Second-law analysis for an inclined channel containing porous-clear fluid layers by using the differential transform method

In this study, convection in a porous medium for a laminar, incompressible, non-Darcy model flow in an inclined channel has been investigated. The flow field considered is composed of porous and clear viscous layers. The solutions are carried out for both clear fluid and porous regions by using the differential transform method (DTM). For the solutions of governing equations, constant values for some parameters such as angle of inclination (φ), porous parameter (σ), and the ratio of the heights of two layers (h) are assigned. In order to verify the applied solution technique, the results obtained are compared to the already existing ones evaluated by perturbation method. It is noticed that the results by two methods are in agreement for small values of Brinkman number (Br). However, for higher values of Br, the solutions carried out by perturbation method lose accuracy but the results of the DTM are still valid. The entropy generation number (N_s) is derived and plotted by using dimensionless velocity and temperature profiles. One of the advantages of this study to similar studies is to give an open form series solution, which gives a tractable and easily applicable recurative form of nonlinear field equations. In similar studies, it is said that the equations are solved; however, neither solution technique nor accuracy or applicability of given technique are clear. In this work, these are well documented.