On the effects of exothermicity and endothermicity upon the temperature fields in a partially-filled porous channel

Forced convection of heat in a two-dimensional channel, partially filled by a porous insert is considered. This system is assumed under fully developed conditions and constant wall heat flux. Further, the fluid and solid phases can feature internal heat generation (exothermicity) and consumption (endothermicity). Analytical solutions are developed for the solid and fluid temperature fields by applying local thermal non-equilibrium (LTNE) conditions and the Darcy-Brinkman model of momentum transport. Two existing interface models (Models A and B) are employed to describe the thermal boundary conditions at the porous-fluid interface. The developed solutions for the temperature fields are compared to those found by applying the local thermal equilibrium (LTE) assumption and, therefore, the validity of the LTE is examined. This is done for a wide range of pertinent parameters including Biot number, conductivity ratio, Darcy number and thickness of the porous insert. It is found that the thermal behaviour of the investigated partially filled system is influenced by the heat sources in both solid and fluid phase. It is further shown that the LTE approach remains an acceptable assumption only for some specific regions of the parametric space. Furthermore, the occurrence of temperature gradient bifurcation on the surface of the porous-fluid interface is examined. It is demonstrated that this effect is highly sensitive to the intensity of the energy sources.