THE RAYLEIGH PROBLEM IN A RADIATING COMPRESSIBLE GAS. PART I: PLATE MACH NUMBER FINITE,
Abstract
The flow of a compressible, viscous, heat-conducting, radiating gray gas near a flat plate set impulsively in motion in its own plane is considered and solved in certain limiting cases. The problem is formulated for general values of the Boltzmann number Bo (convection -radiation ratio). The plate Mach number is assumed to be sufficiently large so that a significant amount of heat is generated by dissipation but not so large that the orders of magnitude of the thermophysical properties are changed. Asymptotic expansions are made for large ratio of the photon to molecular mean free path, N, taking into account the effect of Bo. In the limit N approaching infinity, with Bo finite and plate temperature equal to the temperature of the gas at rest, the asymptotically optimal scalings split the problem into an optically thin, compressible, viscous boundary layer with radiative emission but no self-absorption and an optically finite, inviscid, acoustic flow with full radiative interaction. The inviscid region beyond the boundary layer may be treated at the acoustic level because the velocity transverse to the plate is small compared with that parallel to the plate, and because the energy transported by radiation is small since the boundary layer is very thin even though it may be emitting quite intensively. The equations in the boundary layer and in the inviscid region are solved numerically for several representative cases. It is found that the velocity profile in the boundary layer is only weakly affected by radiation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1966
- Accession Number
- AD0631734
Entities
People
- Alexander Solan
- Ira M. Cohen
Organizations
- Brown University