A conjugate heat transfer (CHT) immersed boundary (IB and CHTIB) method is developed for use with laminar and turbulent flows with low to moderate Reynolds numbers. The method is validated with the canonical flow of two co-annular rotating cylinders
at $Re=50$ which shows second order accuracy of the $L_{2}$ and $L_{infty}$ error norms of the temperature field over a wide rage of solid to fluid thermal conductivities, $kappa_{s}/kappa_{f} = left(9-100right)$. To evaluate the CHTIBM with turbulent flow a fully developed, heated, turbulent channel $left(Re_{u_{tau}}=150text{ and } kappa_{s}/kappa_{f}=4 right)$ is used which shows near perfect correlation to previous direct numerical simulation (DNS) results. The CHTIB method is paired with a momentum IB method (IBM), both of which use a level set field to define the wetted boundaries of the fluid/solid interfaces and are applied to the flow solver implicitly with rescaling of the difference operators of the finite volume (FV) method (FVM).
The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities.
