Xinhui Si

The exterior unsteady viscous flow and heat transfer due to a porous expanding stretching cylinder

Abstract This paper presents a numerical solution of the flow and heat transfer outside a stretching expanding porous cylinder. Under this special boundary condition, the governing system of partial differential equations is converted to a set of coupled ordinary differential equations by using suitable similarity transformations, which are solved by a collocation method equivalent to the fourth order mono-implicit-Runge–Kutta method with MATLAB. The main purpose of the present study is to investigate the effects of the different physical parameters, namely the stretching Reynolds number, the permeability Reynolds number,the expansion ratio and the Prandtl number on the velocity and temperature distribution. The results are shown graphically.

Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall

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.

The flow of a micropolar fluid through a porous expanding channel

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.

The exterior unsteady viscous flow and heat transfer due to a porous expanding or contracting cylinder.

Since the vessels in the biological tissues are characterized by low seepage Reynolds numbers and contracting or expanding walls, more attention is paid on the viscous flow outside the porous pipe with small expansion or contraction. This paper presents a numerical solution of the flow and heat transfer outside an expanding or contracting porous cylinder. The coupled nonlinear similarity equations are solved by Bvp4c, which is a collocation method with MATLAB. The effects of the different physical parameters, namely the permeability Reynolds number,the expansion ratio and the Prandtl number, on the velocity and temperature distribution are obtained and the results are shown graphically.