Steady hydromagnetic Couette flow in a rotating system with nonconducting walls

Abstract

Steady hydromagnetic Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system with non-conducting walls is studied. Exact solution of the governing equations is obtained in closed form. Expressions for the shear stress at the lower and upper plates due to primary and secondary flows and mass flow rates in primary and secondary flow directions are also derived. Asymptotic behavior of the solution for fluid velocity and induced magnetic field is analyzed for small and large values of rotation parameter K 2 and magnetic parameter M 2 to gain further insight into the flow pattern. Heat transfer characteristics of the flow are considered taking viscous and Joule dissipations into account. The numerical solution of energy equation and numerical values of rate of heat transfer at both plates are obtained with the help of MATLAB software. The numerical values of fluid velocity, induced magnetic field and fluid temperature are depicted graphically versus channel width variable η for various values of M 2 and K 2 while numerical values of primary and secondary shear stress at the lower and upper plates, mass flow rates in primary and secondary flow directions and rate of heat transfer at the lower and upper plates are presented in tabular form for various values of K 2 and M 2 .