  In this paper, considering the variation of the viscous dissipative heat in
the transfer direction, a new theoretical formula for thermal conductivity
measurement was proposed based on the energy equation of the rotational Couette
flow field. This theoretical formula shows that thermal conductivity and
rheology have a synergistic effect. Based on this theoretical formula, the
rheological synergistic thermal conductivity of CMC-based Fe3O4 nanofluids and
Al2O3 nanofluids was experimentally investigated. The experimental results show
that the thermal conductivity rises with the increase of shear rate and volume
fraction, moreover, volume fraction and shear rate have mutually reinforcing
effects on thermal conductivity enhancement. Non-Newtonian effects of rheology
and heat transfer reduce with shear rate and increase with volume fraction,
with consistent synergistic effects. According to the experimental data, the
expressions of the thermal conductivity and dynamic viscosity of these two
nanofluids as functions of shear rate and volume fraction were presented.
