Heat transfer with upstream thermal penetration in flow through porous plate passages

The objective of this study is to develop a series solution for determination of the temperature field in parallel-plate ducts with prescribed wall heat flux. Consideration is also given to ducts filled with fluid saturated porous materials. A simple transformation is used to improve the convergence of this series solution. Temperature variations and heat transfer coefficients are determined for infinitely long parallel-plate ducts when the walls undergo a step change in the applied wall heat flux. Axial thermal penetration near the applied wall heat flux location is studied. The solutions with the contribution of axial conduction in these fluid passages are acquired using a modified Graetz-type solution. Finally, this technique is augmented by the contribution of frictional heating.