Numerical investigations on magnetic field modeling for Carreau non-Newtonian fluid flow past an isothermal sphere

Abstract

In the current study, the effects of radial magnetic field, slip and jump conditions on the steady two-dimensional free convective boundary layer flow over an external surface of an isothermal sphere for an electro-conductive polymer are numerically studied. It is assumed that the studied fluid has a non-Newtonian rheological behavior and follows the Carreau fluid model. In this investigation, the formulation of the Carreau fluid model has been used first time for describing the present boundary layer problem, and then the resulting partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller-Box method. The finding results show that a weak elevation in temperature is accompanied with the increase in the Carreau fluid parameter, whereas a significant acceleration in the flow is computed near the sphere surface. It is shown also that an increase in the thermal slip parameter allows to strongly decrease both the skin friction coefficient and the local Nusselt number. The skin friction coefficient is also depressed with increasing magnetic body force parameter. Moreover, it is observed that an increase in the momentum slip parameter allows to decrease the skin friction coefficient, whereas the local Nusselt number is reduced with the increase in the Carreau fluid parameter. It is found also that the skin friction coefficient is increased with greater stream-wise coordinate, whereas the local Nusselt number is reduced with the increase in this parameter.