Effect of Inner Body Shapes on Natural Convection in Square Enclosures

This review focuses on the effects of inner body shapes on magnetohydrodynamic (MHD) natural convection heat transfer within square enclosures, summarizing advancements from 2015 to 2024 and identifying future research directions. The influence of different geometric shapes such as circular, square, triangular, and elliptical on heat transfer performance and flow behavior is critically examined. The review also addresses the roles of Rayleigh and Hartmann numbers in modulating convection characteristics in the presence of a magnetic field. Key trends and findings are highlighted, along with observed research gaps, to guide future studies aiming to enhance thermal management in MHD driven systems.

Keywords: Natural convection, Magnetic field, Square enclosures, Inner bodies, Hartmann number.

[1] Tasnim, S., A. Mitra, H. Saha, M.Q. Islam, and S. Saha, MHD conjugate natural convection and entropy generation of a nanofluid filled square enclosure with multiple heat-generating elements in the presence of Joule heating. Results in Engineering, 17 (2023) :100993.

[2] Wang, X.-Q. and A.S. Mujumdar, A review on nanofluids-part I: theoretical and numerical investigations. Brazilian journal of chemical engineering, 25 (2008) 613-630.

[3] Kasaeian, A., R. Daneshazarian, O. Mahian, L. Kolsi, A.J. Chamkha, S. Wongwises, and I. Pop, Nanofluid flow and heat transfer in porous media: a review of the latest developments. International Journal of Heat and Mass Transfer, 107 (2017) 778-791.

[4] Das, D., M. Roy, and T. Basak, Studies on natural convection within enclosures of various (non-square) shapes–A review. International Journal of Heat and Mass Transfer, 106 (2017) 356-406.

[5] Biswal, P. and T. Basak, Entropy generation vs energy efficiency for natural convection based energy flow in enclosures and various applications: a review. Renewable and Sustainable Energy Reviews, 80 (2017) 1412-1457.

[6] Sadeghi, M.S., N. Anadalibkhah, R. Ghasemiasl, T. Armaghani, A.S. Dogonchi, A.J. Chamkha, H. Ali, and A. Asadi, On the natural convection of nanofluids in diverse shapes of enclosures: an exhaustive review. Journal of Thermal Analysis and Calorimetry, (2020) 1-22.

[7] Giwa, S., M. Sharifpur, M. Ahmadi, and J. Meyer, A review of magnetic field influence on natural convection heat transfer performance of nanofluids in square cavities. Journal of Thermal Analysis and Calorimetry, 145 (2021) 2581-2623.

[8] Hemmat Esfe, M., M. Afrand, and S. Esfandeh, Investigation of the effects of various parameters on the natural convection of nanofluids in various cavities exposed to magnetic fields: a comprehensive review. Journal of Thermal Analysis and Calorimetry, 140 (2020) 2055-2075.

[9] Chen, S., W. Gong, and Y. Yan, Conjugate natural convection heat transfer in an open-ended square cavity partially filled with porous media. International Journal of Heat and Mass Transfer, 2018. 124: p. 368-380.

[10] Belhaj, S. and B. Ben-Beya, Numerical simulation of unsteady MHD natural convection of CNT-water nanofluid in square cavity heated sinusoidally from below. Particulate Science and Technology, 37(7) (2019) 851-870.

[11] Joshi, P.S. and A. Pattamatta, Enhancement of natural convection heat transfer in a square cavity using MWCNT/Water nanofluid: an experimental study. Heat and Mass Transfer, 54 (2018) 2295-2303.

[12] Hidayathulla Khan, B.M., K. Venkatadri, O. Anwar Bég, V. Ramachandra Prasad, and B. Mallikarjuna, Natural convection in a square cavity with uniformly heated and/or insulated walls using Marker-and-Cell Method. International Journal of Applied and Computational Mathematics, 4 (2018) 1-18.

[13] Khatamifar, M., W. Lin, and L. Dong, Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity. Case Studies in Thermal Engineering, 25 (2021) 100952.

[14] Kumar, R., A. Bhattacharyya, and G. Seth, Heat transfer analysis on unsteady natural convection flow of silver nanofluid in a porous square cavity using local thermal non-equilibrium model. Indian Journal of Physics, (2021). 1-14.

[15] Mansour, M. and M. Bakier, Influence of thermal boundary conditions on MHD natural convection in square enclosure using Cu–water nanofluid. Energy Reports, 1 (2015) 134-144.

[16] Ben Hamida, M. and K. Charrada, Natural convection heat transfer in an enclosure filled with an ethylene glycol—copper nanofluid under magnetic fields. Numerical Heat Transfer, Part A: Applications, 67(8) (2015) 902-920.

[17] Sreedevi, P. and P.S. Reddy, Effect of magnetic field and thermal radiation on natural convection in a square cavity filled with TiO2 nanoparticles using Tiwari-Das nanofluid model. Alexandria Engineering Journal, 61(2) (2022) 1529-1541

[18] Haritha, C., B.C. Shekar, and N. Kishan, MHD natural convection heat transfer in a porous square cavity filled by nanofluids with viscous dissipation. J. Nanofluids, 7(5) (2018) 928-938.

[19] Mehryan, S., M. Izadi, A.J. Chamkha, and M.A. Sheremet, Natural convection and entropy generation of a ferrofluid in a square enclosure under the effect of a horizontal periodic magnetic field. Journal of Molecular Liquids, 263 (2018) 510-525.

[20] Mansour, M., S. Siddiqa, R.S.R. Gorla, and A. Rashad, Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity. Thermal Science and Engineering Progress, 6 (2018) 57-71.

[21] Al Kalbani, K.S., M.M. Rahman, S. Alam, N. Al-Salti, and I.A. Eltayeb, Buoyancy induced heat transfer flow inside a tilted square enclosure filled with nanofluids in the presence of oriented magnetic field. Heat Transfer Engineering, 39(6) (2018) 511-525.

[22] Mahapatra, T. and R. Parveen, Entropy generation in MHD natural convection within curved enclosure filled with Cu-water nanofluid. Journal of Nanofluids, 8(5) (2019)1051-1065.

[23] Uddin, M., S. Rasel, M. Rahman, and K. Vajravelu, Natural convective heat transfer in a nanofluid-filled square vessel having a wavy upper surface in the presence of a magnetic field. Thermal Science and Engineering Progress, 19 (2020) 100660.

[24] Rajarathinam, M. and A. Chamkha, Effect of partial open on natural convection heat transfer of CNT–water nanofluid in a square cavity with magnetic field. The European Physical Journal Plus, 136(1) (2021) 52.

[25] Devi, T.S., C.V. Lakshmi, K. Venkatadri, and M.S. Reddy, Influence of external magnetic wire on natural convection of non-Newtonian fluid in a square cavity. Partial Differential Equations in Applied Mathematics, 4 (2021) 100041.

[26] Nishad, S., S. Jain, and R. Bhargava, Numerical simulation of natural convection within wavy square enclosure filled with nanofluid under magnetic field using EFGM with parallel algorithm. International Journal of Numerical Methods for Heat & Fluid Flow, 31(12) (2021) 3505-3526.

[27] Munshi, M.J.H., A. Bhuiyan, and M. Alim, A numerical study of natural convection in a square enclosure with non-uniformly heated bottom wall and square shape heated block. Am. J. Eng. Res.(AJER),4(5) (2015) 124-137.

[28] Boulahia, Z., A. Wakif, and R. Sehaqui, Natural convection heat transfer of the nanofluids in a square enclosure with an inside cold obstacle. International journal of innovation and scientific research, 21(2) (2016) 367-375.

[29] Munshi, M.J.H., M. Alim, A. Bhuiyan, and G. Mostafa, Effect of a Magneto-hydrodynamic Natural Convection in a Square Cavity with Elliptic Shape Adiabatic Block. American Journal of Engineering Research, 4 (2015) 10-22.

[30] Adegun, I., S. Ibitoye, and A. Bala, Effect of selected geometric parameters on natural convection in concentric square annulus. Australian Journal of Mechanical Engineering, 20(4) (2022) 1142-1153.

[31] Cho, H.W., M.Y. Ha, and Y.G. Park, Natural convection in a square enclosure with two hot inner cylinders, Part II: The effect of two elliptical cylinders with various aspect ratios in a vertical array. International Journal of Heat and Mass Transfer, 135 (2019) 962-973.

[32] Zhang, P., X. Zhang, J. Deng, and L. Song, A numerical study of natural convection in an inclined square enclosure with an elliptic cylinder using variational multiscale element free Galerkin method. International Journal of Heat and Mass Transfer, 99 (2016) 721-737.

[33] Park, S.H., Y.M. Seo, M.Y. Ha, and Y.G. Park, Natural convection in a square enclosure with different positions and inclination angles of an elliptical cylinder Part I: A vertical array of one elliptical cylinder and one circular cylinder. International Journal of Heat and Mass Transfer, 126 (2018) 173-183.

[34] Ibrahim, M.N.J., K.A. Hammoodi, A.D. Abdulsahib, and M.A. Flayyih, Study of natural convection inside inclined nanofluid cavity with hot inner bodies (circular and ellipse cylinders). International Journal of Heat and Technology, 40(3) (2022) 699-705.

[35] Hossain, S.A., M. Alim, and S. Saha, A finite element analysis on MHD free convection flow in open square cavity containing heated circular cylinder. American Journal of Computational Mathematics, 5(01) (2015) 41-54.

[36] Shruti, B., M.M. Alam, A. Parkash, and S. Dhinakaran, Darcy number influence on natural convection around porous cylinders in an enclosure using Darcy-Brinkman-Forchheimer model: LBM study. Case Studies in Thermal Engineering, 45 (2023) 102907.

[37] Ahmed, S.E. and A.M. Aly, Natural convection in a nanofluid-filled cavity with solid particles in an inner cross shape using ISPH method. International Journal of Heat and Mass Transfer, 141 (2019) 390-406.

[38] Ali, M.M., R. Akhter, and M. Alim, Hydromagnetic natural convection in a wavy-walled enclosure equipped with hybrid nanofluid and heat generating cylinder. Alexandria Engineering Journal, 60(6) (2021) 5245-5264.

[39] Vijaybabu, T. and S. Dhinakaran, MHD Natural convection around a permeable triangular cylinder inside a square enclosure filled with Al2O3? H2O nanofluid: An LBM study. International Journal of Mechanical Sciences, 153 (2019) 500-516.

[40] Cho, H.W., Y.M. Seo, G.S. Mun, M.Y. Ha, and Y.G. Park, The effect of instability flow for two-dimensional natural convection in a square enclosure with different arrays of two inner cylinders. International Journal of Heat and Mass Transfer, 114 (2017) 307-317.

[41] Alsabery, A., A. Chamkha, H. Saleh, and I. Hashim, Natural convection flow of a nanofluid in an inclined square enclosure partially filled with a porous medium. Scientific reports, 7(1) (2017) 2357.

[42] Alsabery, A., A. Chamkha, H. Saleh, and I. Hashim, Heatline visualization of conjugate natural convection in a square cavity filled with nanofluid with sinusoidal temperature variations on both horizontal walls. International Journal of Heat and Mass Transfer, 100 (2016) 835-850.

[43] Rahmati, A. and A. Tahery, Numerical study of nanofluid natural convection in a square cavity with a hot obstacle using lattice Boltzmann method. Alexandria engineering journal, 57(3) (2018) 1271-1286.

[44] Alturaihi, M.H., L. Jassim, A.R. ALguboori, L.J. Habeeb, and H.K. Jalghaf, Porosity influence on natural convection heat transfer from a heated cylinder in a square porous enclosure. Journal of Mechanical Engineering Research and Developments, 43(6) (2020) 236-254.

[45] Ghalambaz, M., A. Doostani, E. Izadpanahi, and A.J. Chamkha, Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity. Journal of Thermal Analysis and Calorimetry, 139(3) (2020) 2321-2336.

[46] El Mehdi, B., Lattice Boltzmann Computations of Natural Convection Heat Transfer of Nanofluid in a Square Cavity Heated by Protruding Heat Source. Journal of Thermal Science and Engineering Applications, 20 (2020) 001000-1.

[47] Cho, C.-C., Effects of porous medium and wavy surface on heat transfer and entropy generation of Cu-water nanofluid natural convection in square cavity containing partially-heated surface. International Communications in Heat and Mass Transfer, 119 (2020) 104925.

[48] Hamid, M., M. Usman, W.A. Khan, R.U. Haq, and Z. Tian, Characterizing natural convection and thermal behavior in a square cavity with curvilinear corners and central circular obstacles. Applied Thermal Engineering, 248 (2024) 123133.

[49] Tezer-Sezgin, M., C. Bozkaya, and ?. Türk, Natural convection flow of a nanofluid in an enclosure under an inclined uniform magnetic field. European Journal of Computational Mechanics, 25(1-2) (2016) 2-23.

[50] Bouamoud, B. and S. Houat, Mesoscopic study of natural convection in a square cavity filled with alumina-based nanofluid. Energy Procedia. 139 (2017)  758-765.

[51] Arjun, K. and K. Rakesh, MHD natural convection heat transfer in a nanofluid filled finned square cavity. Journal of Mechanical Engineering Research & Developments, 40 (2017) 481-489.

[52] Chandra, H., P. Bera, and A.K. Sharma, Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls. Numerical Heat Transfer, Part A: Applications, 77(3) (2020) 317-341.

[53] Purusothaman, A., H. Oztop, N. Nithyadevi, and N.H. Abu-Hamdeh, 3D natural convection in a cubical cavity with a thermally active heater under the presence of an external magnetic field. Computers & Fluids, 128 (2016) 30-40.

[54] Mamourian, M., K.M. Shirvan, and I. Pop, Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by Response Surface Methodology. International Communications in Heat and Mass Transfer, 79 (2016) 46-57.

[55] Sivaraj, C. and M.A. Sheremet, Natural convection coupled with thermal radiation in a square porous cavity having a heated plate inside. Transport in Porous Media, 114(2016) 843-857.

[56] Mehryan, S., M. Ghalambaz, M.A. Ismael, and A.J. Chamkha, Analysis of fluid-solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane. Journal of Magnetism and Magnetic Materials, 424 (2017) 161-173.

[57] Tayebi, T. and A.J. Chamkha, Effects of various configurations of an inserted corrugated conductive cylinder on MHD natural convection in a hybrid nanofluid-filled square domain. Journal of Thermal Analysis and Calorimetry, 143(2) (2021) 1399-1411.

[58] Javed, T., Z. Mehmood, and Z. Abbas, Natural convection in square cavity filled with ferrofluid saturated porous medium in the presence of uniform magnetic field. Physica B: condensed matter, 506 (2017) 122-132.

[59] Cherifa, B., B. Mohamed, M. Abderrahim, and K. Fatima-Zohra, Unsteady natural convection in a porous square cavity saturated by nanofluid using buongiorno model: variable permeability effect on homogeneous porous medium. CFD Letters, 14(7) (2022) 42-61.

[60] Acharya, N., Finite element analysis on the hydrothermal pattern of radiative natural convective nanofluid flow inside a square enclosure having nonuniform heated walls. Heat Transfer, 51(1) (2022) 323-354.

[61] Hussein, A.K., H. Ashorynejad, S. Sivasankaran, L. Kolsi, M. Shikholeslami, and I. Adegun, Modeling of MHD natural convection in a square enclosure having an adiabatic square shaped body using Lattice Boltzmann Method. Alexandria Engineering Journal, 55(1) (2016) 203-214.

[62] Li, Z., A.K. Hussein, O. Younis, M. Afrand, and S. Feng, Natural convection and entropy generation of a nanofluid around a circular baffle inside an inclined square cavity under thermal radiation and magnetic field effects. International Communications in Heat and Mass Transfer, 116 (2020) 104650.

[63] Bouchair, R., A. Bourouis, and A. Omara, Conjugate MHD natural convection in a square cavity with a non-uniform heat source thick solid partition. International Journal for Computational Methods in Engineering Science and Mechanics, 23(5) (2022) 396-411.

[64] Sivarami Reddy, C., V. Ramachandra Prasad, and K. Jayalakshmi, Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid. Heat Transfer50(6), (:2021 ) 5267-5285.

[65] Sivaraj, C. and M.A. Sheremet, MHD natural convection in an inclined square porous cavity with a heat conducting solid block. Journal of Magnetism and Magnetic materials, 426 (2017) 351-360.

[66] Scott, T.O., D.R. Ewim, and A.C. Eloka-Eboka, Experimental investigation of natural convection Al2O3-MWCNT/water hybrid nanofluids inside a square cavity. Experimental Heat Transfer, 37(3) (2024) 294-312.