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Unsteady laminar flow of gas near an infinite flat plate

Published online by Cambridge University Press:  24 October 2008

C. R. Illingworth
C. R. Illingworth
Affiliation:
Department of MathematicsUniversity of Manchester
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Abstract

Boundary-layer equations for the unsteady flow near an effectively infinite flat plate set into motion in its own plane are subjected to von Mises's transformation. Solutions are obtained for the flows in which gravity is neglected, the Prandtl number σ is arbitrary, and the plate has a constant temperature and a velocity that is either uniform or, with dissipation neglected, non-uniform. Explicit solutions are obtained for the case in which the viscosity μr varies directly as the absolute temperature Tr. Solutions are also obtained for the diffusion of a plane vortex sheet in a gas, and for the boundary layer near a uniformly accelerated plate of constant temperature when gravity is not neglected. For the non-uniform motion of a heat-insulated plate, dissipation not being negligible, a solution is obtained when σ is 1 and μr ∝ Tr. The relative importance of free convection due to gravity and forced convection due to viscosity is discussed, and a solution is obtained, with μr ∝ Tr, for the free convection current set up near a plate that is at rest in a gas at a temperature different from that of the plate, dissipation being neglected.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 4 , October 1950 , pp. 603 - 613
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

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