Adjoint RANS for optimized heat transfer on dimpled surfaces

We derive the adjoint equation system for the RANS equation augmented with an thermal diffusion system in order to define an adjoint optimization approach. The design gaol is to maximize heat transfer on the boundary in order to improve heat exchanger geometries. Based on the sensitivities from the primal and adjoint equation system the geometry deformation is controlled via Radial Basis Function mesh deformation. The derived optimization approach is applied to dimpled surfaces.