Injection moulding is a manufacturing process widely used in industry. A major step in this technique is the design of efficient cooling channels for the molten material. In this paper we develop a mathematical model for the automatic generation of conformal cooling channels which follow the shape of the mould. We focus on the core of the mould and then we extend the technique to the correspondent cavity. We start by decomposing the core mould into approximate convex regions and then we classify them. While for narrow regions we use a strategy hereby called zigzagging, in the remaining cases we automatically generate cooling channels with spiral shapes. The design of those smooth spiral curves is guided by the iso-contours of a boundary-distance map. Our approach encompasses decomposition, classification and design in an automatic integrated system. The development of an algorithm for the automatic generation of cooling channels represents a big contribution to the typical methodology used by mould designers, since it dramatically decreases the time spent by a specialist on this task.