Journal of Applied and Computational Mechanics
Mixed Convection Heat Transfer and Entropy Generation in a Water-filled Square Cavity Partially Heated from Below: The Effects of Richardson and Prandtl Numbers
Document Type : Research Paper
Authors
1 Faculty of Process Engineering, University of Salah Boubnider Constantine 3, 25016, Algeria
2 Laboratory of Biotechnology, National Higher School of Biotechnology (ENSB), Constantine 3, Algeria
3 Mechanical Engineering Department, Computational Fluid Dynamics Laboratory, Istanbul Medeniyet University, Turkey
4 Faculty of Sciences and Applied Sciences, University of Larbi BenM'hidi, Oum el Bouaghi, 04000 , Algeria
Abstract
In the present study, fluid flow, heat transfer, and entropy generation for mixed convection inside a water-filled square cavity were investigated numerically. The sidewalls of the cavity, which move upwards, are kept at low-temperature Tc while only a part in the center of the bottom wall is kept at high-temperature Th and the remaining parts are kept adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Particular attention was paid to the influence of the Prandtl numbers of 5.534, 3.045 and 2, corresponding respectively to the water temperatures of 303.15 K, 333.15 K and 363.15 K. The numerical results are presented in the form of streamlines, isotherms, and entropy generation contours for different values of the Richardson numbers at an arbitrary Reynolds number Re=102. Besides this, the evolution of the average Nusselt number and the average entropy generation is also reported. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve stable symmetric and non-symmetric steady-state solutions, as well as unsteady regimes, depending on specific values of the Richardson and Prandtl numbers. It is additionally observed that the average Nusselt number increases and the average entropy generation decreases when both the Richardson and Prandtl numbers increase.
Keywords
- Mixed convection
- Entropy generation
- Finite difference method
- Prandtl number
- Richardson number
- Nusselt Number
Main Subjects
Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
[1] Ait Hssain, M., Mir, R., and El Hammami, Y., Numerical Simulation of the Cooling of Heated Electronic Blocks in Horizontal Channel by Mixed Convection of Nanofluids, Journal of Nanomaterials, 2020, Article ID 4187074, 11 p.
[2] Vasiliev, A. Yu., Sukhanovskii, A. N., Stepanov, R. A., Convective turbulence in a cubic cavity under nonuniform heating of a lower boundary, Journal of Applied Mechanics and Technical Physics, 61, 2020, 1049-1058.
[3] Dhahad, H.A., Al-Sumaily, G.F., Habeeb, L.J., Thompson, M.C., The Cooling Performance of Mixed Convection in a Ventilated Enclosure With Different Ports Configurations, Journal of Heat Transfer, 142(12), 2020, 122601.
[4] Vasiliev, A., Sukhanovskii, A., Turbulent convection in a cube with mixed thermal boundary conditions: low Rayleigh number regime, International Journal of Heat and Mass Transfer, 174, 2021, 121290.
[5] Hu, Z.X., Cui, G.X., Zhang, Z.S., Numerical study of mixed convective heat transfer coefficients for building cluster, Journal of Wind Engineering and Industrial Aerodynamics, 172, 2018, 170-180.
[6] Sheikholeslami, M., Farshad, S.A., Shafee, A., Babazadeh, H., Performance of solar collector with turbulator involving nanomaterial turbulent regime, Renewable Energy, 163, 2021, 1222-1237.
[7] Kumar, A., Ray, R.K., Sheremet, M.A., Entropy generation on double-diffusive MHD slip flow of nanofluid over a rotating disk with nonlinear mixed convection and Arrhenius activation energy, Indian Journal of Physics, 2021, doi: 10.1007/s12648-021-02015-2.
[8] Youcef , A., Saim, R., Numerical Analysis of the Baffles Inclination on Fluid Behavior in a Shell and Tube Heat Exchanger, Journal of Applied and Computational Mechanics, 7, 2021, 312-320.
[9] Ghalambaz, M., Jun Zhang, J., Conjugate solid-liquid phase change heat transfer in heatsink filled with phase change material-metal foam, International Journal of Heat and Mass Transfer, 146, 2020, 118832.
[10] Ghalambaz, M., Mehryan, S.A.M., Hajjar, A, Veismoradi, A., Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium, Advanced Powder Technology, 31(3), 2020, 954-966.
[11] Hajjar, A., Mehryan, S.A.M., Ghalambaz, M., Time periodic natural convection heat transfer in a Nano-encapsulated phase-change suspension, International Journal of Mechanical Sciences, 166, 2020, 105243.
[12] Ghalambaz, M., Zadeh, S. M. H., Mehryan, S.A.M., Pop, I., Wen, D.S., Analysis of melting behavior of PCMs in a cavity subject to a non-uniform magnetic field using a moving grid technique, Applied Mathematical Modelling, 77(2), 2020, 1936-1953.
[13] Bejan, A., A study of entropy generation in fundamental convective heat transfer, Journal of Heat Transfer, 101(4), 1979, 718-725.
[14] Bejan, A., The thermodynamic design of heat and mass transfer processes and devices, Journal of Heat and Fluid Flow, 8, 1987, 258-275,
[15] Izadi, S., Armaghani, T., Ghasemiasl, R., Chamkha, A.J., Molana, M., A comprehensive review on mixed convection of nanofluids in various shapes of enclosures, Powder Technology, 343, 2019, 880–907.
[16] Mustafa Abdul Salam, M., Hasanen Mohammed, H., Auday Awad, A., Laith Jaafer, H., Review on Mixed Convective Heat Transfer in Different Geometries of Cavity with Lid Driven, Journal of Mechanical Engineering Research and Developments, 43(7), 2020, 12-25.
[17] Yang, L., Kai Du, K., A comprehensive review on the natural, forced, and mixed convection of non‑Newtonian fluids (nanofluids) inside different cavities, Journal of Thermal Analysis and Calorimetry, 140, 2020, 2033–2054.
[18] Oztop, H.F., Al-Salem, K., A review on entropy generation in natural and mixed convection heat transfer for energy systems, Renewable and Sustainable Energy Reviews, 16(1), 2012, 911–920.
[19] Sciacovelli, A., Verda, V., Sciubba, E, Entropy generation analysis as a design tool-a review, Renewable & Sustainable Energy Reviews, 43, 2015, 1167–1181.
[20] Biswal, P., Basak T., Entropy generation vs energy efficiency for natural convection based energy flow in enclosures and various applications: A review, Renewable & Sustainable Energy Reviews, 80, 2017, 1412-1457.
[21] Sheikholeslami, M., Arabkoohsar, A., Ismail, K.A.R., Entropy analysis for a nanofluid within a porous media with magnetic force impact using non-Darcy model, International Communications in Heat and Mass Transfer, 112, 2020, 104488.
[22] Sheikholeslami, M., Farshad, S.A., Shafee, A., Babazadeh H., Numerical modeling for nanomaterial behavior in a solar unit analyzing entropy generation, Journal of the Taiwan Institute of Chemical Engineers, 112, 2020, 271-285.
[23] Selimefendigil, F., Öztop, H.F., Sheikholeslami, M., Impact of local elasticity and inner rotating circular cylinder on the magneto-hydrodynamics forced convection and entropy generation of nanofluid in a U-shaped vented cavity, Mathematical Methods in the Applied Sciences, 2020, doi: 10.1002/mma.6930.
[24] Rabbi, K.Md, Sheikholeslami, M., Karim, A., Shafee, A., Li, Z., Tlili, I., Prediction of MHD flow and entropy generation by Artificial Neural Network in square cavity with heater-sink for nanomaterial, Physica A: Statistical Mechanics and its Applications, 541(1), 2020, 123520.
[25] Mondal, P., Mahapatra, T.R., Parveen, R., Entropy generation in nanofluid flow due to double diffusive MHD mixed convection, Heliyon, 7, 2021, e06143.
[26] Ebrahimi, D., Yousefzadeh, S., Akbari, O.A., Montazerifar, F., Rozati, S.A., Nakhjavani, S., Safaei, M.R., Mixed convection heat transfer of a nanofluid in a closed elbow‑shaped cavity (CESC), Journal of Thermal Analysis and Calorimetry, 2021, doi: 10.1007/s10973-021-10548-1.
[27] Khosravi, R., Rabiei, S., Khaki, M., Safaei, M.R., Goodarzi, M., Entropy generation of graphene-platinum hybrid nanofluid flow through a wavy cylindrical microchannel solar receiver by using neural networks, Journal of Thermal Analysis and Calorimetry, 2021, doi: 10.1007/s10973-021-10828-w.
[28] Cimpean, D.S. and Pop, I. (2021), Entropy generation of a nanofluid in a porous cavity with sinusoidal temperature at the walls and a heat source bellow, International Journal of Numerical Methods for Heat & Fluid Flow, 2021, doi: 10.1108/HFF-10-2020-0654.
[29] Maougal, A., Bessaih, R., Heat Transfer and Entropy Analysis for Mixed Convection in a Discretely Heated Porous Square Cavity, Fluid Dynamics & Materials Processing, 9(1), 2013, 35-59.
[30] Roy, M., Roy, S., Basak, T., Analysis of entropy generation on mixed convection in square enclosures for various horizontal or vertical moving wall(s), International Communications in Heat and Mass Transfer, 68, 2015, 258-266.
[31] Roy, M., Basak, T., Roy, S., Pop, I., Analysis of Entropy Generation for Mixed Convection in a Square Cavity for Various Thermal Boundary Conditions, Numerical Heat Transfer, Part A: Applications, 68(1), 2015, 44-74
[32] Roy, M., Basak, T., Roy, S., Analysis of Entropy Generation During Mixed Convection in Porous Square Cavities: Effect of Thermal Boundary Conditions, Numerical Heat Transfer, Part A, 68, 2015, 925–957.
[33] Roy, M., Biswal, P., Roy, S., Basak, T., Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities, Numerical Heat Transfer, Part A: Applications, 71(4), 2017, 423-447.
[34] Bhatti, M.M., Ali Abbas, M., Rashidi, M., Entropy Generation in Blood Flow With Heat and Mass Transfer for the Ellis Fluid Model, Heat Transfer Research, 49(8), 2018, 747-760.
[35] Bhatti, M.M., Sheikholeslami, M., Shahid, A., Hassan, M., Abbas, T., Entropy generation on the interaction of nanoparticles over a stretched surface with thermal radiation, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 570(5), 2019, 368-376.
[36] Khan,I., Khan, W.A., Qasim, M., Idrees Afridi, A., Sayer O. Alharbi, S.O., Thermodynamic Analysis of Entropy Generation Minimization in Thermally Dissipating Flow Over a Thin Needle Moving in a Parallel Free Stream of Two Newtonian Fluids, Entropy, 21(1), 2019, 74.
[37] Öğüt, E.B., Second Law Analysis of Mixed Convection of Magneto hydrodynamic Flow in an Inclined Square Lid-Driven Enclosure, Journal of Thermal Engineering, 5(6), 2019, 240-251.
[38] Mehta, S.K., Pati, S., Numerical study of thermo‑hydraulic characteristics for forced convective flow through wavy channel at different Prandtl numbers, Journal of Thermal Analysis and Calorimetry, 141, 2020, 2429–2451.
[39] Kashyap, D., Dass, A.K., Oztop, H.F., Abu-Hamdeh, N., Multiple-relaxation-time lattice Boltzmann analysis of entropy generation in a hot-block-inserted square cavity for different Prandtl numbers, International Journal of Thermal Sciences, 165, 2021, 106948.
[40] Sahaya Jenifer, A., Saikrishnan, P., Lewis, R.W., Unsteady MHD Mixed Convection Flow of Water over a Sphere with Mass Transfer, J. Appl. Comput. Mech., 7(2), 2021, 935-943.
[41] Abanoub, G. K., Eman H. H., Sarwat N. H., Numerical simulation of three-sided lid-driven square cavity, Engineering Reports, 2, 2020, e12151.
[42] Bejan, A., Entropy Generation Through Heat and Fluid Flow, First Edition, Willey & Sons, 1982.
[43] Micula, S., Pop, I, Numerical results for the classical free convection flow problem in a square porous cavity using spline functions. Int. J. Numer. Methods Heat Fluid Flow, 31(3), 2021, 753–765.
[44] Kawamura, T., Takami, H., Kuwahara, K., New higher order upwind scheme for incompressible Navier-Stokes equations. Ninth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, 1985, 218, 291-295.
[45] Bejan, A., Heat Transfer, Wiley, New York, 1993
[46] Dinçer, I., Zamfirescu, C., Dring Phenomena: Theory and Applications, First Edition, John Wiley & Sons, 2016.
[47] Ferziger, J.H., and M. Peric, M., Computational Methods for Fluid Dynamics, Springer, 2002.
[48] Pallares, J., Arroyo, M.P., Grau, F.X., and, Giralt F., Experimental laminar Rayleigh-Benard convection in a cubical cavity at moderate Rayleigh and Prandtl numbers, Experiments in Fluids, 31(2), 1998, 208–218.
[49] Goodarzi, M., Safaei, M. R, Oztop, H. F., Karimipour, A., Sadeghinezhad, E, Dahari, M., Kazi, S. N. and Jomhari1, N., Numerical Study of Entropy Generation due to Coupled Laminar and Turbulent Mixed Convection and Thermal Radiation in an Enclosure Filled with a Semitransparent Medium, The Scientific World Journal, Article ID 761745, 2014, 8 p.
[50] Patil, P.M, Latha, D.N., Chamkha, A.J., Non-similar Solutions of MHD Mixed Convection over an Exponentially Stretching Surface: Influence of Non-uniform Heat Source or Sink, J. Appl. Comput. Mech., 7(3), 2021, 1334-1347.
[51] Asad, M.F.A. , Nur Alam, M., Tunç, C., Sarker., M.M.A., Heat Transport Exploration of Free Convection Flow inside Enclosure Having Vertical Wavy Walls, J. Appl. Comput. Mech., 7(2), 2021, 520-527.
[52] Jani, S., Mahmoodi, M., Amini, M., Magnetohydrodynamic Free Convection in a Square Cavity Heated from Below and Cooled from Other Walls, International Journal of Mechanical and Mechatronics Engineering, 7(4), 2013,750-755.
[53] Aydin, O., Yang, W. J., Mixed convection in cavities with a locally heated lower wall and moving sidewalls, Numerical Heat Transfer Part A, 37, 2000, 695-710.
[54] Cheng, T.S., Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers, International Journal of Thermal Sciences, 50(2), 2011, 197-205.
[55] Biswas, N., Manna, N.K., Transport phenomena in a sidewall-moving bottom-heated cavity using heatlines, Sādhanā, 42(2), 2017, 193–211.
[56] Evgrafova, A., Sukhanovskii, A., Specifics of heat flux from localized heater in a cylindrical layer, International Journal of Heat and Mass Transfer, 135, 2019, 761-768.
[57] ] Evgrafova, A., Sukhanovskii, A., Dependence of boundary layer thickness on layer height for extended localised heaters, Experimental Thermal and Fluid Science, 121, 2021, 110275.
[58] Nadeem, S., Khan, A.U., Saleem S., A comparative analysis on different nanofluid models for the oscillatory stagnation point flow, Eur. Phys. J. Plus, 131, 2016, 261.
[59] Khetib, Y., Alahmadi, A.A., Alzaed, A., Azimy, H., Sharifpur, M., Cheraghian, G., Effect of Straight, Inclined and Curved Fins on Natural Convection and Entropy Generation of a Nanofluid in a Square Cavity Influenced by a Magnetic Field, Processes, 9(8), 2021, 1339.
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