Mixed Convection Boundary Layer Flow from a Solid Sphere with Newtonian Heating in a Micropolar Fluid

Abstract

The steady mixed convection boundary layer flow from a solid sphere in a micropolar fluid, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The governing boundary layer equations are first transformed into a system of nondimensional equations via the non-dimensional variables, and then into nonsimilar equations before they are solved numerically using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient, wall temperature and heat transfer coefficient, as well as the velocity and temperature profiles with several parameters considered, namely the mixed convection parameter, the material or micropolar parameter, and the Prandtl number.

Effects of pressure stress work and thermal radiation on free convection flow around a sphere embedded in a porous medium with Newtonian heating

“…The results are obtained in terms of velocity profiles, temperature distributions, skin friction coefficient, and the rate of heat transfer and presented graphically and tabular form for selected values of the thermal radiation parameter, Darcy number, Newtonian heating parameter, and the pressure stress work. In order to verify the accuracy of the present method, the present results are compared with those reported by Salleh et al [18]. It is found that the agreement between the previously published results with the present ones is very good, as shown in the tab.…”

“…Table 1. Comparisons of the present numerical results of C f for the Pr = 0.7, 1, and 7.0 without effect of the thermal radiation-conduction, stress work, and porous medium with those obtained by Salleh et al [18] x Pr = 0. The effect of radiation parameter on skin friction and rate of heat transfer, Nu, are considered in tab.…”

“…The non-linear system of PDE (15) and (16) subjected to the boundary condition and (17) and (18) is solved numerically by using an implicit finite difference method together with Newtons linearization scheme which was first introduced by Keller [19] and described by Cebeci and Bradshaw [19]. The computations were performed using non-uniform grid in the y-direction and it was defined by y i = sin h[(j -1) / 100] where j = 1,2,..., 170 and Δx = 0.01.…”

“…Chaudhary and Jain [16] studied unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating. Recently, Salleh et al [17,18] studied the effect of Newtonian heating on mixed and free convection boundary-layer flow on a solid sphere in a micropolar fluid.…”

Numerical solutions of radiation effect on magnetohydrodynamic free convection boundary layer flow about a solid sphere with Newtonian heating

“…Pop et al [11] presented results for the problem of free convection boundary layer flow along a vertical surface in a porous medium with newtonian heating. Recently, Salleh et al [12][13][14][15] studied the free and mixed convection boundary layer flows past a sphere with Newtonian heating in a viscous and micropolar fluid using the Keller-box method.…”