The first Molten Salt Reactor (MSR) was designed and tested at Oak Ridge National Laboratory (ORNL) in the 1960's, but recent technological advancements now allow for new components, such as heat exchangers, to be created for the next generation of MSR's and molten salt-cooled reactors. The primary (fuel salt-to-secondary salt) heat exchanger (PHX) design is shown here to make dramatic improvements over traditional shell-and-tube heat exchangers when changed to a compact heat exchanger design. While this paper focuses on the application of compact heat exchangers on a Molten Salt Reactor, many of the analyses and results are similarly applicable to other fluid-to-fluid heat xchangers. The heat exchanger design in this study seeks to find a middle-ground between shell- and-tube designs and new ultra-efficient, ultra-compact designs. Complex channel geometries and microscale dimensions in modern compact heat exchangers do not allow routine maintenance to be performed by standard procedures, so extended surfaces will be omitted and hydraulic diameters will be kept in the minichannel regime (minimum channel dimension between 200 μm and 3 mm) to allow for high-frequency eddy current inspection methods to be developed. High aspect ratio rectangular channel cross-sections are used. Various plant layouts of smaller heat exchanger banks in a "modular" design are introduced. FLUENT was used within ANSYS Workbench to find optimized heat transfer and hydrodynamic performance. With similar boundary conditions to ORNL's Molten Salt Breeder Reactor's shell-and-tube design, the compact heat exchanger interest in this thesis will lessen volume requirements, lower fuel salt volume, and decrease material usage. / Master of Science