Heat conduction in the hollow sphere with a power-law variation of the external heat transfer coefficient

The conduction phenomenon in an insulated sphere is re-worked through a dimensionless approach, where the heat transfer coefficient dependence on the external radius and on the surface temperature, as in the case of forced and free convection, is taken into account. Assuming a power law variation of the convection coefficient [1, 2], and using the results of Sparrow [3], equations and graphs for the most important dimensionless parameters are presented. The developed equations show, for example, that as the insulation thickness increases the heat transfer rate tends to a positive value, independent of the considered case: constant convection coefficient, forced or free convection.