Heat transfer simulation in stirring boundary layer using the semiempirical turbulence theory

I. V. Kudinov ; A. N. Branfileva ; A. V. Eremin ; M. P. Skvortsova

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 157-169.

Résumé

The dynamic and thermal boundary layer equations are derived for the stirring boundary layer using Prandtl semiempirical turbulence theory. Based on definition of the thermal perturbations front and supplementary boundary conditions the method of constructing an exact analytical solution of the boundary value problem simulating the formation of the thermal boundary layer in the dynamic boundary layer is obtained and applied to find the exact analytical solutions of thermal boundary layer differential equation almost with a given degree of accuracy. The velocity distribution in stirring dynamic boundary layer and its thickness were taken by the well — known relations, found from experiments. The supplementary conditions fulfillment is equivalent to the fulfillment of the initial differential equation in the boundary point and in the thermal perturbations front. So, the more supplementary conditions we use the better fulfillment of the initial differential equation in the thermal boundary layer we have, because the range of thermal perturbations front changing includes the whole range of transverse spatial variable changing. Analysis of calculations results allows to conclude that the layer thickness within a stirring dynamic boundary layer more than twice less than thermal layer thickness in a laminar dynamic boundary layer. The study of the received in this paper criteria-based equation shows that the difference of heat transfer coefficients in the range $20\,000\leqslant {\rm Re}\leqslant 30\,000$ of the Reynolds number on the experimental not exceed $7$ %.

Détail

Keywords: stirring dynamic and thermal border layers, semiempirical theory of turbulence, integral method of heat balance, supplementary boundary conditions, criteria-based heat transfer equation.
Mots-clés : thermal perturbations front

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