MATHEMATICAL MODELLING OF COUETTE FLOW OF AN ELECTRICALLY CONDUCTING FLUID BOUNDED BY TWO PARALLEL POROUS PLATES

Abstract

This thesis presents mathematical model for steady and unsteady Couette flow of an electrically conducting viscous incompressible fluid bounded by two parallel nonconducting porous plates incorporating species equation, temperature-dependent viscosity and thermal radiation. The partial differential equations governing the phenomenon were non-dimensionalized, using some dimensionless quantities. The conditions for the existence and uniqueness of solution of the model were established using Lipschitz continuity approach. The properties of solution were examined using upper and lower solution method and Kolodner and Pederson lemma. The dimensionless equations were transformed and considered in three forms: Transient state with time dependent pressure gradient; transient state with constant pressure gradient and steady state with constant pressure gradient. The equations for each case considered were solved using perturbation method and eigenfunction expansion technique and direct integration. The results obtained were presented graphically and discussed. From the results obtained, it was observed that the fluid concentration is at maximum value ( , ) 2.5 yt   when 0.5 y  while the secondary velocity is at maximum value ( , ) 8.0 w y t  when 0.5 y  . It was also observed that increase in Reynolds number and pressure gradient leads to enhancement in the velocity profiles while suction parameter, Hartman number and porosity parameter reduced velocity profiles. Also, radiation parameter enhanced the temperature profile while Reynolds number, suction parameter and Prandtl number reduced the temperature profile. Fluid flow is observed to attain maximum velocity ( ) 55 u y  when 0y  . Reynolds number, suction parameter, constant pressure gradient chemical reaction parameter and thermo diffusion parameter enhanced the concentration profile while radiation parameter and Eckert number reduced the concentration profile. The result from this research work is of importance to industries that produce domestic consumables like toothpaste and food industries in production of tomato paste and fruit juice.