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Turbulent boundary layer on a plate. Reynolds analogy and new formulations of the temperature defect law
Author(s) -
Vigdorovich Igor
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510240
Subject(s) - stanton number , boundary layer , turbulence , turbulent prandtl number , prandtl number , law of the wall , mechanics , reynolds number , reynolds stress , heat flux , thermodynamics , shear velocity , film temperature , physics , heat transfer , law , nusselt number , political science
A consistent asymptotic theory describing hydrodynamic and thermal turbulent boundary layers on a flat plate in zero pressure gradient is developed. The fact that the flow depends on a limited number of governing parameters allows us to formulate algebraic closure conditions that relate the turbulent shear stress and turbulent heat flux to mean velocity and temperature gradients. As a result of an exact asymptotic solution of the boundary‐layer equations, the known laws of the wall for the velocity and temperature and the velocity and temperature defect laws as well as the expressions for the skin‐friction coefficient, Stanton number, and Reynolds‐analogy factor are obtained. The latter implies two new formulations for the temperature defect law one of which is completely similar to the velocity defect law and does not contain the Stanton number and the turbulent Prandtl number, and the other does not contain the skin‐friction coefficient. A heat‐transfer law is obtained that relates only thermal quantities. The theoretical conclusions agree well with experimental data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)