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A conjugate heat transfer (CHT) immersed boundary (IB and CHTIB) method isdeveloped for use with laminar and turbulent flows with low to moderateReynolds numbers. The method is validated with the canonical flow of twoco-annular rotating cylinders at $Re=50$ which shows second order accuracy ofthe $L_{2}$ and $L_{\infty}$ error norms of the temperature field over a widerage of solid to fluid thermal conductivities, $\kappa_{s}/\kappa_{f} =\left(9-100\right)$. To evaluate the CHTIBM with turbulent flow a fullydeveloped, heated, turbulent channel $\left(Re_{u_{\tau}}=150\text{ and }\kappa_{s}/\kappa_{f}=4 \right)$ is used which shows near perfect correlationto previous direct numerical simulation (DNS) results. The CHTIB method ispaired with a momentum IB method (IBM), both of which use a level set field todefine the wetted boundaries of the fluid/solid interfaces and are applied tothe flow solver implicitly with rescaling of the difference operators of thefinite volume (FV) method (FVM).

A Second Order Thermal and Momentum Immersed Boundary Method for Conjugate Heat Transfer in a Cartesian Finite Volume Solver