Dusty Hydromagnetic Oldryod Fluid Flow in a Horizontal Channel with Volume Fraction and Energy Dissipation

An unsteady magneto-hydrodynamics flow of dusty Oldroyd fluid through a horizontal channel has been investigated under the influence of dissipation of energy and volume fraction. This energy dissipation generates the mechanism of heat transfer in the governing fluid motion and the dust particles absorb the heat through conduction. To study the dusty-visco-elastic fluid flow, Saffman model and Oldroyd model have been used. The visco-elastic responses are exhibited through the two rheological parameters 1 & 2 (relaxation time and retardation time). To restrain the weak turbulent motion, a magnetic field of strength B0 is applied along the transverse direction to the plate. The lower plate of the horizontal channel is kept fixed but the upper one is oscillating with the velocity 0 (1 + ). The governing equations of motion are solved analytically and the results are discussed graphically/ numerically for various values of flow parameters involved in the solution.