The stability of a fluid layer subjected to a step change in temperature: Transient vs. frozen time analyses

Abstract

The linearized behavior of a fluid layer subjected to a step change in surface temperature is examined using two different conceptual approaches. The first approach uses initial value techniques while the second employs two common versions of the “frozen-time” hypothesis. Both surfaces are taken as rigid and conducting. Galerkin's method is used to obtain the approximate solutions, while “exact” solutions are obtained via numerical integration for certain cases. It is shown that, while the first version of the frozen time model (the marginal state analysis) is not applicable to the transient system, the second version (quasi-static analysis) is valid for large time but is of limited usefulness for most cases of interest. The effects of various initial conditions, on the velocity and temperature perturbations, are clarified and discussed. The results presented here complement those available for a semi-infinite fluid with the same boundary conditions at he top surface.