Free convection inside a porous square cavity with convective boundary condition using spline functions

Abstract

Abstract In this paper, we consider the problem of free convection in a square cavity filled with a porous medium with convective boundary condition on the left wall of the cavity. We first transform the governing equations transformed in terms of dimensionless variables and then solve them numerically using a cubic spline colocation method. We discuss the effects of two very important parameters, the Biot (Bi) and Rayleigh (Ra) numbers. We perform a comparison of the average Nusselt number N u ‾ $\overline{Nu}$ at the hot wall with results from the open literature. We can notice that the comparison is very good, which gives us strong confidence that this cubic spline collocation method works very efficiently for such problems. We also state that the present problem has not been considered before by any researcher.

Keywords

• Square cavity
• Free convection
• Porous medium
• Convective boundary condition
• Spline collocation method