Abstract
Rayleigh's problem for perfect compressible fluid is studied analytically, following the principles outlined by Howarth. It is assumed that the initial temperature jump is small in comparison with the temperature at rest, that is, e=|T w -T o |/T o is a small parameter. Moreover, the Mach number is assumed to be of order of e1/2, and using the requirement of equal order of smallness for important terms of the Navier-Stokes equations one is able to determine the scales of all dimensional variables. The final set of dimensionless equations is obtained by setting a limit e→0. Solution for the main component of velocity is expressed in closed form, and that for the variable part of temperature in integral form valid for any Prandtl number. Initial approximations for secondary velocity and density are also expressed in integral form. For a special case of Pr=3ϰ/4, using an expansion of a dissipative function in terms of Hermite polynomials, one obtains closed-form expressions for every unknown quantity in any approximation.
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