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Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field

Chutia Muhim

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 2

5--13

In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette-Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number (M), suction/injection parameter (S), permeability parameter (α) and angle of inclination (θ) on the flow are discussed and presented graphically.

Couple stress fluid past a sphere embedded in a porous medium

Madasu Krishna Prasad, Sarkar Priya

Archive of Mechanical Engineering

2022

LXIX, nr 1

5--19

This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman’s equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results.

Exact solution of flow in a composite porous channel

Singh Sanjeeva Kumar, Verma Vineet Kumar

Archive of Mechanical Engineering

2020

LXVII, nr 1

97--110

This article concerns fully developed laminar flow of a viscous incompressible fluid in a long composite cylindrical channel. Channel consist of three regions. Outer and inner regions are of uniform permeability and mid region is a clear region. Brinkman equation is used as a governing equation of motion in the porous region and Stokes equation is used for the clear fluid region. Analytical expressions for velocity profiles, rate of volume flow and shear stress on the boundaries surface are obtained and exhibited graphically. Effect of permeability variation parameter on the flow characteristics has been discussed.