Transient Natural Convection and Entropy Generation Analysis in a Stratified Square Enclosure

Document Type : Research Article

Authors

1 Department of Chemical Engineering, Z. H. Sikder University of Science and Technology, Shariatpur 8024, Bangladesh

2 Department of Computer Science and Engineering, Z. H. Sikder University of Science and Technology, Shariatpur 8024, Bangladesh

3 Department of Mathematics, Jagannath University, Dhaka 1100, Bangladesh

Abstract

This study examines transient natural convection (NC) heat transfer (HT) and entropy generation (Egen) in a square enclosure containing thermally stratified water. The model considers uniform heating at the bottom wall, stratified vertical walls, and a cooled top boundary. Governing equations are addressed through the finite volume (FV) method, with simulations performed across a range of Rayleigh numbers (Ra) from 100 to 5 × 10⁶, a fixed Prandtl number (Pr) of 7.01, for water. Various physical quantities were analyzed across the spectrum of Ra to capture the complex dynamics of convective flow. This encompasses streamline and isotherm plots, the temporal evolution of temperature, phase-space representations via limit cycles and limit points, along with spectral analysis, including the average Nusselt number (Nu), local entropy generation (El), and local Bejan number (Bel). The results reveal successive bifurcations with increasing Ra: a pitchfork bifurcation (Ra = 8 × 10³–10⁴) leads to symmetry breaking, a Hopf bifurcation (Ra = 2 × 10⁵–3 × 10⁵) induces periodic oscillations, and chaotic flow emerges at Ra = 10⁶–2 × 10⁶. The average Nusselt number at the bottom wall increases from 5.84 for Ra = 2 × 105 to 15.87 for Ra = 2 × 106, corresponding to a 171.75% enhancement in the HT. The numerical framework was validated by comparing it with existing numerical literature, confirming the results’ reliability.

Keywords

Main Subjects

References

  1. Angirasa, G.P. Peterson, Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium, International Journal of Heat and Mass Transfer, 40(18) (1997) 4329-4335.
  2. C. Chen, R. Eichhorn, Natural convection from a vertical surface to a thermally stratified fluid, Journal of Heat Transfer, 98(3) (1976) 446-451.
  3. K. Tripathi, G. Nath, Unsteady natural convection flow over a vertical plate embedded in a stratified medium, International Journal of Heat and Mass Transfer, 36(4) (1993)1125-1128.
  4. M. Rahaman, S. Bhowmick, S. C. Saha, Unsteady Natural Convection and Entropy Generation in Thermally Stratified Trapezoidal Cavities: A Comparative Study, Processes, 13(6) (2025) 1908.
  5. M. Rahaman, S. Bhowmick, R.N. Mondal, S.C. Saha, A computational study of chaotic flow and heat transfer within a trapezoidal cavity, Energies, 16(13) (2023) 5031.
  6. Bhowmick, S.C. Saha, M. Qiao, F. Xu, Transition to a chaotic flow in a V-shaped triangular cavity heated from below, International Journal of Heat and Mass Transfer, 128 (2019) 76-86.
  7. Wang, S. Bhowmick, Z.F. Tian, S.C. Saha, F. Xu, Experimental study of natural convection in a V-shape-section cavity, Physics of Fluids, 33(1) (2021) 014104.
  8. Patterson, J. Imberger, J. Unsteady natural convection in a rectangular cavity, Journal of Fluid Mechanics, 100(1) (1980) 65-86.
  9. S. Lee, Numerical experiments with fluid convection in tilted nonrectangular enclosures, Numerical Heat Transfer, 19(4) (1991), 487-499.
  10. Ma, F. Xu, Unsteady natural convection and heat transfer in a differentially heated cavity with a fin for high Rayleigh numbers, Applied Thermal Engineering, 99 (2016) 625-634.
  11. Varol, H.F. Oztop, I. Pop, Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall, International Communications in Heat and Mass Transfer, 35(1) (2008) 56-64.
  12. C. Saha, Unsteady natural convection in a triangular enclosure under isothermal heating, Energy and Buildings, 43(2-3) (2011) 695-703.
  13. Bouafia, O. Daube, Natural convection for large temperature gradients around a square solid body within a rectangular cavity, International Journal of Heat and Mass Transfer, 50(17-18) (2007) 3599-3615.
  14. Xu, J.C. Patterson, C. Lei, Unsteady flow and heat transfer adjacent to the sidewall wall of a differentially heated cavity with a conducting and an adiabatic fin, International Journal of Heat and Fluid Flow, 32(3) (2011) 680-687.
  15. Iyican, L.C. Witte, Y. Bayazitoglu, An experimental study of natural convection in trapezoidal enclosures, Journal of Heat Transfer, 102(4) (1980) 648-653.
  16. Natarajan, S. Roy, T. Basak, Effect of various thermal boundary conditions on natural convection in a trapezoidal cavity with linearly heated side wall (s), Numerical Heat Transfer, Part B: Fundamentals, 52(6) (2007) 551-568.
  17. M. Rahman, M.A. Hye, M.M. Rahman, M.M. Rahaman, Numerical simulation on MHD free convection mass and heat transfer fluid flow over a vertical porous plate in a rotating system with induced magnetic field, Annals of Pure and Applied Mathematics, 7(2) (2014) 35-44.
  18. De Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, International Journal for Numerical Methods in Fluids, 3(3) (1983) 249-264.
  19. Basak, S. Roy, A.R. Balakrishnan, Effects of thermal boundary conditions on natural convection flows within a square cavity, International Journal of Heat and Mass Transfer, 49(23-24) (2006) 4525-4535.
  20. Raji, M. Hasnaoui, M. Firdaouss, C. Ouardi, Natural convection heat transfer enhancement in a square cavity periodically cooled from above, Numerical Heat Transfer, Part A: Applications, 63(7) (2013) 511-533.
  21. Pesso, S. Piva, Laminar natural convection in a square cavity: low Prandtl numbers and large density differences, International Journal of Heat and Mass Transfer, 52(3-4) (2009) 1036-1043.
  22. Kouroudis, P. Saliakellis, S.G. Yiantsios, Direct numerical simulation of natural convection in a square cavity with uniform heat fluxes at the vertical sides: Flow structure and transition, International Journal of Heat and Mass Transfer, 115 (2017) 428-438.
  23. H. Deng, Fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source–sink pairs, International Journal of Heat and Mass Transfer, 51(25-26) (2008) 5949-5957.
  24. Barakos, E. Mitsoulis, D.O. Assimacopoulos, Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions, International Journal for Numerical Methods in Fluids, 18(7) (1994) 695-719.
  25. A. Bawazeer, M.S. Alsoufi, Natural Convection in a Square Cavity: Effects of Rayleigh and Prandtl Numbers on Heat Transfer and Flow Patterns, Case Studies in Thermal Engineering, 73 (2025)106680.
  26. Bejan, Entropy generation minimization: The new thermodynamics of finite‐size devices and finite‐time processes, Journal of Applied Physics, 79(3) (1996) 1191-1218.
  27. Biswal, T. Basak, Entropy generation based approach on natural convection in enclosures with concave/convex side walls, International Journal of Heat and Mass Transfer, 82 (2015) 213-235.
  28. Bouabid, M. Magherbi, N. Hidouri, A.B. Brahim, Entropy generation at natural convection in an inclined rectangular cavity, Entropy, 13(5) (2011) 1020-1033.
  29. D.C. Oliveski, M.H. Macagnan, J.B. Copetti, Entropy generation and natural convection in rectangular cavities, Applied Thermal Engineering, 29(8-9) (2009) 1417-1425.
  30. M. Rahaman, S. Bhowmick, G. Saha, F. Xu, S.C. Saha, Transition to chaotic flow, bifurcation, and entropy generation analysis inside a stratified trapezoidal enclosure for varying aspect ratio, Chinese Journal of Physics, 91 (2024) 867-882.
  31. M. Rahaman, S. Bhowmick, S.C. Saha, Thermal Performance and Entropy Generation of Unsteady Natural Convection in a Trapezoid-Shaped Cavity, Processes, 13(3) (2025) 921.
  32. K. Singh, S. Roy, T. Basak, Analysis of entropy generation due to natural convection in tilted square cavities, Industrial & Engineering Chemistry Research, 51(40) (2012) 13300-13318.
  33. G. Ilis, M. Mobedi, B. Sunden, Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls, International Communications in Heat and Mass Transfer, 35(6) (2008) 696-703.
  34. A. Sheremet, T. Grosan, I. Pop, Natural convection and entropy generation in a square cavity with variable temperature side walls filled with a nanofluid: Buongiorno’s mathematical model, Entropy, 19(7) (2017) 337.
  35. H. Saboj, P. Nag, G. Saha, S.C. Saha, Entropy production analysis in an octagonal cavity with an inner cold cylinder: a thermodynamic aspect, Energies, 16(14) (2023) 5487.
  36. M. Shavik, M.N. Hassan, A.M. Morshed, M.Q. Islam, Natural convection and entropy generation in a square inclined cavity with differentially heated vertical walls, Procedia Engineering, 90 (2014) 557-562.
  37. M. Rahaman, S. Bhowmick, R.N. Mondal, S.C. Saha, Unsteady natural convection in an initially stratified air-filled trapezoidal enclosure heated from below, Processes, 10(7) (2022) 1383.
  38. M. Rahaman, S. Bhowmick, B.P. Ghosh, F. Xu, R.N. Mondal, S.C. Saha, Transient natural convection flows and heat transfer in a thermally stratified air-filled trapezoidal cavity, Thermal Science and Engineering Progress, 47 (2024) 102377.
  39. Bhowmick, F. Xu, M.M. Molla, S.C. Saha, Chaotic phenomena of natural convection for water in a V-shaped enclosure, International Journal of Thermal Sciences, 176 (2022) 107526.
  40. Bhowmick, S.C. Saha, M. Qiao, F. Xu, Transition to a chaotic flow in a V-shaped triangular cavity heated from below, International Journal of Heat and Mass Transfer, 128, (2019) 76-86.
AUT Journal of Mechanical Engineering
Volume 10, Issue 2
April 2026
Pages 153-166

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