Compressible laminar boundary-layer flows of a dusty gas over a semi- infinite flat plate.

*(English)*Zbl 0643.76082The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region for downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes- interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

##### MSC:

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

76T99 | Multiphase and multicomponent flows |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

76M99 | Basic methods in fluid mechanics |

##### Keywords:

compressible laminar boundary-layer flows; dilute gas-particle mixture; semi-infinite flat plate; two-phase interaction; large-slip region; moderate-slip region; small-slip region; finite-difference solutions; six-point schemes; skin friction; wall heat-transfer; Stokes-interaction relation; non-Stokes relation
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\textit{B. Y. Wang} and \textit{I. I. Glass}, J. Fluid Mech. 186, 223--241 (1988; Zbl 0643.76082)

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