Optimal Control in Thermal Engineering pp 257-281 | Cite as

# Optimization of Pin Fin Profiles

## Abstract

Direct and indirect optimal control methods are used. Two different objective functions are considered. First, the transferred heat flux is maximized and the resulting optimal pin fin shape is a cylinder. Second, the pin volume is minimized for given value of the heat flux. Then, the optimum pin fin profile consists of two regions. In the first region, close to the basis, the pin thickness decreases linearly. In the second region the pin thickness is constant or may decrease, depending on thermal loads and operation. The optimal control solution is usually singular but may be very well approximated by a bang-bang solution. The technology and design constraints have important effects on pin fin profile.

## Keywords

Heat Flux Optimal Control Problem Biot Number Optimal Control Method Cylinder Volume## References

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