To compute thermal conductivity of nanofluids I add enthalpy term into heat flux computation, as can be seen in the attached.
Now the heat flux vector is like this:
vector[9] = {jc[0]+jv[0],jc[1]+jv[1],jc[2]+jv[2],jc[0],jc[1],jc[2],jc[0]+jv[0]+jh[0],jc[1]+jv[1]+jh[1],jc[2]+jv[2]+jh[2]}
jh means enthalpy term of heat flux, which is referenced from "J. Eapen, J. Li, and S. Yip, Phys. Rev. Lett. 98, 028302 (2007) ", title of the article is “Mechanism of Thermal Transport in Dilute Nanocolloids”
If you compute thermal conductivity of base fluids, you need not include the enthalpy term, but if you compute thermal conductivity of nanofluids, then you have to include it.
Xiaoliang

compute_heat_flux.cpp (6.32 KB)
compute_heat_flux.h (1.09 KB)