The architecture of heat exchangers is a classical subject that has been studied extensively in the past. In this paper, we address the fundamental question of what the size of the heat exchanger should be, in addition to what architectural features it should have. The answer to the size question follows from the tradeoff between (1), the useful power lost because of heat transfer and fluid flow and (2), the power destroyed during transportation, manufacturing, and maintenance. Changes in heat exchanger size induce changes in the opposite sign in the power requirements (1), and (2). This fundamental tradeoff regarding size is illustrated by considering one side of a heat exchanger (one flow passage) in laminar flow and in fully rough turbulent flow, with several duct cross sectional shapes and arrays of channels in parallel. The size tradeoff is present in heat exchanger applications across the board, from vehicles to stationary power plants. Published by AIP Publishing.