This paper gives similarity transformations for laminar film condensation on a vertical flat plate with variable temperature distribution and finds analytical solutions for arbitrary Prandtl numbers and condensation rates. The work contrasts with Sparrow and Gregg’s assertion that wall temperature variation does not permit similarity solutions. To resolve the long debatable issue regarding heat...

In numerical Rayleigh-BCnard convection at Rayleigh number lo5 and 5 x 105, Prandtl numbers 0.07, 0.7, and 7, and aspect ratios 3, 4 or 6, large-scale patterns are sought. For aspect ratio 6 and Pr = 0.7, saturation of the mean velocity is only observed after 20 convective timescales. Three-dimensional visualization shows a strong influence of the confining sidewalls and corners for all Prandtl...

In numerical Rayleigh-B enard convection at Rayleigh number 10 5 and 5 10 5 , Prandtl numbers 0.07, 0.7, and 7, and aspect ratios 3, 4 or 6, large-scale patterns are sought. For aspect ratio 6 and P r = 0:7, saturation of the mean velocity is only observed after 20 convective timescales. Three-dimensional visualization shows a strong innuence of the connning sidewalls and corners for all Prandt...

In this study, we construct a seven-dimensional Lorenz Model (7DLM) to discuss the impact of an extended nonlinear feedback loop on solutions’ stability and illustrate the hierarchical scale dependence of chaotic solutions. Compared to the 5DLM, the 7DLM includes two additional high wavenumber modes that are selected based on an analysis of the nonlinear temperature advection term, a Jacobian t...

An experimental investigation was performed to determine the local value of heat transfer coefficient with a free-surface axisymmetric downward jet lubricating oil impinging on fixed plate. A large range Prandtl numbers considered (148<Pr<925) in order fill data gap highly viscous fluids, especially regarding measurements. In Reynolds (170 < Re 2225), dependencies similar literature were identi...

We study the asymptotic expansion of solutions to the linearized compressible Navier-Stokes equations with highly oscillatory forces in the half-plane with nonslip boundary conditions for small viscosity. The wave length of oscillations is assumed to be proportional to the square root of the viscosity. By means of asymptotic analysis, we deduce that the zero-viscosity limit of solutions satisfi...

A linear stability analysis is performed on a thermal, stratified liquid layer with a deformable thermocapillary surface. The objective is to investigate the possibility and conditions for existence of oscillatory cellular convection in the linear thermocapillary system. In general, the principle of the exchange of stabilities for the onset of cellular convection in liquid layers with deformabl...