Stochastic modeling of heating of a one-dimensional porous slab by a flow of incompressible fluid

Abstract

This paper concentrates on an investigation of the temperature difference between the fluid and solid phases during heating of a porous slab initially at a low temperature by a flow of a higher temperature incompressible fluid for the case of a random heat transfer coefficient between the fluid and solid phases. A two energy equation model is employed to simulate the temperature difference between the solid and fluid phases. It is shown that the temperature difference forms a wave localized in space. The stochastic response of the temperature difference wave is presented in terms of the mean value and the standard deviation. In numerical examples, the probability density functions of both the uniform and truncated normal distributions are considered to simulate the random behavior of the heat transfer coefficient.