ANALYTICAL SOLUTION OF UNSTEADY STRATIFIED VISCOUS FLUID PAST A PERMEABLE BED
K. AVINASH *
Department of Mathematics, Sreyas Institute of Engineering and Technology, GSI Bandlaguda, Telangana, Hyderabad, India
Department of Mathematics, Mahatma Gandhi Institute of Technology (MGIT), Gandipet, Telangana, Hyderabad, India
*Author to whom correspondence should be addressed.
Unsteady flow of a conducting stratified fluid over a permeable bed is studied. The flow region is divided into two zones. The flow region between the permeable bed and the impermeable plate is taken as zone1. Here the flow is governed by Navier-stokes equations. The flow region in permeable bed is termed as zone2. Here the flow is according to the modified Darcy’s law. The velocity field, the mass flow rate and its fractional increase are obtained. It is observed that the velocity increases from the lower permeable bed to a fixed value on the upper impermeable rigid plate. For fixed y, the velocity decreases with increase in the stratification factor β in the channel. The velocity decreases with an increase in the magnetic parameter M between the permeable bed and upper impermeable rigid plate. As stratification factor β increases the fractional increase F also increases for a given slip parameter α. It is established that induced magnetic field and stratification parameters are held responsible for retardation in the motion of the fluid. It is observed that the Fractional Increase F increases with the stratification factor for fixed Darcy number Da. The decrease in the α increases F. This means that the viscosity stratification is favorable to the mass flow rate which is similar to the one observed by Channabasappa and Ranganna .
Keywords: Magnetic field, permeable bed, Darcy number and stratification parameters