Unsteady free convection from a heated sphere in the presence of internal heat generation or absorption

• This paper is concerned with the unsteady, laminar, free convective flow over a heated sphere with the effect of internal heat generation/absorption.
• As the Prandtl number, Pr, increases, the friction factor decreases while the heat transfer rate increases.
• With an increase of internal heat generation, the friction factor increases while the heat transfer rate reduces. The reverse pattern is found with the heat absorption parameter.
• The momentum and thermal boundary layers become thicker with an increase of the heat generation parameter.

This paper is concerned with an unsteady, laminar, free convective flow over a heated sphere with the effect of internal heat generation/absorption. The dimensionless governing equations have been solved employing the finite difference method as well as a perturbation method for short time and an asymptotic method for long time. We examine the effects of the physical parameters, such as, the Prandtl number, Pr, and the heat generation/absorption parameter, γ, on the friction factor and heat transfer rate as well as the velocity and temperature profiles. It is observed that when the Prandtl number, Pr, is increased, the friction factor decreases while the heat transfer rate increases. In the presence of internal heat generation, the friction factor increases while the heat transfer rate reduces. The reverse pattern is found with the heat absorption parameter. The momentum and thermal boundary layers become thicker with an increase of the heat generation parameter. A comparison among the numerical solutions, the perturbation solutions for short time and the asymptotic solutions for long time has been presented which provides a good agreement among the solutions.