Lattice Boltzmann simulations of conjugate heat transfer in high-frequency oscillating flows

The thermal lattice Boltzmann method (LBM) is used to simulate the conjugate heat transfer of high-frequency oscillating flows between two flat plates with different outer surface temperatures. The thermal boundary condition at the fluid–solid interface assumes that the unknown energy distribution functions of the fluid and the solid are in equilibrium with the counter-slip internal energy. The counter-slip internal energy was determined by constraints in the continuities of temperature and heat flux at the solid–fluid interface. Velocity, temperature and heat flux distributions are presented for various Stokes numbers, pressure oscillation amplitudes and plate to fluid thermal conductivity ratios. For relatively low-frequency oscillations (30 kHz) and small pressure amplitudes, the periodically averaged heat fluxes of the oscillating flow are almost equal to those of pure heat conduction. The averaged heat flux of the oscillating flow decreases with increasing pressure amplitudes and are less than those of pure heat conduction for relatively low frequencies (30 kHz) and large pressure amplitude oscillations. For high-frequency oscillations, the heat transfer is enhanced markedly by nonlinear acoustic streaming, where the average velocity rapidly increases with frequency.