A numerical analysis of the Graetz problem using the method of moments

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.In this paper, we investigate the classic Graetz problem which is concerned with the thermal development length of a fluid flowing in a pipe or channel. In our particular study, we are interested in the thermal development length associated with a rarefied gas in a 2D channel. When the gas is in a rarefied state, the boundary conditions have to be modified to account for velocity-slip and temperature-jump. Although a number of previous studies have considered rarefaction effects, they have usually taken the form of modifying the boundary conditions of the Navier-Stokes equations. Our study has involved using the Method of Moments, which represents a higher-order set of equations involving transport of stress and heat flux. The results show that the moment method captures the non-equilibrium flow features and is in good agreement with kinetic data.