Conjugate heat transfer shape optimization based on the continuous adjoint method

In this paper, the continuous adjoint method for use in gradient-based op- timization methods for coupled problems including heat transfer between bodies (solids) and fluids flowing over or inside them is developed. This kind of problems are usually referred to as Conjugate Heat Transfer (CHT) problems. Emphasis is given to expand- ing the Enhanced-Surface Integral (E-SI) adjoint formulation recently published by the authors’ group for shape optimization problems in fluid mechanics only, to tackle CHT problems. This formulation ensures that the gradient of the objective function is accu- rately computed, while the computational cost is kept as low as possible