Graetz problem with coupled heat and mass flows

Example 7.4 Modified Graetz problem with coupled heat and mass flows The Graetz problem originally addressed heat transfer to a pure fluid without the axial conduction with various boundary conditions. However, later the Graetz problem was transformed to describe various heat and mass transfer problems, where mostly heat and mass flows are uncoupled. In drying processes, however, some researchers have considered the thermal diffusion flow of moisture caused by a temperature gradient. 

Consider a fully developed flow of a Newtonian fluid between parallel plates with a parabolic velocity distribution 

Ds and Dd are the coefficients representing the Soret and Dufour effects, respectively, Du is the self-diffusion coefficient, and Dik is the diffusion coefficient between components / and k. Equations (7.149) and (7.150) may be nonlinear because of, for example, reference frame differences, an anisotropic medium for heat and mass transfer, and temperature- and concentration-dependent thermal conductivity and diffusion coefficients. 

Substitution of Eqs. (7.149) and (7.150) into mass and heat balance equations yield 

The boundary conditions for temperature of the upper (U) and lower (L) plates are 

---

Example 7.6 Modified Graetz problem with coupled heat and mass flows... 

---