On solving nonlinear transient heat transfer problems with random parameters Original Research Article

A variational methodology is proposed for nonlinear transient heat transfer systems with random parameters defined by their first two probabilistic moments. The finite element formalism is based on the combination of the second-order perturbation and mean-based second moment analysis. A hierarchical system of first-order partial differential equations is obtained and solved for the first two probabilistic moments of the random temperature field. Numerical aspects of the problem are discussed and illustrative results are given. The approach presented may be employed for a wide class of field problems.