The linearized Boltzmann equation with Cercignani–Lampis boundary conditions: Heat transfer in a gas confined by two plane-parallel surfaces

Abstract

The analytical discrete-ordinates method is used to solve the problem of heat transfer for a single-species gas confined by two plane-parallel surfaces. The formulation of the problem is based on the linearized Boltzmann equation for rigid-sphere interactions between gas particles and the Cercignani–Lampis kernel for gas–surface interactions. Accurate numerical results are reported for the density, temperature, and heat-flow perturbations from a reference (equilibrium) state and are compared with similar results from five kinetic models. An interesting finding of this work is that there are combinations of the four numerical values of the accommodation coefficients used to define the Cercignani–Lampis boundary conditions that give rise to heat flows that are larger for the transition regime than for the free-molecular regime, an effect not observed when the standard (Maxwell) boundary conditions are used.