The flow of a rarefied gas in a rectangular enclosure due to the non-isothermal walls with no synergetic contributions from external force fields is investigated. The top and bottom walls are maintained at constant but different temperatures and along the lateral walls a linear temperature profile is assumed. Modeling is based on the direct numerical solution of the Shakhov kinetic equation and the Direct Simulation Monte Carlo (DSMC) method. Solving the problem both deterministically and stochastically allows a systematic comparison and verification of the results as well as the exploitation of the numerical advantages of each approach in the investigation of the involved flow and heat transfer phenomena. The thermally induced flow is simulated in terms of three dimensionless parameters characterizing the problem, namely, the reference Knudsen number, the temperature ratio of the bottom over the top plates, and the enclosure aspect ratio. Their effect on the flow configuration and bulk quantities is thoroughly examined. Along the side walls, the gas flows at small Knudsen numbers from cold-to-hot, while as the Knudsen number is increased the gas flows from hot-to-cold and the thermally induced flow configuration becomes more complex. These flow patterns with the hot-to-cold flow to be extended to the whole length of the non-isothermal side walls may exist even at small temperature differences and then, they are enhanced as the temperature difference between the top and bottom plates is increased. The cavity aspect ratio also influences this flow configuration and the hot-to-cold flow is becoming more dominant as the depth compared to the width of the cavity is increased. To further analyze the flow patterns a novel solution decomposition into ballistic and collision parts is introduced. This is achieved by accordingly modifying the indexing process of the typical DSMC algorithm. The contribution of each part of the solution is separately examined and a physical interpretation of the flow configuration, including the hot-to-cold flow close to the side walls, in the whole range of the Knudsen number is provided.

The well-known Knudsen paradox observed in pressure driven rarefied gas flows through long capillaries is quantitatively explored by decomposing the particle distribution function into its ballistic and collision parts. The classical channel, tube, and duct Poiseuille flows are considered. The solution is obtained by a typical direct simulation Monte Carlo algorithm supplemented by a suitable particle decomposition indexation process. It is computationally confirmed that in the free-molecular and early transition regimes the reduction rate of the ballistic flow is larger than the increase rate of the collision flow deducing the Knudsen minimum of the overall flow. This description interprets in a precise, quantitative manner the appearance of the Knudsen minimum and verifies previously reported qualitative physical arguments.

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