Optimization-based method for conjugate heat transfer problems

We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an optimization-based approach for heat transfer across the fluid-solid interface. In the semi-implicit method, the convective term in the momentum equation is treated explicitly, ensuring computational efficiency, while maintaining stability when a CFL condition involving fluid velocity is satisfied. Heat exchange between the fluid and solid domains is formulated as a constrained optimization problem, which is efficiently solved using a sequential quadratic programming method. Numerical results are presented to demonstrate the effectiveness and performance of the proposed approach.