On the weak-equilibrium condition for derivation of algebraic heat flux model

Analogous to an algebraic Reynolds stress model, the algebraic heat flux model (AHFM) is derived from a second-moment closure by invoking the weak-equilibrium condition. The present study investigates this condition in detail as it applies to the advection and diffusive-transport terms. For the advection term, the correct form of this condition in non-inertial frames is obtained by means of an invariant Euclidean transformation. The validity of the diffusive-transport condition is examined through an a priori test using a DNS database for rotating turbulent channel flow with heat transfer. It is shown that the weak-equilibrium condition applied to diffusive-transport term tends to fail in the near-wall region. An alternative form is proposed that is based on an asymptotic analysis of the transport equation budget in the near-wall region. An evaluation of proposed form shows that it has the potential to improve the predictive ability of an ARSM for flows involving system rotation and/or streamline curvature.