One of the most important industrial processes is heat transfer, carried out by heat exchangers in single and multiphase flow applications. Despite the existence of well-developed theoretical models for different heat transfer mechanisms, the expanding need for industrial applications requiring the design and optimization of heat exchangers, has created a solid demand for experimental work and effort. This thesis concerns the use of numerical approaches to analyze and optimize heat transfer and fluid flow in power generation industry, with emphasis on pin fin technology. This research begins with a review on heat transfer characteristics in surfaces with pin fins. Different pin fins shapes with various flow boundaries were studied, and thermal and hydraulic performances were investigated. The impact of parameters such as inlet boundary conditions, pin fin shapes, and duct cross-section characteristics on both flow and heat transfer were examined. Two important applications in power generation industry were considered for this study: power transformer cooling, and condenser for CO2 capturing application in oxy-fuel power plants. Available experimental data and correlations in the literature have been used for models validation. For each case, a model based on current configuration was built and verified, and was then used for optimization and new design suggestions. All numerical modeling was performed using commercial CFD software. A basic condenser design was suggested and examined, supplemented by the use of pin fin technology to influence the condensation rate of water vapour from a CO2/H2O flue gas flow. Moreover an extensive review of numerical modeling approaches concerning this condensation issue was conducted and presented. The analysis results show that the drop-shaped pin fin configuration has heat transfer rates approximating those of the circular pin configuration, and the drop-shaped pressure losses are less than one third those of the circular. Results for the power transformer cooling system show those geometrical defects in the existing system are easily found using modeling. Also, it was found that the installation of pin fins in an internal cooling passage can have the same effect as doubling the radiator’s height, which means a more compact cooling system could be designed. Results show that a condensation model based on boundary layer theory gives a close value to experimental correlations. Considering a constant wall temperature, any increase in CO2 concentration results in lower heat transfer coefficients. This is a subsequence of increased diffusivity resistance between combustion gas and condensing boundary layer. Also it was shown that sensitivity of heat transfer rate to inlet temperatures and velocity values decreased when these parameters increased. The application of numerical methods concerning the condensation process for CO2 capturing required significant effort and running time as the complexity of multiphase flow was involved. Also data validation for the CO2/H2O condenser was challenging since this is quite a new application and less experimental data (and theoretical correlations) exist. However, it is shown that models based on numerical approaches are capable of predicting trends in the condensation process as well as the effect of the non-condensable CO2 presence in the flue gas. The resulting data, conclusions, applied methodology can be applied to the design and optimization of similar industrial heat exchangers, such as oil coolers which are currently working at low efficiency levels. It can also be used in the design of electronic components, cooling of turbine blades, or in other design applications requiring high heat flux dissipation. Finally, the finding on water vapour condensation from a binary mixture gas can be referenced for further research and development in this field.