0000000000163524
AUTHOR
M. T. Laitinen
Heat transfer in conducting and radiating bodies
Abstract We introduce briefly some nonlocal models for heat transfer in conducting and radiating media. The goal is to give an idea of the general mathematical structure and related existence results for such models.
Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials
In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system us…