By just applying a temperature difference to a micro-system filled with rarefied gas, it is possible to engender a displacement or a compression of the gas in the temperature gradient direction. This is the Thermal Transpiration phenomenon. In the present work, thermal transpiration has been studied both through an experimental approach, which exploits an original measuring system, and through a numerical approach, which is modeled on the basis of the Shakhov model kinetic equation. In both studies, a circular cross section glass micro-tube is submitted to a temperature gradient. The obtained results for Helium, such as the thermal molecular pressure difference, the thermal molecular pressure ratio and the thermal molecular pressure exponent at the final zero-flow stage, are analyzed in the case of a tube submitted to a temperature difference of 51 K. Finally, the obtained thermal molecular pressure ratio results are also compared to the semi-empirical formulas of Liang (1951) and Takaishi and Sensui (1963). These semi-empirical formulas are still in use nowadays to introduce correction factors for pressure measurements done when the pressure gauge functions at different temperatures in respect to the temperature of the operating gas. For the here working pressure conditions and the used tube dimensions the gas rarefaction conditions go from near free molecular to slip regime.