The present study focuses on evaluating fully-coupled conjugate heat transfer simulation in a ribbed cooling passage with a fully developed flow assumption using LES with the immersed boundary method (IBM-LES-CHT). The IBM-LES and the IBM-CHT frameworks are validated prior to the main simulations by simulating purely convective heat transfer in the ribbed duct, and a laminar boundary layer flow over a 2D flat plate with heat conduction, respectively. For the main conjugate simulations, a ribbed duct geometry with a blockage ratio of 0.3 is simulated at a bulk Reynolds number of 10,000 with a conjugate boundary condition applied to the rib surface. The nominal Biot number is kept at 1, which is similar to the comparative experiment. As a means to overcome a large time scale disparity between the fluid and the solid regions, the use of a high artificial solid thermal diffusivity is compared to the physical diffusivity. It is shown that while the diffusivity impacts the instantaneous fluctuations in temperature, heat transfer and Nusselt numbers, it has an insignificantly small effect on the mean Nusselt number. Comparison between IBM-LES-CHT and iso-flux heat transfer simulations shows that the iso-flux case predicts higher local Nusselt numbers at the back face of the rib. Furthermore, the local Nusselt number augmentation ratio (EF) predicted by IBM-LES-CHT is compared to experiment and another LES conjugate simulation. Even though there is a mismatch between IBM-LES-CHT predictions and other two studies at the front face of the rib, the area-averaged EF compares reasonably well in other regions between IBM-LES-CHT prediction and the comparative studies.