Advection and Thermal Diode

We prove that under the condition of closed boundary to mass flux, pure advection is not a valid mechanism to make a practical thermal diode. Among the various designs of thermal diodes, many of them involve circulating fluid flow, such as in thermosyphons. However, those designs often employ natural convection, which is basically a nonlinear process. It thus remains unclear how the pure advection of temperature field induced by a decoupled velocity field influences the symmetry of heat transfer. Here we study three typical models with pure advection: one with open boundary, one with closed boundary at unsteady state, and one with closed boundary at steady state. It is shown that only the last model is practical, while it cannot become a thermal diode. Finally, a general proof is given for our claim by analyzing the diffusive reciprocity.