The Knudsen number, Kn = mfp /L, is a dimensionless parameter used to describe potential micro-

The Knudsen number, Kn = λ_mfp/L, is a dimensionless parameter used to describe potential micro- or nanoscale effects. Derive an expression for the ratio of the thermal resistance due to molecule–surface collisions to the thermal resistance associated with molecule–molecule collisions, R_t,m–s/R_t,m–m, in terms of the Knudsen number, the thermal accommodation coefficient α_t, and the ratio of specific heats γ, for an ideal gas. Plot the critical Knudsen number, K_ncrit, that is associated with R_t,m–s /R_t,m-m = 0.01 versus αt, for γ = 1.4 and 1.67 (corresponding to air and helium, respectively).