Physical Equalities Among Mass, Heat, and Momentum Transfer

2 Physical Equalities Among Mass, Heat, and Momentum Transfer 

In this section, we want to discuss situations in which mass transfer, heat transfer, and fluid flow occur at the the same rate. Such equivalence may be startling, for much of our earlier discussion emphasized differences between these processes. To be sure, the previous section described the parallel equations called Pick s law, Fourier s law, and Newton s law but this parallelism was one of mathematics. The diffusion coefficient, the thermal conductivity or diffusivity, and the viscosity all had different numerical values, and so should give different rates. 

Nonetheless, the rates of mass, heat, and momentum transfer can be essentially the same for fluids in turbulent flow. This subject was first studied by the Enghshman 

Reynolds argued that mass or heat transport into a flowing fluid must involve two simultaneous processes 1. the natural diffusion of the fluid when at rest [and] 2. the eddies caused by visible motion which mixes the fluid up and brings fresh particles into contact with the surface. He went on The first of these causes is independent of the velocity of the fluid [but] the second cause, the effect of eddies, arises entirely from the motion of the fluid. Note that Reynolds implies that any flowing fluid contains eddies. Nine years later, Reynolds discovered the distinction between laminar flow and turbulent flow, and that eddies occur only in the latter. 

These arguments have considerable value even when restricted to turbulent flow. To see this, we write expressions for the various fluxes. For example, the mass flux should be 

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