This project studied the effect of different parameters on the conjugate heat transfer in tube-in-block heat exchangers for various engineering applications. These included magnetic coolers (or heaters) associated with a magnetic refrigeration system, high heat flux coolers for electronic equipment, and hydronic snow melting system embedded in concrete slabs. The results of this research will help in designing the cooling/heating systems and select their appropriate geometrical dimensions and material for specific applications. Types of problems studied in this project are: steady state circular microchannels with heat source in the gadolinium substrate, transient heat transfer in circular microchannels with time varying heat source in a gadolinium substrate, transient heat transfer in composite trapezoidal microchannels of silicon and gadolinium with constant and time varying heat source, steady state heat transfer in microchannels using fluids suspended with nanoparticl es, and analysis of steady state and transient heat transfer in a hydronic snow melting system. For each of these problems a numerical simulation model was developed. The mass, momentum, and energy conservation equations were solved in the fluid region and energy conservation in the solid region of the heat exchanger to arrive at the velocity and temperature distributions. Detailed parametric study was carried out for each problem. Parameters were Reynolds number, heat source value, channel diameter or channel height, solid materials and working fluids. Results are presented in terms of solid-fluid interface temperature, heat flow rate, heat transfer coefficient, and Nusselt number along the length of the channel and with the progression of time. The results showed that an increase in Reynolds number decreases the interface temperature but increases the heat flow rate and Nusselt number. When the heat source varied with time, by applying and removing the magnetic field, the interface temperature, heat flow rate, and Nusselt number attained a periodic variation with time. The decrease in the diameter at constant Reynolds number decreases the interface temperature and increases the heat flow rate at the fluid-solid interface.