The prediction of heat and mass transfer coefficients for turbulent flow in pipes at all values of the Prandtl or Schmidt number

Abstract

A simple model of turbulent heat or mass transfer based on a modified form of the Reynolds analogy, is proposed. Equations have been derived from which heat or mass transfer coefficients, and temperature or concentration profiles, may be predicted at any value of N Pr or N sc . In deriving the equations it is assumed (i) that, in pipe flow, the transport mechanism is such that there is no significant molecular transport in the turbulent core even at low N Pr , and (ii) that eddy transport is a function of the flow pattern only. The equation is of the form N St ( или N Sh) = ƒ/2 ϑ and ϑ is given both in algebraic form and as a plot of ϑ versus N Pr (or N Sc ) for smooth pipes. Computations of N' u and temperature profiles agree well with experimental data. Particular attention is given to results at low N Pr , where the assumptions made as to transport in the turbulent core have the greatest effect; in this region the proposed equations predict experimental results more closely than do other correlations. In the intermediate range of N Pr , or N Sc the proposed equations agree with other analyses, and at high values of N Sc the equations reduce to those of Lin et al. [1] which are in excellent agreement with experimental data.