ANALYTICAL SOLUTION OF UNSTEADY MHD FREE CONVECTION FLOW OF CASSON FLUID
THROUGH A VERTICAL CHANNEL
Abstract
Unsteady flow of Casson fluid past through a vertical channel has been
studied by some researchers due to its importance applications in
science and technology. Therefore, the main purpose of this paper is to
obtain exact solutions for unsteady free convection flows of Casson fluid
with effects of magnetohydrodynamics (MHD) past through vertical
channel. Dimensional governing equations are converted into
dimensionless forms by using appropriate dimensionless variables.
Dimensionless parameters are obtained through dimensionless process such
as Casson fluid, time, Prandtl number, Grashof number and magnetic
field. Laplace transform method is used to solve the dimensionless
equations with associated initial and boundary conditions. Solutions for
velocity and temperature profiles are obtained. Skin friction and
Nusselt number are also calculated. The obtained analytical results for
velocity and temperature are plotted graphically to discuss the
influence of dimensionless parameters on profiles. It is observed that
fluid velocity increases with increases of Grashof number, Gr and time,
t whereas it decreases with increases of Casson parameter, γ, magnetic
field parameter, M and Prandtl number, Pr. Besides that, it is found
that temperature profiles decrease with high value of Prandtl number, Pr
while increases with high value of time, t. In order to validate the
results, the obtained results in limiting cases are compared with the
published results and it is found to be in a mutual agreement.