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 Maxwelltype 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.