Thermal transpiration and mechanocaloric effect in a long cylindrical tube are studied by use of the Hansen and Morse polyatomic gas model of the linearized Wang–Chang and Uhlenbeck equation and Maxwellian diffuse–specular reflection model for the gas–surface interaction. For all rarefactions, the dimensionless phenomenological coefficients for mass and energy flows due to axial pressure and temperature gradients are calculated as a function of the fraction of incident molecules that are reflected diffusely at the surface. The calculated thermal transpiration effect ratios were compared with the experimental data to obtain α for Xe, Ar, Ne, He, and H2, and CO2 in the transition flow regime, and Kr, Ar, Ne, and He in the near-continuum regime. The values of α were found to lie in the range of 0.8–1.0 and are in general agreement with the reported experimental results.