Level-set based topology optimization in conjugate heat transfer with large solid-to-fluid thermal conductivity ratios

• Level-set based topology optimization is implemented for conjugate conduction–convection heat transfer with large solid–fluid thermal conductivity ratios. • The optimization algorithm yields realistic designs for conjugate heat transfer, ensuring all heat transfer paths from fluid to solid boundary. • The proposed forward solver is verified against reference results for a benchmark conjugate heat transfer problem. A numerical framework is developed to solve topology optimization problems for conjugate conduction–convection heat transfer (CHT) in OpenFOAM. An arbitrary solid geometry represented by a level-set function is embedded in a Cartesian grid system. This allows smooth change of the physical properties between the two phases in a transition region with a prescribed thickness around the solid–fluid interface. The accurate interface represented by the level-set function and high-fidelity simulation data are directly used in optimization without any filtering and modification. A gradient-based optimization algorithm is derived by adjoint method so as to minimize a cost functional given by a weighted sum of the total drag and the total heat transfer by taking into account conjugate heat transfer. The developed methodology is applied to conjugate heat transfer problems of a single square fin sandwiched between adiabatic and heated walls at low Reynolds numbers. The increase in the relative weight of heat transfer in the cost functional and the increase in the solid thermal conductivity have similar effects on the optimal shapes, resulting in complex secondary fin-like structures generated from the primary fin. With proper weights, heat transfer can be enhanced by 22% compared to the initial square fin, while drag can also be reduced by 17%. Furthermore, this study highlights the significance of taking into account the thermal conduction inside solid in topology optimization, which guarantees heat transfer paths from the fluid to the heated boundary, unlike the unrealistic optimal structure with isolated solids obtained using our previous algorithm under an isothermal condition.