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

Abstract

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 α0 to the final state α1. 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.

Three-Dimensional Flow of an Oldroyd-B Fluid with Variable Thermal Conductivity and Heat Generation/Absorption

“…In this work, the conservation laws of mass, momentum and energy are reduced to nonlinear ordinary differential systems. The outcoming problems are solved by homotopy analysis method (HAM) [21] – [29] . The velocity components and temperature are analyzed through their graphical representations.…”

Asymmetric Flow of a Nanofluid Between Expanding or Contracting Permeable Walls With Thermal Radiation

“…where ( 1,2,3,4,5,6) i ci  are constants. For further details of HAM, we refer the reader (Hatami et al 2013;Srinivas et al 2015;Hayat et al 2011;Si et al 2011a;Srinivas et al 2014;Liao 2014).…”

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Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel

“…The fluid flow in a channel has abundant practical applications in industry from mathematical and engineering point of view [1][2][3][4][5]. In particular, those fluids in which the shear stresses are not linear proportional to the velocity gradient are characterized as non-Newtonian fluids which are of much interest among the researchers.…”