This work aims to determine the optimal heat sink fin shape to promote the efficient rise of hot air away from the heat sink. The heat transfer and convective flow dynamics external to a commercial Stirling engine are investigated. In particular, this study employs an adjoint optimization approach based on CFD simulations to determine the sensitivity of the objective function to the shape of the heat sink and influence on the natural convection heat flow away from the external heat sink. This deterministic optimization approach increases the heat transfer rate of the heat sink by nearly 20% in this study when performing a small number of design iterations.

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