Brinkman number effect and Conjugate heat transfer in a porous microchannel

The problem of conjugate heat transfer in a fully saturated porous medium confined in a microchannel between parallel plates is analyzed. Two conjugate heat transfer parameters were defined in the microchannel wall and in the fluid. It was found that the values of these parameters have certain limits under which, longitudinal temperature gradients can occur both in the wall and in the porous medium. Additionally, we studied the effects of the Darcy number Da and the Brinkman number Br, on fluid and wall temperature profiles for different values of the conjugate heat transfer parameters. Finally, several values of the Peclet number are analyzed in order to find out which of them promotes longitudinal (axial) heat conduction in the fluid and also in the wall of the microchannel. The main objective of this work is to determine for which Brinkman values the viscous dissipation effects are more important than the longitudinal heat conduction effects in the microchannel wall.