Uncertainty quantification of heat transfer in a microchannel heat sink with random surface roughness

Abstract

To numerically investigate the stochastic heat transfer performance of a microchannel heat sink, a randomly generated, rough surface profile with a prespecified autocorrelation function is applied to its bottom surface. The magnitude of the maximum relative roughness of the surface is treated as a Gaussian random input with specified uncertainty, and uncertainty in the output is modeled via polynomial chaos expansions. According to deterministic analysis of the simulation results, an increase in surface roughness enhances the heat transfer. As found through stochastic analysis of the joint probability density functions of the local surface height and local Nusselt number, the local surface height alone is insufficient to explain changes in the local Nusselt number, and the sensitivity of the local Nusselt number to other factors increases with the absolute value of the local surface height. Polynomial chaos expansions are used to identify the peaks and ridges of the surface as regions where the Nusselt number and velocity magnitude are more sensitive to the local surface roughness than in valleys. Probability density functions are estimated from the polynomial chaos expansions of the local Nusselt number, spanwise-averaged Nusselt number, and three global outputs: the average Nusselt number over the rough bottom surface, the pressure drop over the channel, and the performance factor of the bottom surface. Because of nonlinear propagation of the Gaussian random input, the distributions of the local and spanwise-averaged Nusselt numbers can not generally be assumed to have a Gaussian shape. In contrast, the global outputs can be treated as Gaussian as a good approximation.