Second-Order Model for Transient Heat Conduction in a Sphere

A second-order model to solve the transient heat conduction problems in the case of a spherical solid is developed. The solid is placed in a medium at variable temperature f(t) and a constant convection coefficient h is considered at the external surface of the sphere. When the fluid temperature is constant [F(t) = 1T], the analytical solution can be calculated by employing the separation of variables techniques. A first-order is used to calculate the first-order step response. To show the accuracy of the second-order model, the obtained step responses to the analytical solution given by the infinite series are compared. The comparison showed that the second-order model gives accurate results and is close to the analytical solution even for an infinite Biot number. The accuracy of the second-order model can ensures that the model can be used safely for engineering calculations.