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A parametric model of the pin fin shape has been developed. The pin fin profile optimization is performed without adopting the “length-of-arc” approximation. The model is based on the accurate treatment of the arc length. The heat transfer coefficient h is not constant but variable along the length of the pin fin. The objective is to minimize the pin fin volume for given value of the transferred heat...
Direct optimal control methods are used. The pin fin's volume is minimized for given heat flux value. Schmidt's criterion is not adopted. The optimal pin fin profile is neither parabolic nor circular. It 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...
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