The physical models of the outer and inner half coil jackets were simplified to two types of coiled ducts. The mathematic models of incompressible fluid at the condition of laminar flow and heat transfer in the two types of jackets for cooling process reactor were set up and solved by the semi-implicit method for pressure linked equations consistent (SIMPLEC) algorithm based on a control volume method. The flow and temperature fields were given and the effects of Dean and Prandtl numbers on flow and heat transfer were studied. The results show that flow in the inner half coil jacket is found to exhibit transition of secondary flow pattern from two vortices to four vortices when the Dean number increases, but that in the outer half coil jacket is not found. The critical Dean number is about 96. The inner half coil jacket has stronger heat transfer ability than the outer half coil jacket and this superiority is more evident with larger Prandtl number. However, as the Dean number is greater than 105, the flow resistance enhances more severely in the inner jacket than the outer jacket. For both jackets, the centers of the heated wall are the poorest for heat transfer.