Analytical prediction of heat transfer by unsteady natural convection at vertical flat plates in air

Abstract

The following study presents an analytical calculation procedure which allows a prediction of the heat transfer by unsteady natural convection at vertical flat plates in air. The development of this procedure relies on experimental investigations and phenomenological observations of a previous elaboration, which included laminar, transitional and turbulent flow regimes with Grashof numbers of up to 5.5×1010 (isothermal surface) or 2.0×1013 (homogeneous heat flux density). Thereby, the mean deviation of heat transfer by unsteady natural convection from a quasi-stationary approach is approximated for cyclic and step-like variations of the boundary conditions. Furthermore, the model allows to predict the temporal development of the momentary convective heat transfer in the unsteady case. The calculation procedure is based on a physical model in which a variable proportion of potential and kinetic energy of the fluid molecules is assumed for the unsteady case. A validation of the prediction results shows a good overall agreement with the referenced measurement data both for the mean deviations of the unsteady heat transfer from a quasi-stationary approach and for the corresponding momentary values.