Numerical shape optimization of a confined cavity in natural convection regime

The aim of this work is to optimize the geometric shape in enclosures similar to the square cavity in natural convection regime. The desired configuration differs from the classical cavity by the geometrical form of the hot wall to be defined. The procedure is based on a sequential quadratic programming in which the wall is parameterized by Bezier curves. The numerical optimization method developed is the outcome of combining a flow calculation method and a constrained minimization method. Investigations have been performed for different inclination angles and various Rayleigh numbers. The numerical results show that optimization is relevant since the heat transfer rate decreases considerably by comparison with the square and the undulated cavities. It is also found that the beneficial optimization occurs for high Rayleigh numbers.

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