Unsteady Flow in a Porous, Elastic Circular Tube : Part 1, The Wall Contracting or Expanding in an Axial Direction

Zhang

et al. 2011

Open Physics

Abstract:The flow of a micropolar fluid in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for the velocity fields and microrotation fields. Graphs are sketched for the effects of some values of parameters, especially the expansion ratio, on the velocity and microrotation fields and associated dynamic characteristics are analyzed in detail. PACS

Section: Introductionmentioning

confidence: 99%

The flow of a micropolar fluid through a porous channel with expanding or contracting walls

Zhang

et al. 2011

Open Physics

“…Ohki [10] investigated unsteady flow in a semi-infinite tube with porous, elastic wall whose length varied with time, but its cross section does not vary. In order to simulate the laminar flow field in cylindrical solid rocket motors, Goto et al [11] analyzed the laminar incompressible flow in a semiinfinite porous pipe whose radius varied with time.…”

Section: Introductionmentioning

confidence: 99%

Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

Zhang

et al. 2011

Acta Mech Sin

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method (HAM) is employed to obtain the expressions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

“…Uchida and Aoki [8] first examined the viscous flow inside an impermeable tube with a contracting cross section. Ohki [9] investigated the unsteady flow in a semi-infinite tube with a porous and elastic wall whose length varied with time while cross section remained the same. To simulate the laminar flow in cylindrical solid rocket motors, Goto and Uchida [10] analyzed the laminar incompressible flow in a semi-infinite porous pipe whose radius varied with time.…”

Section: Introductionmentioning

confidence: 99%

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

Appl. Math. Mech.-Engl. Ed.

et al. 2011

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.