Mathematical modelling of the nonlinear heat transfer process in a gray shell surrounded by a non-participating medium (Q1371534)

When a heat conducting ``thin'' shell exchanges heat with the sorrounding medium by means of radiation, a fraction of the radiation emitted and reflected by a surface element of the shell surface reaches other points of the same body. Such a complex situation gives rise to a heat conduction model in which heat sources are due not only to internal heat production and to external impingent radiation, but also to the overall contribution of the radiation coming from the shell surface. This amounts in integral terms containing the fourth power of the absolute temperature \(T\) and complicated coefficients related to the geometry of the body and to its radiative properties. Such a model has been proved to possess a unique solution satisfying the requirement \(T>0\). The technique employed is a successive approximations method.