Linear kinetic heat transfer: Moment equations, boundary conditions, and Knudsen layers

A linear kinetic equation for heat transfer is solved by means of the method of moments. The moment equations are solved with Maxwell-type boundary conditions for steady state energy transport. The results exhibit marked Knudsen boundary layers. The accuracy of the description is examined, and it is shown that already a relatively small number of moments can give satisfactory resolution of Knudsen layers for Knudsen numbers ε≤1. The implications for moment equations for more complicated kinetic equations (such as the Boltzmann equation) are discussed.