We consider in this paper the gas dynamic field associated with liquid-vapour phase change between two parallel liquid surfaces. The full nonlinear equations for a compressible, viscous, heat conducting gas are considered with no limitations on the Mach number. First the inviscid problem is formulated and the exact solutions found for the temperature and velocity fields. While these solutions are qualitatively similar to those found using linearized analyses significant quantitative differences exist, especially at higher mass fluxes. Next the nonlinear, viscous field is obtained for a vapour with a Prandtl number of 0.75, as the equations simplify for this case. The results obtained show dramatic departures from the inviscid solutions: the temperature profiles, which may no longer be monotonic, can manifest both undershoots and overshoots. Cases exist, whose relevance to the phase change problem is yet to be established, where the overshoot is many times the applied temperature difference. Asymptotic solutions are also developed for small and large values of the height parameter
§/H
which show interesting features; for small heights the temperature profile is, surprisingly, quadratic in
y
while for large heights the flow field is uniform with boundary layers at both surfaces. The restriction on the Prandtl number is then removed. The solutions for arbitrary Prandtl number are shown to merge smoothly to the appropriate inviscid solution as Pr-> 0. These solutions also show that
Pr
= 3/4 is a very good approximation for most gases and vapours of interest. The remarkable predictions that have been made here show that the role of viscosity in the gas dynamic field in liquid vapour phase change has so far been vastly underestimated. The present results will necessitate serious rethinking on the inviscid, linearized theoretical framework that has so far, by and large, been used. These results will also have a serious bearing on any future experimental investigations of the phenomenon.
Liquid-Vapour Phase Change Rates and Interfacial Entropy Production