A new physical quantity, E-h = 1/2Q(vh)T, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction. This quantity, which will be referred to as entransy, corresponds to the electric energy stored in a capacitor. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes as a measure of the heat transfer irreversibility. The concepts of entransy and entransy dissipation were used to develop the extremum principle of entransy dissipation for heat transfer optimization. For a fixed boundary heat flux, the conduction process is optimized when the entransy dissipation is minimized, while for a fixed boundary temperature the conduction is optimized when the entransy dissipation is maximized. An equivalent thermal resistance for multi-dimensional conduction problems is defined based on the entransy dissipation, so that the extremum principle of entransy dissipation can be related to the minimum thermal resistance principle to optimize conduction. For examples, the optimum thermal conductivity distribution was obtained based on the extremum principle of entransy dissipation for the volume-to-point conduction problem. The domain temperature is substantially reduced relative to the uniform conductivity case. Finally, a brief introduction on the application of the extremum principle of entransy dissipation to heat convection is also provided. (C) 2007 Elsevier Ltd. All rights reserved.