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

Si, Xinhui; Zheng, Liancun; Zhang, Xinxin; Ying, Chao

doi:10.1007/s10409-011-0430-3

Cited by 37 publications

(11 citation statements)

References 31 publications

(32 reference statements)

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“…In seeking further generalization, Xu et al [20] discussed the multiple solutions for this model using HAM. Si et al [21] obtained the analytical solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls using HAM.…”

Section: Introductionmentioning

confidence: 99%

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

Zheng

Zhang

et al. 2011

Applied Mathematical Modelling

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a b s t r a c tThe flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the porous upper plate is investigated and an analysis is made to determine the heat and mass transfer. The unsteady Navier-Stokes equations are reduced to a generalization of the Proudman-Johnson equation retaining the effect of wall motion using a suitable similarity transformation. The analytical solution for stream function and heat transfer characteristics are obtained by employing homotopy analysis method. The effects of various physical parameters like expansion ratio, Prandtl number, Reynolds number on various momentum and heat transfer characteristics are discussed in detail.

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Section: Introductionmentioning

confidence: 99%

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

Zheng

Zhang

et al. 2011

Applied Mathematical Modelling

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“…Asghar et al [15] discussed the flow in a slowly deforming channel with a weak permeability using the Adomian decomposition method (ADM). Si et al [16] obtained the analytic solution of the asymmetric laminar flow in a porous channel with expanding or contracting walls. Si et al [17][18] also considered the flow of a micropolar fluid in a porous expanding channel.…”

Section: Introductionmentioning

confidence: 99%

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

Zheng

et al. 2011

Appl. Math. Mech.-Engl. Ed.

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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.

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“…HAM is used to get analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation by Rashidi [18]. Si et al [19] derived HAM solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls. Recent developments of HAM, like convergence of HAM solution, Optimality of convergence control parameter were discussed by Turkyilmazoglu [20,21].…”

Section: Introductionmentioning

confidence: 99%

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

Srinivasacharya

Kaladhar

2011

Acta Mech Sin

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The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.

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

Cited by 37 publications

References 31 publications

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall

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

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

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