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Compact heat exchangers are widely used in industries due to their compactness, reduced space, energy requirement and desired thermal performance. The proposed ceramic plate fin heat exchanger (PFHE) based on the offset strip fin design is used in applications which require extreme operating temperatures. It is well known that the compact heat exchanger requires small fins and channels to achieve high heat transfer rate and thermal performances. The fins in the ceramic heat exchanger ensure periodic restart of the boundary layer region which increases the thermal performance or heat transfer enhancement of the heat exchanger. In this dissertation a novel fin configuration for high temperature ceramic plate fin heat exchanger is developed using three-dimensional computational fluid dynamics (CFD). The heat exchanger model developed in this dissertation is based on the conceptual design developed by Ceramatec, Inc. The working fluids used in the model are sulfur trioxide, sulfur dioxide, oxygen, helium and water vapor. The proposed material of the heat exchanger for this study is silicon carbide (SiC). The operational temperature of the heat exchanger used in the current study ranges from 973 K to 1173 K and due to this high temperature, thermal stresses are induced in the heat exchanger components. The thermal and hydraulic analysis in this work is followed by finite element analysis (FEA) in ANSYS structural module to study the effect of principal stress on different types of fin designs and arrangements. The thermal and mechanical stress results obtained under steady and transient conditions are used for calculating the safety factor based on the Coulomb-Mohr failure criteria. The goal of this research is to obtain a novel fin configuration that can be used in the ceramic plate fin heat exchanger with optimal stress, pressure drop and high heat transfer. After an extensive literature survey it is found that much work has been done on the standard rectangular and triangular fins. Hence in this dissertation, detailed three-dimensional analysis on fluid flow, heat transfer and stress analysis on many different configurations of fins are studied and analyzed. The ripsaw fin design with thickness of 0.05 mm gives the maximum heat transfer performance with less pressure drop and friction factor. Semi-analytical study is also carried out for different types of fins and is compared with the numerical results. In order to reduce the complexity, analysis is carried out on rectangular fin. The obtained fluid flow and heat transfer results from the numerical analysis are validated with the analytical results for all fin designs. The numerical analysis on chemical reaction is carried out to study the decomposition of sulfur trioxide to sulfur dioxide and oxygen. From the parametric studies it is found that the decomposition percentage of sulfur trioxide can be significantly enhanced by decreasing the reactant mass flow rate, increasing the length of the channel and the operation pressure. From the study it is found that the ripsaw fin design with thickness of 0.05 mm is found to be the best design with high heat transfer effectiveness, sulfur trioxide decomposition percentage, safety factor and less pressure drop.