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The effects of magnetic field and porosity on non-coaxial rotation of incompressible second grade fluid in mixed convection flow have been studied in this article. The problem is modelled in terms of partial differential governing equations with initial and oscillating boundary conditions. These equations are transformed into non-dimensional forms by using the suitable non-dimensional variables. The exact solutions are obtained by using the Laplace transform technique. Expressions for velocity and temperature are obtained. Numerical computations carried out and the results are plotted. The effects of various embedded parameters such as second grade fluid, magnetic, porosity, Prandtl number and Grashof number are discussed. It is found that, when porosity increases, both primary and secondary velocities increase, but quite the opposite effect is noted for magnetic field. Exact solutions obtained in this study can be used as a references for other results obtained via experimental and numerical schemes. [ABSTRACT FROM AUTHOR]

In this paper, the boundary layer magnetohydrodynamics (MHD) flow of Williamson nanofluids over a stretching sheet with Newtonian heating in the presence of thermal radiation effect is analyzed. Using a similarity transformation, the governing equations are reduced to a set of nonlinear ordinary differential equations (ODEs). These equations are solved numerically using a shooting method. The effects of Williamson parameter, magnetic parameter, radiation parameter, Prandtl number, Lewis number, Schmidt number, heat capacities ratio, thermophoretic diffusivity and conjugate parameter on velocity, temperature and concentration fields are shown graphically and discussed. It is found that the rate of heat transfer is higher for Williamson nanofluids compared to the classical viscous fluid. Also, the comparisons with existing results are provided in the literature. [ABSTRACT FROM AUTHOR]

This article discussed the effect of ramped wall temperature on rotating second grade fluid in mixed convection flow. The unsteady two dimensional momentum and energy equations of the incompressible fluid are modelled in the form of partial differential equations with initial and oscillating boundary conditions. The governing equations are transformed into non dimensional equations by using the corresponding non dimensional variables. The Laplace transform method is applied into non dimensional equations in order to obtain the analytical solutions of velocity and temperature profiles. Computations are carried out and presented graphically to analyse the effect of second grade fluid parameter, rotation parameter, Grashof number, phase angle, Prandtl number and time on the profiles. It is found that, when Grashof number increases, the velocity increases in primary and secondary velocities. Both velocity and temperature are observed decrease when phase angle and Prandtl number increase. It can be concluded that, the velocity profiles in rotating flow obtained in this study is lower to compare with non-rotating flow. Whereas, the temperature profiles are remain the same for both cases. It is worth to mention that, the exact solutions obtained in this study can be used to check the correctness of the results obtained through numerical schemes. [ABSTRACT FROM AUTHOR]

An analysis to establish the exact solution of second grade fluid problem for unsteady magneto hydrodynamic (MHD) flows and rotating effects past an infinite inclined plate in a porous medium is presented in this paper. It is assumed that the bounding infinite inclined plate has an isothermal plate. Based on Boussinesq approximation the expressions for dimensionless velocity, temperature and concentration are obtained by using Laplace transform method. The derived solutions satisfying the involved differential equations with imposed boundary and initial conditions. The graphical result on the influence of various parameters on the velocity has been analyzed and discussed in this paper. [ABSTRACT FROM AUTHOR]

The effects of rotation on coupled heat and mass transfer by unsteady magnetohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate has been investigated. Exact solution using Laplace transforms technique has been obtained for the velocity, temperature and concentration fields. The analytical expressions for nondimensional skin-friction, Nusselt number and Sherwood number have been computed. The solutions of rotation parameters and inclination angle influences the flow fields have been discussed in detail. It is found that inclination angle tend to retard fluid flow in the primary and secondary flow directions, whereas rotation has a retarding influences on the primary flow direction but to accelerate in the secondary flow direction. [ABSTRACT FROM AUTHOR]