Characteristic Study of Combined effects of Dufour and Coriolis Force on Free Convection in a Rectangular Cavity with Isotropic and Anisotropic Porous Media

Authors(3) :-Sudhir Patel, Dinesh P A, Suma S P

This study investigates the effects of dufour and coriolis force on classic Rayleigh -B?nard problem for an laminar, viscous, unsteady incompressible fluid flow heated from below is extended to 3-dimesional convection in a finite geometry with isotropic and anisotropic porous media rotating with constant angular velocity. For the given physical set-up, g partial differential equations of the physical configuration are transformed to a set of non-dimensional ordinary differential equations using similarity transformation. This demands to apply Fourier series method to study the characteristic of velocity, temperature and concentration for the effect of Taylors number, Rayleigh number, Hartmann’s number and Prandtl number for both anisotropic and isotropic porous media. The results of steam function and isotherms on various parameters have been discussed and found to be good agreement for the physical system.)

Authors and Affiliations

Sudhir Patel
Department of Mathematics, New Horizon College of Engineering Bangalore-560103, India
Dinesh P A
Department of Mathematics Ramaiah Institute of Technology Bangalore-560054, India
Suma S P
Department of Mathematics Cambridge Institute of Technology Bangalore-560036, India

Isotropic and anisotropic porous media, Free convection, Coriolis force, MHD.

  1. Sathish Kumar, M., Sandeep, N., Rushi Kumar, B., & Dinesh, P. A. (2017). A comparative analysis of magnetohydrodynamic non-Newtonian fluids flow over an exponential stretched sheet. Alexandria Engineering Journal.
  2. Suresh Babu, R., Kumar, B. R., & Dinesh, P. A. (2018). Soret and Dufour Effects on MHD Mixed Convection Flow over a Vertical Plate with Variable Fluid Properties. Defect and Diffusion Forum, 389, 1–17.
  3. J. Yan, S.K. Chou, U. Desideri, X. XiaInnovative and sustainable solutions of clean energy technologies and policies (Part II), Appl Energy, 136 (2014), pp. 756-758.
  4. H. Cho, A.D. Smith, P. Mago, Combined cooling, heating and power: a review of performance improvement and optimization Appl Energy, 136 (31) (2014), pp. 168-185. J. Yan, S.K. Chou, U. Desideri,
  5. X. Xia, Innovative and sustainable solutions of clean energy technologies and policies (Part I) Appl Energy, 130 (2014), pp. 447-449..
  6. U. Erturun, K. Erermis, K. Mossi, Influence of leg sizing and spacing on power generation and thermal stresses of thermoelectric devices Applied Energy, 159 (2015), pp. 19-27.doi. 10.1016/j.apenergy.2015.08.112.
  7. Gelfgat, A. Y., Bar-Yoseph, P. Z., & Solan, A. (2001). Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration. Journal of Crystal Growth, 230(1-2), 63–72.
  8. Yang KT. Transitions and bifurcations in laminar buoyant flows in confined enclosures. J Heat Transfer 1988;110:1191–204.
  9. Koschmieder EL. Be´nard cells and taylor vortices. Cambridge: Cambridge Univ. Press; 1993.
  10. Fusegi T, Hyun JM, Kuwahara K, Farouk B. A numerical study of three dimensional natural convection in a differentially heated cubical enclosure. Int J Heat Mass Transfer 1991;34(6):1543–57.
  11. Janssen RJA, Henkes RAW, Hoogendoorn CJ. Transition to time periodicity of a natural convection flow in a 3D differentially heated cavity. Int J Heat Mass Transfer 1993;36(11):2927–40
  12. G. 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.
  13. M. Hortmann, M. Peric´, G. Scheuerer, Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions, Int. J. Numer. Methods Fluids 11 (2) (1990) 189–207.
  14. T. Saitoh, K. Hirose, High-accuracy bench mark solutions to natural convection in a square cavity, Comput. Mech. 4 (6) (1989) 417–427.
  15. P. Le Quéré, Accurate solutions to the square thermally driven cavity at high Rayleigh number, Comput. Fluids 20 (1) (1991) 29–41.
  16. M. Ravi, R. Henkes, C. Hoogendoorn, On the high-Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure, J. Fluid Mech. 262 (1994) 325–351.
  17. G.W.D.C. Wan, BSV Patnaik, A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Numer. Heat Transf.: Part B: Fundam. 40 (3) (2001) 199–228.
  18. G.D. Mallinson, G.D.V. Davis, Three-dimensional natural convection in a box: a numerical study, J. Fluid Mech. 83 (01) (1977) 1–31.
  19. G. Labrosse, E. Tric, H. Khallouf, M. Betrouni, A direct (pseudo-spectral) solver of the 2D/3D stokes problem: transition to unsteadiness of natural-convection flow in a differentially heated cubical cavity, Numer. Heat Transf. 31 (3) (1997) 261–276.
  20. F. Trias, M. Soria, A. Oliva, C. Pérez-Segarra, Direct numerical simulations of two-and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4, J. Fluid Mech. 586 (2007) 259– 293.
  21. F. Trias, A. Gorobets, M. Soria, A. Oliva, Direct numerical simulation of a differentially heated cavity of aspect ratio 4 with Rayleigh numbers up to 10 11–part I: numerical methods and time-averaged flow, Int. J. Heat Mass Transf. 53 (4) (2010) 665–673.
  22. R. Janssen, R. Henkes, C. Hoogendoorn, Transition to time-periodicity of a natural-convection flow in a 3D differentially heated cavity, Int. J. Heat Mass Transf. 36 (11) (1993) 2927–2940.
  23. E. Tric, G. Labrosse, M. Betrouni, A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions, Int. J. Heat Mass Transf. 43 (21) (2000) 4043– 4056.
  24. J. Salat, S. Xin, P. Joubert, A. Sergent, F. Penot, P. Le Quere, Experimental and numerical investigation of turbulent natural convection in a large air-filled cavity, Int. J. Heat Fluid Flow 25 (5) (2004) 824–832.
  25. Bories, “Natural Convection in porous media”, Advances in Transport Phenomena in Porous Media, NATO ASI Series book series, Vol. 128, pp 77-141.
  26. Sutton, F. M. (1970). Onset of Convection in a Porous Channel with Net Through Flow. Physics of Fluids, 13(8), 1931.

Publication Details

Published in : Volume 4 | Issue 9 | November-December 2019
Date of Publication : 2019-12-30
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 207-216
Manuscript Number : CSEIT1949139
Publisher : Technoscience Academy

ISSN : 2456-3307

Cite This Article :

Sudhir Patel, Dinesh P A, Suma S P, "Characteristic Study of Combined effects of Dufour and Coriolis Force on Free Convection in a Rectangular Cavity with Isotropic and Anisotropic Porous Media", International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT), ISSN : 2456-3307, Volume 4, Issue 9, pp.207-216, November-December-2019. |          | BibTeX | RIS | CSV

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