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Length Dimensions in Thermal Design

Steady state convective heat transfer is proportional to the temperature difference between fluid flow and wall, and at the same time to the rate of change of this temperature difference. This is the hallmark of exponential decay associated with a certain length scale. It is shown that the majority of temperature change and heat transfer takes place inside roughly two times the length scale and the total heat transfer as if the initial temperature difference is present over one length'. This is important in applications where size and weight are important as it means that not all material contributes equally efficient to the thermal function. It is further demonstrated that if two different length scales are applicable on the same physical part, for instance in combined cooling of the wall and heating of the flow, or in heat exchangers, the most efficient use of material is when the two length scales are equal. Typical cases for air and water flows show that at equal speeds and volume flows, water flows have longer heating lengths and shorter characteristic lengths compared to air cooling, and thus water-cooled and air-cooled applications will have different shape factors for maximum efficiency.