Compact heat exchangers are used in a wide variety of applications. Typical among these are automobile radiators, air-conditioning evaporators and condensers, electronic cooling devices, recuperators and regenerators, and cryogenic exchangers. The need for lightweight, space saving, and economical heat exchangers has driven the development of compact surfaces. A mathematical model to predict the overall performance of such heat exchanges has been presented here. The computational domain considered was a threedimensional rectangular duct with an array of circular pin fins in the staggered arrangement and mounted on the heated channel bed maintained at a constant temperature. The values of different parameters chosen were based on the practical working conditions. The governing Reynolds-averaged Navier-Stokes and thermal energy equations for the complex turbulent convective heat transfer were numerically solved using the control volume approach and by applying appropriate thermal boundary conditions within the domain. The numerical simulations were performed using two different turbulent models, namely, the standard k-ɛ model and the RNG k-ɛ model along with the wall functions to treat the turbulence in the vicinity of the solid walls. The details of the governing equations, numerical procedure, mesh employed, and grid independence study have been presented in this chapter. The predictions have been compared with the experimental data reported in the literature and a good agreement