Mass convection Reynolds analogy

The convective mass transfer coefficient hm can be obtained from correlations similar to those of heat transfer, i.e. Equation (1.12). The Nusselt number has the counterpart Sherwood number, Sh = hml/Di, and the counterpart of the Prandtl number is the Schmidt number, Sc = p/pD. Since Pr k Sc k 0.7 for combustion gases, the Lewis number, Le = Pr/Sc = k/pDcp is approximately 1, and it can be shown that hm = hc/cp. This is a convenient way to compute the mass transfer coefficient from heat transfer results. It comes from the Reynolds analogy, which shows the equivalence of heat transfer with its corresponding mass transfer configuration for Le = 1. Fire involves both simultaneous heat and mass transfer, and therefore these relationships are important to have a complete understanding of the subject. 

Each of the modified Reynolds analogy relations (5.217) and (5.218) includes an additional Sc and Pr dependency, respectively. These relationships are often referred to as the Chilton-Colbum analogies [20, 53] (p. 364). Experimental analyses show that (5.217) and (5.218) can be used for a number of convective heat and mass transfer systems, and might be sufficiently accurate even for problems involving complex geometries [53]. 

We start this chapter with a general physical description of the convection mechanism. We then discuss (he velocity and thermal botmdary layers, and laminar and turbitlent flows. Wc continue with the discussion of the dimensionless Reynolds, Prandtl, and Nusselt nuinbers, and their physical significance. Next we derive the convection equations on the basis of mass, momentiim, and energy conservation, and obtain solutions for flow over a flat plate. We then nondimeiisionalizc Ihc convection equations, and obtain functional foiinis of friction and convection coefficients. Finally, we present analogies between momentum and heat transfer. 

Although heal transfer and mass transfer are quite analogous in these situations, none of the above equations for transfer to a sphare obey an analogy relationship between emss transfer and momentum tmasfer except at high Reynolds numbers where oaly the forced convection term is of importance. Even here only the skin friction contribution to momentum transfer can be used. 

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