector modified with latent heat thermal energy storage and two side serpentine absorber design, Journal of Energy Storage. 56 (2022) 105968.

DOI: 10.1016/j.est.2022.105968

[40] T. Montrol, J. Jay, S. Xin, R. Knikker, M. L. Decrescenzo, Construction d'un modèle thermique nodal pour la phase de prédimensionnement d'un équipement roue et frein aéronautique: méthodologie et simplifications. 2ème Congrès de l'Association Marocaine de Thermique- Efficacité énergétique dans l'industrie, Casablanca, Maroc. hal-00966866 (2012).

DOI: 10.1016/s0035-3159(99)80056-7

[41] I. Jarrah, R. Uddin, Nodal integral method for 3D time-dependent anisotropic convection-diffusion equation, Annals of Nuclear Energy. 163 (2021) 108550.

DOI: 10.1016/j.anucene.2021.108550

[42] M. Raj, N. Ahmed, S. Singh, Analytical nodal method for solution of neutron diffusion equation in polar coordinates, Annals of Nuclear Energy. 165 (2022) 108659.

DOI: 10.1016/j.anucene.2021.108659

[43] H. Guillard, B. Nkonga, Chapter 8 - On the Behaviour of Upwind Schemes in the Low Mach Number Limit: A Review, Handbook of Numerical Analysis. 18 (2017), pp.203-231.

DOI: 10.1016/bs.hna.2016.09.002

[44] X. Wang, K. Liu, Y.  Su, X. Wang, H.  Cao, A.  Hua, Q. Ouyang, D.  Zhang, Synergistic enhancing effect of tungsten-copper coated graphite flakes and aluminum nitride nanoparticles on microstructure, mechanical and thermal properties of copper matrix composites, Materials Science and Engineering: A. 857 (2022) 143987.

DOI: 10.1016/j.msea.2022.143987

[45] Y. Wang, Z. Zhang, Z. Tian, Y. Lu, T. Ren, X. Peng, Determination of soil bulk density dynamic in a Vertisol during wetting and drying cycles using combined soil water content and thermal property sensors, Geoderma.428 (2022) 116149.

DOI: 10.1016/j.geoderma.2022.116149

[46] A. A. Merrouni, A. Mezrhab, A. Mezrhab, PV sites suitability analysis in the Eastern region of Morocco, Sustainable Energy Technologies and Assessments.18 (2016) 6-15.

DOI: 10.1016/j.seta.2016.09.006

[47] H. Fathabadi, Novel solar collector: Evaluating the impact of nanoparticles added to the collector's working fluid, heat transfer fluid temperature and flow rate, Renewable Energy. 148 (2020) 1165-1173.

DOI: 10.1016/j.renene.2019.10.008

[48] C. A. Gueymard, 1.10 - Solar Radiation Resource: Measurement, Modeling, and Methods, Comprehensive Renewable Energy (Second Edition). 1 (2022), pp.176-212.

DOI: 10.1016/b978-0-12-819727-1.00101-1

[49] J. Zou, J. Liu, J. Niu, Y. Yu, C. Lei, Convective heat loss from computational thermal manikin subject to outdoor wind environments, Building and Environment. 188 (2021) 107469.

DOI: 10.1016/j.buildenv.2020.107469

[50] Z. Yi, Y. Xu, X. Chen, Numerical study on heat transfer characteristics of supercritical CO2 in a vertical heating serpentine micro-tube, Applied Thermal Engineering. 212 (2022) 118609.

DOI: 10.1016/j.applthermaleng.2022.118609

[51] M. G. Nugraha, R. Andersson, B. Andersson, On the Sherwood number correction due to Stefan flow, Chemical Engineering Science. 249 (2022) 117292.

DOI: 10.1016/j.ces.2021.117292

[52] C. A. Catlin, Equilibrium mass transfer coefficients for a dilute species diffusing between laminar counter flowing streams derived from the corresponding eigenvalue problem for the advection–diffusion equation, Chemical Engineering Science: X. 14 (2022) 100121.

[53] D. Chen, Y. Li, Z. Abbas, D. Li, R. Wang, Network flow calculation based on the directional nodal potential method for meshed heating networks, Energy. 243 (2022) 122729.

DOI: 10.1016/j.energy.2021.122729

[54] D. Chen, X. Hu, Y. Li, Z. Abbas, R. Wang, D. Li, Nodal conservation principle of potential energy flow analysis for energy flow calculation in energy internet, Energy. 263 (2023) 125562.

DOI: 10.1016/j.energy.2022.125562

[55] K. Kumari, D. A. Donzis, A generalized von Neumann analysis for multi-level schemes: Stability and spectral accuracy, Journal of Computational Physics. 424 (2021) 109868.

DOI: 10.1016/j.jcp.2020.109868

[56] S. A. Pasha, Y. Nawaz, M. S. Arif, On the nonstandard finite difference method for reaction–diffusion models, Chaos, Solitons & Fractals. 166 (2023) 112929.

DOI: 10.1016/j.chaos.2022.112929

[57] C. Xu, Computation and theory of Euler sums of generalized hyperharmonic numbers, Comptes Rendus Mathematique. 356 (2018) 243-252.

DOI: 10.1016/j.crma.2018.01.004

[58] L. Hu, L. Yuan, A simple FORCE-type centered scheme accurate for contact discontinuities: Application to compressible Euler flows, Computers & Fluids. 227 (2021) 105021.

DOI: 10.1016/j.compfluid.2021.105021

[59] Q. Tang, Y. Huang, Stability and convergence analysis of a Crank–Nicolson leap-frog scheme for the unsteady incompressible Navier–Stokes equations, Applied Numerical Mathematics. 124 (2018) 110-129.

DOI: 10.1016/j.apnum.2017.09.012

[60] F. Delarue, F. Lagoutière, N. Vauchelet, Convergence order of upwind type schemes for transport equations with discontinuous coefficients, Journal de Mathématiques Pures et Appliquées. 108 (2017) 918-951.

DOI: 10.1016/j.matpur.2017.05.012

[61] C. A. Gueymard, 1.10 - Solar Radiation Resource: Measurement, Modeling, and Methods, Comprehensive Renewable Energy (Second Edition). 1 (2022), pp.176-212.

DOI: 10.1016/b978-0-12-819727-1.00101-1

[62] A. Djaafari, A. Ibrahim, N. Bailek, K. Bouchouicha, M. A. Hassan, A. Kuriqi, N. Al-Ansari, E. S. M. El-kenawy, Hourly predictions of direct normal irradiation using an innovative hybrid LSTM model for concentrating solar power projects in hyper-arid regions, Energy Reports. 8 (2022) 15548-15562.

DOI: 10.1016/j.egyr.2022.10.402