We study the extended Reynolds analogy (the relation between the shear stress and the energy flux transferred to the boundary plate) for the Rayleigh flow problem of a monatomic gas. In the case when the temperature of the undisturbed gas equal to the surface temperature we show that the extended Reynolds analogy depends weakly on time and is close to 0.5. Additionally, for the wide intervals of temperatures and velocities, we prove that at any fixed dimensionless time the extended Reynolds analogy depends on the plate velocity and temperature and undisturbed gas temperature mainly via the Eckert number. For Eckert numbers of order of unity or less we generalize an extended Reynolds analogy and show that the generalized Reynolds analogy depends mainly only on dimensionless time. Our main tool for establishing these results is the direct simulation Monte-Carlo (DSMC) method.
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