Modeling of heat transfer in free down flowing laminar liquid films with development wavy structure at the regime of evaporation from the interface

Abstract

A mathematical model of heat transfer in laminar, heated to the saturation temperatures liquid films with the developed wavy structures on the free interface have been developed. The model takes into consideration cyclic relaxation of transient temperature field which happens right after the passage of a powerful big wave. The developed mathematical model describes the time history of the two dimensional temperature fields as a function of the Peclet number and the core characteristic of the wavy motion (the length of big waves). Based upon the proposed model a set of correlations have been obtained. These are proposed as a means for the generalization of heat transfer experimental data, obtained within the experimental studies of liquid films, heated to the saturation temperatures and evaporating from the interface. A generalized equation has been derived, which can be used for the calculations of Heat Transfer Coefficients (HTC) to the saturated sugar solutions liquid films. This equation contains wavy characteristics of down flowing films and valid within the range of parameters characteristic for the sugar industry evaporators, namely: concentrations – 0…70 % dry matter; liquid mass flow rate density–0.01×10-3…0.6×10-3 m2/sec, the Peclet number range – 400…25000. The mathematical model of the temperature field cyclic relaxation turned out efficient for generalization of heat transfer experimental data not only laminar, but turbulent liquid films either, despite of the fact that the transport equations do not contain turbulent characteristics.