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Heat transfer simulation in stirring boundary layer using the semiempirical turbulence theory. (Russian. English summary) Zbl 1413.80001
Summary: 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 \(20\,000\leq \mathrm{Re}\leq 30\,000\) of the Reynolds number on the experimental not exceed 7%.
MSC:
80A17 Thermodynamics of continua
76F40 Turbulent boundary layers
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[1] [1] Yudaev B. N., Teploperedacha [Heat Transfer], Vysshaia shkola, Moscow, 1981, 319 pp. (In Russian)
[2] [2] Loytsansky L. G., Mekhanika zhidkosti i gaza [Fluid and gas mechanics], Drofa, Moscow, 2003, 840 pp.
[3] [3] Isaev S. I., Kozhinov I. A., Kofanov V. I., etc., Teoriia teplomassoobmena [Theory of heat and mass transfer], ed. A. I. Leont’ev, Vysshaia shkola, Moscow, 1979, 496 pp. (In Russian)
[4] [4] Mikheev M. A., Mikheeva I. M., Osnovy teploperedachi [Fundamentals of heat transfer], Energiia, Moscow, 1977, 344 pp. (In Russian)
[5] [5] Pribytkov I. A., Levitsky I. A., Teoreticheskie osnovy teplotekhniki [Theoretical fundamentals of heat engineering], Akademiia, Moscow, 2004, 465 pp. (In Russian)
[6] [6] Shlikhting G., Teoriia pogranichnogo sloia [Boundary layer theory], Nauka, Moscow, 1969, 742 pp. (In Russian)
[7] [7] Stefanyuk E. V., Kudinov V. A., “Obtaining analytical solutions of equations of hydrodynamic and thermal boundary layers by means of introduction of additional boundary conditions”, High Temperature, 48:2 (2010), 272–284
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