An investigation is made for unsteady magnetohydrodynamic (MHD) thin film flow of a third grade fluid down an inclined plane. The non-linear partial differential equation governing the flow and heat transfer are reduced to a system of non-linear algebraic equations using implicit finite difference approximation to obtain velocity and temperature profile. The effect of various physical parameter on both velocity and temperature profile obtained are studied through several graphs. It is noticed that the velocity and temperature profile decreases due to increase in third grade parameter and magnetic parameter.

In this paper, we considered the flow of an incompressible MHD third grade fluid in the annulus of concentric rotating cylinders with isothermal wall and Joule heating. The flow was assumed to be induced by the axial pressure gradient. The resulting governing equations of flow were solved using the regular perturbation method. Results showed that at an angular velocity ω =1.0 the velocity of the fluid tended to be at equilibrium but with ω < 1.0 the velocity was drastically reduced and when ω >1.0 it became greatly enhanced. Furthermore, it was shown that the temperature reduces by increasing angular velocity and Brinkman number.

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A general analysis has been developed to study the combined effect of the free convective heat and mass transfer on the unsteady two-dimensional boundary layer flow over a stretching vertical plate. The flow is subject to magnetic field normal to the plate. The governing nonlinear partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by the similarity transformations. The resulting equations are solved numerically by using Runge-Kutta the shooting technique. The effects of the Magnetic field Parameter M, buoyancy parameter N, Prandtl number Pr and Schmidt number Sc are examined on the velocity, temperature and concentration profiles. Numerical data for the skin-friction coefficients, Nusselt and Sherwood numbers have been tabulated for various parametric conditions.

The effects of shear deformation and rotary inertia on the dynamics of anisotropic plates traversed by varying moving load resting on Vlasov foundation is investigated in this work. The problem is solved for concentrated loads with simply supported boundary conditions. An analytic solution based on the Galerkin's method is used to reduce the fourth order partial differential equation into a system of coupled fourth order differential equation and a modification of the Struble's technique and Laplace transforms are used to solve the resulting fourth order differential equation. Results obtained indicate that shear deformation and rotary inertia have significant effect on the dynamics of the anisotropic plate on the Vlasov foundation. Solutions are obtained for both the moving force and the moving mass problems. From the graphical results obtained, the amplitude of vibrations of the plate under moving mass is greater than that of the moving force and increasing the value of rotary inertia R 0 reduces the amplitude of vibration of the plate. increasing the mass ratio increases the amplitude of vibration of the plate.

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