International Journal of Heat and Mass Transfer, Vol.83, 51-63, 2015
Modified ballistic-diffusive equations for transient non-continuum heat conduction
For the modeling of non-continuum phonon transport, the phonon Boltzmann transport equation is regarded as an accurate model when the wave effect is negligible. However it is difficult and computational intensive to solve. The ballistic-diffusive approach (BDE) proposed by Chen (2001) greatly simplifies the solution procedure and reduces the computational cost by modeling the ballistic and diffusive parts separately and using the first-order spherical harmonic function to approximate the diffusive intensity. The accuracy of the BDE remains to be improved particularly near the boundary and at large time scales. In this paper, a deficiency in the BDE is identified, and a new physically sound boundary model is proposed, which leads to a new set of ballistic-diffusive equations. Several benchmark problems are employed to validate the performance of the modified ballistic-diffusive approach, and results indicate the new approach is much more accurate than the origin BDE and yet retains the same level of efficiency. Hence it is an effective method for the modeling of transient non-continuum heat conduction. (C) 2014 Elsevier Ltd. All rights reserved.
Keywords:Non-continuum phonon transport;Boltzmann transport equation;Ballistic-diffusive approximation