Solving stochastic heat transfer problems

Abstract

Randomness in heat transfer problems is found in both the sources (input) and in the properties. In contrast to structural problems in which damping tends to be small or moderate, in heat transfer it is the dominant effect. As a consequence the resulting temperature fields are almost always random fields whose statistical properties vary strongly with time. The evolution of these properties is best determined through the polynomial chaos approach. However, the full solution is usually so computationally expensive that simpler and more approximate approaches are often used.