Unsteady hydromagnetic Couette flow of fluid-particle suspension in a porous channel

Semi-analytic solution representing the time-dependent Couette flow of conducting fluid-particle in a permeable channel is presented in the existence of a magnetic field. The magnetic field is anticipated to be positioned either with the conducting fluid-particle or positioned with the moving wall. Solution to the coupled flow equations is found and given in the Laplace domain. Expressions for fluid-particle velocity and their corresponding skin friction are also found. Influence of a number of flow parameters on flow formation in the permeable channel is demonstrated. Results indicate that, increase in Hartmann number dampens both fluid velocity and particle fluid velocity when the magnetic field is positioned relative to the conducting fluid, while it augments the flow when the magnetic field is positioned relative to the moving plate. In conclusion, it is realized that growing the injection velocity augments the momentum boundary layer yielding an increase in fluid-particle velocity.