In the current study, direct simulation Monte Carlo DSMC method is applied to obtain entropy, entropy generation, heat flux and the local gradient Knudsen number in the nano thermal cavity. In this geometry, the heat flux boundary condition is imposed on the bottom wall by the iterative method. The rarefaction effects are surveyed on entropy and entropy generation at slip and early transition regimes. Our investigation shows that the distribution of entropy contour in the rarefied gas is similar to the temperature contour. The formula of entropy generation has two main terms, i.e., thermal and fluid terms that the consequence of them shows the highest rate entropy generates at the bottom corns of thermal cavity. The increase of the non-equilibrium triggers the rise of entropy generation. We investigate the appropriate definition for the local gradient Knudsen number. The local gradient Knudsen number contours are like entropy generation. It means that in regions with the highest rarefaction effect, the largest entropy is produced.

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