Theoretical investigation of the influences of thermal boundary conditions upon the heat transfer characteristics in a channel partially filled by a porous material

Yaser Mahmoudi, University of Cambridge
Nader Karimi, University of Glasgow


Enhancement of forced convective heat transfer is analytically investigated in a channel partially filled with a porous medium under Local Thermal Non-Equilibrium. The flow inside the porous material is modeled by the Darcy-Brinkman equation. The thermal boundary conditions at the interface between the porous medium and the clear region are described by two different models (models A and B). For each interface model exact solutions are developed for the solid and fluid temperature fields. The Nusselt number (Nu) associated with each interface model is derived in terms of the porous insert normalized thickness (S) and other pertinent parameters such as thermal conductivity ratio (k), Biot number (Bi), and Darcy number (Da).