Using Burnett Equations to Derive an Analytical Solution to Pressure-Driven Gas Flow and Heat Transfer in Micro-Couette Flow

The aim of the present study is deriving an analytical solution to incompressible thermal flow in a micro-Couette geometry in the presence of a pressure gradient using Burnett equations with first- and second-order slip boundary conditions. The lower plate of the micro-Couette structure is stationary, whereas the upper plate moves at a constant velocity. Non-dimensional axial velocity and temperature profiles were obtained using the slip boundary conditions and were compared with the transition flow regime (0.1≤ Kn ≤10). The results showed that in this regime, rarefaction exerts a considerable effect on both the velocity and the temperature profiles. Because of the presence of the pressure gradient in the direction of the flow, the non-dimensional velocity and temperature profiles behave in a parabolic trend and flatten as the Knudsen number increases. The Poiseuille and Nusselt numbers, obtained using the derived analytical solution, decrease with increasing the Knudsen number. In the absence of an axial pressure gradient, the velocity profile behaves linearly and shows good agreement with the results of the previous works.