Exact solutions of free convection flow in rotating magnetohydrodynamics second grade fluid past an infinite vertical plate

Abstract

The second grade fluid is one of the most popular subclass of non-Newtonian fluids. Due to their importance in industry and engineering, most of researchers have concentrated on the flows dealing with these fluids. Therefore, the main purpose of this thesis is to obtain exact solutions for unsteady free convection flows of rotating second grade fluid with the effects of isothermal and ramped wall temperatures. Specifically, a free convection flow is studied in the presence of magnetohydrodynamics and porosity. Using the constitutive equations, the governing equations are modeled. Some suitable non-dimensional variables are used to write these equations into non-dimensional form. Laplace transform method is used to solve these equation with imposed initial and boundary conditions. Solutions for velocity and temperature fields are obtained. Skin friction and Nusselt number are also evaluated. For the sake of physical understanding, analytical results for velocity are plotted graphically for the emerging flow parameters. As the velocity is a complex function, the graphs for both real and imaginary parts are shown separately. Both cases, isothermal and ramped wall temperatures, are discussed. It is observed that when the second grade parameter increases, the velocity shows an oscillating behavior which decreases and then increases, for both real and imaginary parts. For larger values of rotation parameter, the fluid velocity decreases for the real part whereas it increases for the imaginary part. It is further noted that velocity decreases when magnetic parameter increases for both real and imaginary parts. However, an opposite behavior is observed when the porosity parameter is increased. Both real and imaginary parts of the velocity are found to increase with increasing values of the porosity parameter. An interesting result for the velocity is observed from the comparison of ramped and isothermal temperatures. It is found that fluid moves slowly in case of ramped wall temperature compared to isothermal case. In limiting cases, the present solutions are found identical to published results.