  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, $\kappa_{s}/\kappa_{f} =
\left(9-100\right)$. To evaluate the CHTIBM with turbulent flow a fully
developed, heated, turbulent channel $\left(Re_{u_{\tau}}=150\text{ and }
\kappa_{s}/\kappa_{f}=4 \right)$ 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).
