Stochastic heat transfer in fins and transient cooling using polynomial chaos and wick products

Stochastic heat transfer problems are often solved using a perturbation approach that yields estimates of mean values and standard deviations for properties and boundary conditions that are random variables. Methods based on polynomial chaos and Wick products can be used when the randomness is a random field or white noise to describe specific realizations and to determine the statistics of the response. Polynomial chaos is best suited for problems in which the properties are strongly correlated, while the Wick product approach is most effective for variables containing white noise components. A transient lumped capacitance cooling problem and a one-dimensional fin are analyzed by both methods to demonstrate their usefulness.