In thermal-fluid energy systems, there is a great need for accurate calculations of the conjugate heat transfer between the solid components and the fluid in the system. In the context of nuclear applications, particularly the Molten Salt Research Reactor, an added layer of complexity arises due to the internal heat generation within the fluid, solid, or possibly both. In such scenarios, it is necessary to consider the accuracy of standard Nusselt number correlations since they are predominantly based on analytical or experimental data without considering heat generation. In this work, Nusselt number correlations are first established via computational fluid dynamics simulations for laminar, developing flow in a cylindrical domain with internal heat generation in the flow, and an imposed heat flux condition at the wall. The correlations were created by applying a power-law curve fit to the simulated Nusselt local numbers as a function of the axial position in cylinder normalized by the cylinder diameter. These predictive correlations developed are then used within a conduction analysis on a large network of flow passages using finite volume analysis. This allows an accurate representation of the temperature distribution within the solid material between neighboring flow channels. Of particular importance is the peak temperature within that solid material and this metric is further analyzed to assess its sensitivity to the accuracy of the Nusselt number correlations. Using the predictive Nusselt correlations from simulation, the peak temperature of the solid material was reduced by up to 10% from the correlations previously used. This decrease in the peak temperature demonstrates the usefulness that the new Nusselt correlations can provide to increase the accuracy in representing the true interaction between the fluid and solid components with conjugate heat transfer. The geometry and flow conditions considered are of fundamental importance in a liquid-fueled molten salt nuclear reactor. The efforts presented here will ultimately be coupled with other system components in a multiphysics framework.