Shape Optimisation of a Heat Source in a Thermal Convection Field Considering Perimeter Constraint Condition

In this study, we present an investigation of shape optimisation analysis for a heat convection problem taking into account perimeter constraint condition. The incompressible Navier–Stokes equation using the Boussinesq approximation, the equation of continuity and the energy equation are employed for the governing equations in the heat convection field. The mixed interpolation method is applied to solve the flow field, and the quadratic and linear triangular elements are, respectively, employed for the velocity and the pressure. The quadratic triangular element is applied to interpolate the temperature. The purpose of this study is to find the optimal shape of a heat source so as to maximise the quantity of radiation on the outer boundary. The adjoint variable method is applied to obtain the optimal shape, and the perimeter constraint condition for the heat source is considered in this optimisation problem. The perimeter constraint condition is adapted in the traction method.