A random field model based on nodal integration domain for stochastic analysis of heat transfer problems

In this paper, a random field model based on nodal integration domain is presented to solve stochastic heat transfer problems. In the proposed model, the uncertainty of the inputs are considered as random field, which is discretized into a number of node-based subdomains and the properties of the uncertainties under random field can be considered at the nodes. The proposed method is efficient to model non-uniform material under random field with constitutive equation, meanwhile, the random field with arbitrary geometry can be simulated conveniently and efficiently by using the Karhunen-Loève expansion truncated in this work. The statistical moments of the structural responses using the perturbation method is also performed and compared with the solutions of Monte Carlo simulation. The proposed method is successfully applied to the steady-state heat transfer problem with spatially varying random material parameter introduced in the thermal conductivity in this work. Finally, we demonstrate the accuracy and performance of the proposed method through a series of numerical examples both in 2D and 3D steady-state heat transfer problems under different random fields.