Paper Titles in Periodical
International Letters of Chemistry, Physics and Astronomy
Volume 55


Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

ILCPA > Volume 55 > Mixed Convection of Heat Transfer in a Square...
< Back to Volume

Mixed Convection of Heat Transfer in a Square Lid-Driven Cavity

Full Text PDF


Three dimensional steady state mixed convection in a lid driven cubical cavity heating from below has been investigated numerically. Two sided walls are maintained at a constant ambient temperature Ttop > Tbottom, while the vertical walls are thermally insulated. Governing equations expressing in a dimensionless form are solved by using finite element method. The Reynolds number is fixed at Re=100, while the Richardson number is varied from 0.001 to 10. Parametric studies focusing on the effect of the Richardson number on the fluid flow and heat transfer have been performed. The flow and heat transfer characteristics, expressed in terms of streamlines, isotherms and average wall Nusselt number are presented for the entire range of Richardson number considered. Multiple correlations in terms of the heat transfer rate and Richardson number has been established.


International Letters of Chemistry, Physics and Astronomy (Volume 55)
N. Ben Mansour et al., "Mixed Convection of Heat Transfer in a Square Lid-Driven Cavity", International Letters of Chemistry, Physics and Astronomy, Vol. 55, pp. 180-186, 2015
Online since:
Jul 2015

[1] R. Iwatsu and J.M. Hyun, Three-dimensionel driven-cavity flows with a vertical temperature gradient.

[2] A.A. Mohamed, R. Viskanta, Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid, Appl. Math. Modelling 19 (1995) 465-472.

DOI: 10.1016/0307-904x(95)00030-n

[3] M. K. Moallemi and K. S. Jang, Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity, hf. J. Hear Mass Transfer. Vol. 35, No. 8, pp.1881-1892, (1992).

DOI: 10.1016/0017-9310(92)90191-t

[4] A. K. Prasad and J.R. Koseff, Combined forced and natural convection heat transfer in a deep lid-driven cavity flow, Int.J. Heat Fluid Flow, Vol. 17, pp.460-467, (1996).

DOI: 10.1016/0142-727x(96)00054-9

[5] M.A.R. Sharif, Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Applied Thermal Engineering 27 (2007) 1036-1042.

DOI: 10.1016/j.applthermaleng.2006.07.035

[6] R. Peyret, T.D. Taylor, Computational Methods for Fluid Flow, Springer-Verlag, Berlin, Germany, (1983).

[7] Y. Achdou, J.L. Guermond, Convergence analysis of a finite element projection/Lagrange Galerkin method for the incompressible Navier–Stokes equations, SIAM J. Numer. Anal. 37 (2000) 799–826.

DOI: 10.1137/s0036142996313580

[8] S.V. Patankar, A calculation procedure for two-dimensional elliptic situations, Numer. Heat Transfer 34 (1981) 409–425.

DOI: 10.1080/01495728108961801

[9] F. Moukhalled, M. Darwish, A unified formulation of the segregated class of algorithm for fluid flow at all speeds, Numer. Heat Transfer, Part B: Fundamentals 37 (2000) 103– 139.

DOI: 10.1080/104077900275576

[10] M.H. Kobayachi, J.M.C. Pereira, J.C.F. Pereira, A conservative finite-volume second-order-accurate projection method on hybrid unstructured grids, J. Comput. Phys. 150 (1999) 40–75.

DOI: 10.1006/jcph.1998.6163

[11] T. Hayase, J.A.C. Humphrey, R. Greif, A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures, J. Comput. Phys. 98 (1992) 108 -118.

DOI: 10.1016/0021-9991(92)90177-z

[12] W.H. Press, et al., second edition, Numerical Recipes in Fortran 77: The Art of Scientific Computing, vol. 1, Cambridge Press, London, UK, (1997).

[13] M. Hortmann, M. Peric, G. Scheuerer, Finite volume multigrid prediction of laminar natural convection: benchmark solutions, Int. J. Numer. Meth. Fluids 11 (1990) 189– 207.

DOI: 10.1002/fld.1650110206

[14] M.S. Mesquita, M.J.S. de Lemos, Optimal multigrid solutions of dimensional convection–conduction problems, Appl. Math. Comput. 152 (2004) 725–742.

DOI: 10.1016/s0096-3003(03)00591-5

[15] E. Nobile, Simulation of time-dependent flow in cavities with the correction multigrid method, Part I: Mathematical formulation, Numer. Heat Transfer, Part B: Fundamentals 30 (1996) 341–350.

DOI: 10.1080/10407799608915086

[16] N. Ben-Cheikh, B. Ben-Beya, T. Lili, Benchmark solution for time-dependent natural convection flows with an accelerated full-multigrid method, Num. Heat Trans. (B), 52 (2007) 131-151.

DOI: 10.1080/10407790701347647

[17] Nasreddine Ouertatani, Nader Ben Cheikh, BrahimBenBeya , TaiebLili, Antonio CampoMixed convection in a double lid-driven cubic cavity, Int. J. Therm. Sciences. Vol. 48, p.1265–1272, (2009).

DOI: 10.1016/j.ijthermalsci.2008.11.020

[18] Numerical Study of Mixed Convection Heat Transfer and Fluid Flow in Cubical Lid-Driven Cavity, Eur. J. Sci. Research, Vol. 72 No. 3 (2012), pp.460-473.

Show More Hide