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The modified model of magneto-hydrodynamic (MHD) flow and heat transfer of power-law fluid over a stretching permeable surface with prescribed heat flux in the presence of heat generation or absorption is investigated. The thermal conductivity is assumed to be dependent on the power law of velocity gradient. The general boundary conditions are given and Lie-group method is used to determine the appropriate boundary conditions suitable for the similarity solution. By using the achieved similarity transformations, the similarity equations are obtained and solved numerically by Bvp4c with Matlab. Graphical solutions for the dimensionless velocity and temperature as well as skin-friction coefficient and Nusselt number for various parameters are presented and discussed. [ABSTRACT FROM AUTHOR]

In this paper, the flow of a micropolar fluid through a porous channel with deforming walls is investigated. The Lie group method is applied to determine symmetry reductions of partial differential equations. Compared with previous work, the similar variable for the microrotation velocity also is obtained, which is an extension of the case corresponding to the Newtonian fluids (Boutros et al., 2007). This problem we study here can be considered as an extension of the model discussed in Boutros et al. (2007). The effect of the permeation Reynolds number Re , the micropolar parameter K and the expansion ratio α are studied numerically and the results are plotted. Furthermore, the multiple solutions also can be found for some values of parameters. [ABSTRACT FROM AUTHOR]

Abstract: Considering the influence of the viscous dissipation in the energy equation, we investigate the flow and heat transfer of an incompressible micropolar fluid in a channel with expanding or contracting walls. By introducing suitable similarity transformations, the nonlinear partial differential equations are reduced to a system of ordinary differential equations. Homotopy analysis method (HAM) is employed to obtain the series solutions for the velocity, microrotation and temperature distribution. In order to analyze the influence of the micropolar parameter, the Reynolds number and the deformation of the wall, the graphs for velocity components, microrotation, temperature, couple stress and shear stress in the channel are presented and discussed in detail. [Copyright &y& Elsevier]

Abstract: In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed. [Copyright &y& Elsevier]

This paper is concerned with asymptotic solutions of a nonlinear boundary value problem (BVP), which arises in a study of laminar flow in a uniformly porous channel with retractable walls and an applied transverse magnetic field. For different ranges of the control parameters (i.e. α , Re and M ) arising in the BVP, four cases are considered using different singular perturbation methods. For the first case, unlike those in the existing literature, we make use of the Lighthill method and successfully construct an asymptotic solution with high-order derivatives at the center of the channel. For the second case, under large suction we consider M 2 = O (1) and M 2 = O ( Re ), respectively, which will further extend the applying range of asymptotic solutions. In other cases, asymptotic solutions with a boundary layer are successfully constructed. In addition, numerical solutions presented for each case agree well with asymptotic solutions, which illustrates that the asymptotic solutions constructed in this paper are more reliable. Finally, the influences of some parameters on flow field are discussed to develop a better understanding of the flow problem. [ABSTRACT FROM AUTHOR]