The extended Graetz problem with specified heat flux for multicomponent fluids with Soret and Dufour effects

A simple and efficient method for solving the extended Graetz problem with specified heat flux in a circular pipe for a multicomponent fluid with Soret and Dufour effects is proposed. With a help of linear transformation of temperature and concentrations, the mass transfer equation and boundary conditions for each component are reduced to the form, which is completely identical to the thermal Graetz problem. The case when only the Soret effect is relevant is studied separately. It is shown that the above-described reduction fails when thermal and solutal Peclet numbers are equal. An alternative method of solution is proposed in this case. Examples of heat and mass transfer in a circular pipe for low Peclet numbers in a model fluid and for high Peclet numbers in the water-alumina nanofluid are considered. The proposed method can be extended to a parallel plate channel as well as annular region between cylindrical pipes with specified heat flux. However, the method cannot be applied to problems, where the temperature is specified on the impermeable pipe wall.