Comments on “heat transfer in a square porous cavity in presence of square solid block”

Abstract

Purpose The purpose of this paper is to discuss the need to attend correctly to the accuracy and the manner in which the value of the streamfunction is determined when two or more impermeable boundaries are present. This is discussed within the context of the paper by Nandalur et al. (2019), which concerns the effect of a centrally located conducting square block on convection in a square sidewall-heated porous cavity. Detailed solutions are also presented which allow the streamfunction to take the natural value on the surface of the internal block. Design/methodology/approach Steady solutions are obtained using finite difference methods. Three different ways in which insulating boundary conditions are implemented are compared. Detailed attention is paid to the iterative convergence of the numerical scheme and to its overall accuracy. Error testing and Richardson’s extrapolation have been used to obtain very precise values of the Nusselt number. Findings The assumption that the streamfunction takes a zero value on the boundaries of both the cavity and the embedded block is shown to be incorrect. Application of the continuity-of-pressure requirement shows that the block and the outer boundary take different constant values. Research limitations/implications The Darcy–Rayleigh number is restricted to values at or below 200; larger values require a finer grid. Originality/value This paper serves as a warning that one cannot assume that the streamfunction will always take a zero value on all impermeable surfaces when two or more are present. A systematic approach to accuracy is described and recommended.