Achievement of wall temperature uniformity by axially graded porous materials

An analysis based on local thermal non-equilibrium was made on thermally developing forced convective flows in a channel filled with axially graded porous materials so as to find a way to control its wall temperature distribution. Both analytical and numerical methods were exploited and compared to confirm the validity of the results. A collection of axially graded metal foams were considered under equal solid volume fraction with local porosity decreasing downstream following a power function of axial distance with an exponent n. The Brinkman-Forchheimer extended Darcy model was employed to investigate the axial development of the velocity field, which reveals a weak secondary flow towards the heated wall of the channel, working favorably in view of wall cooling. The wall temperature variation is found quite sensitive to the axial gradient of the local porosity. Depending on the value of the exponent n controlling the axial gradient of the porosity, the axial variation of the wall temperature changes drastically. By adjusting the exponent n, the wall temperature can stay nearly constant throughout the channel for the case of n = 1.0, or can increase from the inlet for the case of n = 1.5, attain its maximum, and then, decreases towards the exit. The results obtained in this study provides useful information for designing effective cooling systems, where control of not only the desired working temperature but also its uniformity are required such as in EV batteries and PEMFC.