Characterization of energy transport by mass diffusion including an application to elliptic channel flow

Energy transport in diffusing systems is studied with special attention devoted to the transport that occurs as a result of mass diffusion,∑ cpkj→k · ∇T. Dimensionless parameters are presented for determining the importance of this transport mechanism; as an example of the application to heat and mass transfer, mixing of a binary gas in a heated, elliptic channel flow is studied. It is shown that the energy transport by mass diffusion can be an important transport mechanism which should be considered in non-isothermal systems, e.g. in CVD processes where it has often been neglected. The literature also refers to the divergence of the energy flux by species interdiffusion, ∇ · q→(d)=∇ · ∑ hkj→k. It is pointed out that this term depends on the enthalpy datum states of the species. Therefore, neglecting this term in the energy equation requires that another term also be neglected so that the resulting energy equation is independent of the enthalpy datum states. Neglecting only the divergence of the energy flux by species interdiffusion would be incorrect because the resulting energy equation would then (incorrectly) depend on the enthalpy datum states.