Investigation of forced convection through entrance region of a porous-filled microchannel: An analytical study based on the scale analysis

The thermally developing forced convection heat transfer in a micro-channel filled with a porous material in the slip-flow regime is analyzed. Channel walls are subjected to a constant heat flux. The local thermal non-equilibrium (LTNE) condition is considered and both the fluid and solid phases in the porous region are assumed to have internal heat generation. According to a perturbation analysis assuming small temperature difference between the two phases obtained by the scale analysis, we show that there is no need to apply a thermal boundary condition model at the channel wall. Thus, we obtained an analytical solution for the thermally developing Nusselt number (Nu) using no model. Thermal boundary condition models (A and B) are also used to find the temperature jump at the wall. Comparing Nu of models A and B with the pure perturbation analysis (using no model) and with the solution under local thermal equilibrium (LTE) condition reveals that model B cannot predict the LTE condition when a temperature jump exists on the wall. Hence, model A may be the only valid scenario in the slip-flow regime. In addition, expressions for the thermal entry length (x_developing) are proposed. An increase in β as well as a decrease in the thermal conductivity ratio (k) decrease x_developing.