Simple form of analogy between momentum, heat and mass transfer

Simple form of analogy between momentum, heat and mass transfer 

Consider the fluid to be flowing in a direction parallel to the surface (X-direction) and for momentum and heat transfer to be taking place in a direction at right angles to the surface (Y-direction positive away from surface). 

Suppose a mass M of fluid situated at a distance from the surface to be moving wifli a velocity in the X-direction. If this element moves to the surface where the velocity is zero, it will give up its momentum in time t, say. If the temperature difference between the element and the surface is Qs and Cp is the specific heat of the fluid, the heat transferred to the surface will be M CpBs- If the surface is of area A, the rate of heat transfer is given by  

If the shear stress at the surface is Rq, it will equal the rate of change in momentum, per unit area. 

A similar argument can be applied to the mass ttansfer process when a concentration gradient exists. Thus, if the molar concentration of A remote from the surface is and at the surface it is Caw, the moles of A transferred to the surface will be (M/p) Cas — Caw), if the density (p) can be assumed to be constant over the range of concentrations encountered. Thus the moles of A transferred to the surface per unit area and unit time (—Aa) v=o is given by  

---