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.
The combined effects of chemical reaction, radially applied magnetic field and Hall effect on entropy generation of a steady third grade magnetohydrodynamic fluid flowing through a uniformly circular pipe was studied. The governing equations are presented and the resulting non-linear dimensionless equations are solved numerically using Galerkin Weighted Residual Method. The velocity, temperature and concentration profile were obtained and utilized in computing the entropy number. A parametric study of germane parameters involved are presented graphically and discussed. It was observed that irreversibility due to heat transfer dominates the flow compared to fluid friction and Hall parameter inhibits the Bejan number while Magnetic parameter enhances the Bejan number.
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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