A comment on change of Nusselt number sign in a channel flow filled by a fluid-saturated porous medium with constant heat flux boundary conditions

Abstract

The aim of this Letter is to show that, the Nusselt number sign might be changed without changing of heat transfer direction at the wall of channels, even for flows without viscous dissipation. The sign of the Nusselt number is important for deciding on heat transfer direction at a solid wall. The change of the Nusselt number signmay be interpreted as the change of the direction of the heat transfer at a wall. There are studies, such as internal heat and fluid flow in a channel with viscous dissipation (Hung and Tso 2008, 2009; Mitrovic and Maletic 2007; Mobedi et al. 2010) or with an asymmetric heat flux boundary conditions (Cekmer et al. 2011) in which the sign of the wall Nusselt number changes. Nield and Kuznetsov (2008) studied in a very interesting paper the counter flow in a channel whose boundaries are asymmetrically heated and is consisted of two porous layers with different permeability values. These authors showed that even the sign of an overall Nusselt number defined based on the average wall temperatures and heat fluxes, and the mean permeability values of the two porous layers can also be changed and it can take negative values when a strong asymmetry heat flux is imposed to the boundaries. The change of Nusselt number sign at the walls are also observed in other studies of Kuznetsov (Kuznetsov and Nield 2010; Xiong and Kuznetsov 2000).