A numerical simulation was conducted to investigate convective heat transfer from small and compact coiled pipes heat exchangers using computational fluid dynamics (CFD) software Fluent V6. One fluid (air) moves over the coiled pipe while a second fluid (refrigerant R141B) at different temperature flows through the pipe. The studied heat exchanger is composed with bends and straight tubes. Calculations were done for two cases with different outside flow arrangements. The simulation results showed remarkable differences in the flow characteristics and heat transfer rate of different single tubes of the entire heat exchangers. The temperature distribution and heat transfer are mainly influenced by temperature gradient, backflow conditions, exterior flow velocity, and surface area. The results also show the effect of the bends on the flow in straight tubes and vice-versa.