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Steady flow of a viscous fluid through a porous medium OF FINITE thickness the bottom of which is impermeable and thermally insulated and the other side is stress free kept at a constant TEMPERATURE WITH a constant heat source distributed uniformly in the flow region

K.Moinuddin1, Prof.N.Ch.Pattabhi Ramacharyulu2

1Faculty of Mathematics , DDE, Maulana Azad Nation Urdu University, Hyderabad. A.P.India

2Former Faculty of Mathematics , NIT Warangal,AndhraPradesh, E-mail id : kmoinuddin71@gmail.com

 

Abstract

       This paper deals with  a steady flow of a viscous fluid  of finite depth in a porous medium over a fixed horizontal, impermeable and thermally insulated bottom where as the other side is stress free and kept at a constant temperature with a constant heat source distributed uniformly in the flow region. Exact solutions of Momentum and Energy equations are obtained when the temperatures on the fixed bottom and on the free surface are prescribed. Flow rate ,Mean velocity , Temperature , Mean Temperature , Mean Mixed Temperature  in the flow region and the Nusselt number  on the free surface have been obtained. The cases of large and small values of porosity coefficient have been obtained as limiting cases. Further  the cases of small depth(shallow fluid) and large depth (deep fluid) are also discussed. The results are illustrated graphically.

Keywords: porous medium, heat source, velocity , temperature, porosity parameter.

 

 

 


International eJournal of Mathematics and Engineering

Volume 3, Issue 1, Pages:  1352 - 1367