Boundary-layer renewal model ($\overline{F}\sim k\Delta T/\sqrt{\kappa \tau }$)

In a renewal model, a diffusive thermal boundary layer grows until a convective instability overturns it, after which growth restarts. A layer reaching thickness $\delta \sim \sqrt{\kappa \tau }$ has mean heat flux of order $k\Delta T/\delta$. A diffusive $t^{-1/2}$ flux averaged over one cycle differs only by an order-one coefficient. Distinct thermal and material layers need not share a renewal time.