Abstract
The paper contains a survey of the present status of knowledge concerning the transfer of heat by forced convection across incompressible turbulent boundary layers. The foundations of the semi-empirical theory are examined from first principles and the limitations of the theory are carefully noted. Elementary theories are described and an outline of D.B. Spalding's mathematically exact theory is given. The limiting cases of very high and very low Prandtl numbers are discussed. Finally, an outline of W. V. R. Malkus' theory of turbulent processes is sketched. A conscientious attempt has been made to clarify all physical assumptions, to identify the major fundamental problems which require attention and to indicate directions in which the semi-empirical theory can be extended.
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