Transient heating of a semitransparent spherical body immersed into a gas with inhomogeneous temperature distribution

The transient heat conduction equation, describing heating of a body immersed into gas with inhomogeneous temperature distribution, is solved analytically, assuming that at a certain distance from the body gas temperature remains constant. This problem is a generalisation of the problem solved earlier where gas, into which the body is immersed, was assumed to be initially homogeneous. This solution is applied to the case when the distribution of gas temperature is chosen such that heat flux in gas initially does not depend on the distance from the body surface in the region close to this surface. The solution is applied to modelling body heating in conditions close to those observed in Diesel engines. It is pointed out that inhomogeneous gas temperature distribution leads to slowing down of body heating compared with the case when the body is immersed into a homogeneous gas. In a long time limit, the distribution of temperature in the body and gas does not depend on the initial distribution of gas temperature. In the case of a body immersed into an inhomogeneous gas, for large times the correction to the Newton law is shown to be essentially the same as predicted by the model, based on the assumption that gas is initially homogeneous. For short times, this correction approaches finite values, well below those predicted by the model, based on the assumption that gas is initially homogeneous. For large gas domains these values are close to 1. These results essentially confirm the earlier finding that ignoring these corrections is expected to lead to unacceptably large errors in computations.