Lattice Boltzmann study on size effect with geometrical bending on phonon heat conduction in a nanoduct

Abstract

Phonon heat transport based on the Boltzmann transport equation (BTE) in a free standing, bent duct with characteristic dimension down to the nanoscale is investigated through the lattice Boltzmann (LB) method. Both the thermal excited transverse and longitudinal phonons are considered. The collision term in BTE is approximated by the relaxation time approximation. Both diffusive and specular phonon scatterings at duct surfaces are considered. An analytical expression for thermal conductivity suitable for an infinitely long, straight duct with constant properties is derived. Results show that the size effect depends strongly on the Knudsen number. For large Knudsen number, heat transport is mainly dominated by the ballistics that results in strong size effect, and vice versa. For the bent duct more phonons take the passageway near the inner corner of the bending region where higher local thermal conductivity is expected. Although the specular boundary scattering introduces no change in the bulk quantities for a straight duct, it, however, brings in the geometric influence as the duct is bent. Compared to the straight duct, the bent duct has the supremacy in conducting heat as the Knudsen number is small. Conversely the straight duct presents higher conductivity when the Knudsen number is large. By the present LB method, jumps in macroscopic quantities, occurring at boundary and wall surface, can be calculated naturally and straightforwardly.