Theory of thermomolecular pressure and of the mechanocaloric effect in a cylindrical channel

A new method to measure the thermal slip coefficient

“…This is a first order solution of the Stokes equations following 1=d. An improvement can be obtained by applying the integro-moment method to the S-model or the BGK kinetic model equations [24,25]. The final representation of the thermal creep mass flow rate for large rarefaction parameters can then be expressed as an expansion in series of 1=d [5].…”

“…On the other hand, by using the integro-moment, method more terms in the expression of the mass flow rate may be found in [24]. Applying this asymptotic methodology (Section 3.3), the experimental values of the mass flow rate _ M T ðd m Þ were fitted through the coefficients A F ; B F ; C F according to expression (27) for a rarefaction parameter d m ranging from 2:8 to 40.…”

“…The coefficients in Eq. (20) as obtained by [24], were A T ¼ 1:125; B T ¼ À1:4687 and C T ¼ 0:6704. It is possible to rewrite the previous expression in the following form…”

“…The final representation of the thermal creep mass flow rate for large rarefaction parameters can then be expressed as an expansion in series of 1=d [5]. The expression of the mass flow rate, used in this work, was obtained by [24] from the S-model kinetic equation and it reads…”

“…Firstly, we extracted the values of the thermal slip coefficient by using the analytical solution of the Stokes equation when imposing the thermal slip boundary condition at the wall (Section 3.1). Secondly, by using the expression of the mass flow rate as a function of 1=d m , as it was obtained in [24] (Section 3.3).…”