Numerical solution of unsteady turbulent free convection over a vertical flat plate

• Main Author: Remar, Jaroslav
• Format: Others
• Language: en
• Published: 2015
• Subjects: Heat; Convection; Laminar flow; Plates; Engineering
• Online Access: http://hdl.handle.net/10539/19197

A theoretical treatment of the problem of unsteady turbulent free convection over a vertical flat plate is presented in this dissertation. An exhaustive review of the relevant publications revealed, that at the present time no solution of this problem has been given. The development of a method, by which the abovementioned problem could be tackled, is a substantial part of the dissertation. The equations of conservation of mass, momentum, and energy, written in a general form, were the starting point of the derivation. Various assumptions, simplifying the partial differential equations, were introduced. In the end, boundary layer equations were obtained. Turbulence was simulated by a phenomenological model, consisting of an algebraic law of the wall and a partial differential rate equation. The turbulence model is based on the concept of effective viscosity. Also, a constant turbulent Prandtl number was employed. The problem of an isothermal plate in a stagnant non-stratified fluid was treat; d, and appropriate initial and boundary conditions were formulated„ The system of equations was solved by an explicit finite- difference method. The numerical stability criteria were established. A computer programme, based on the numerical scheme, was developed and employed for calculations. The calculations were carried out for dry air, water, and mercury, representing gases, liquids, and liquid metals, respectively. In this way, a broad range of Prandtl numbers was covered. Temperature velocity, and effective viscosity profiles are presented here together with some other results of the calculations* An important observation is that the overall heat transfer coefficient goes through a temporary minimum before attaining its steady state value. The transient, which is extremely fast, can be divided into throe characteristic stages: the initial conduction regime, an intermediate stage, and the steady state. Our results were verified by comparison with data available from other independent sources. Due to the lack of data covering ■the whole transient, only the first and third stages were considered, The initial conduction regime was compared with an analytical solution and the final steady state results with experimental data of various authors, respectively. The agreement is good and no serious discrepancies were discovered. Although the present method produces reliable results, it cannot be widely employed, because the computing times are almost prohibitive with the present-day computers.