Mathematical Model of Unsteady MHD Couette Flow of Maxwell Viscoelastic Material and Heat Transfer with Ramped Wall Temperature

The time-dependent magnetohydrodynamic (MHD) Couette flow of Maxwell material in a rotating system with ramped wall temperature has been examined under Ohmic (Joule) heating. The Continuity equation, Cauchy’s equation of motion, the constitutive equation for the Maxwell model, and the energy equation with Ohmic heating with relevant initial and boundary conditions are all considered in obtaining a mathematical model for the investigation. The finite element technique is applied to numerically solve the non-dimensionalized governing equations using the mathematical software MATLAB. The values of Weissenberg number, Hartmann number, Eckert number, and angular velocity of the rotating system are varied, and their effects on the fluid temperature and velocity are shown graphically and discussed.