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Special Topics & Reviews in Porous Media: An International Journal
FLOW IN A COMPOSITE POROUS CYLINDRICAL CHANNEL COVERED WITH A POROUS LAYER OF VARIABLE PERMEABILITY
Sanjeeva Kumar Singh
Dr. Rammanohar Lohia Avadh University, Ayodhya
Vineet Kumar Verma
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, India
In the present article we have considered the steady flow of viscous, incompressible fluid in a composite cylindrical
channel. The inner and outer parts of the cylindrical channel is of different permeability. The porous channel consists
of two parts. The inner porous cylinder is of uniform permeability k0 which is covered by an outer porous layer of variable permeability. We have considered two cases of permeability variation of the outer porous cylinder: (i) linear variation, k = k0r and (ii) quadratic variation, k = k0r2. An analytical solution of the problem is obtained by using the Brinkman equation. Exact expressions for the velocity, rate of volume flow, average velocity, and shear stress on the impermeable boundary are obtained and exhibited graphically. The effect of permeability variation parameter and
the gap parameter on the flow characteristics has been discussed. It is found that these parameters have a very strong
effect on the flow.
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