On the calculation of the Poiseuille number in the annular region for non-isothermal gas flow

A slow longitudinal non-isothermal gas flow in the annular region caused by small pressure and temperature drops across a long micro-channel is considered in the paper. A method for calculating the values of the Poiseuille number in the transitional gas flow regime is proposed. The method is based on the solution of the model linearised Bhatnagar-Gross-Krook (BGK) kinetic equation using Chebyshev polynomials. The calculated values are compared with similar results obtained using analytical solutions of the Navier–Stokes equations with no-slip and slip boundary conditions. The effect of the accommodation coefficient of the tangential momentum of the gas molecules and the gas rarefaction parameter on the change in the Poiseuille number is analysed for small ratios of the temperature and pressure gradients of the gas in the channel.