Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated.Two cases are considered,in which opposing walls undergo either uniform or non-uniform motion.In the first case,the homotopy analysis method (HAM) is used to obtain the expressions for the velocity and micro-rotation fields.Graphs are sketched for some parameters.The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid.Following Xu’s model,in the second case which is more general,the wall expansion ratio varies with time.Under this assumption,the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM.In the process,both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α 0 to the final state α 1 .As a result,the time-dependent solutions are found to approach the steady state very rapidly.The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.