In a heat exchanger (10) for transferring heat from a first fluid to a second fluid, which heat exchanger (10) comprises one or more flow passages (12) for a first fluid, the outer wall (26) of these passages is in heat-transferring contact with a flow body (20) made from metal foam for a second fluid. This metal foam has a gradient of the volume density of the metal, so that it is possible to achieve a favorable equilibrium between heat transfer and conduction, on the one hand, and flow resistance, on the other hand.