The extended Reynolds analogy for the Couette problem: Similarity parameters

We consider the extended Reynolds analogy for the Couette problem. That is, we study the relation between the shear stress and the energy flux transferred to the boundary surface at different velocities and temperatures. We use the direct simulation Monte Carlo (DSMC) method. We show that for all considered plates' velocities and temperatures the extended Reynolds analogy for a monatomic gas at any fixed Knudsen number depends on the plates' velocities and temperatures only via the Eckert number (up to statistical fluctuations). Additionally, we generalize an extended Reynolds analogy. For a monatomic gas in the transitional flow regime we show that the generalized Reynolds analogy up to statistical fluctuations depends only on Knudsen number for all considered Eckert numbers. For a gas at any Knudsen number as well as for liquid we show that the sum of the Reynolds analogies for the upper and lower plates in the Couette problem is exactly one.