An efficient hybrid BEM–RBIE method for solving conjugate heat transfer problems

In this paper, a hybrid boundary element method (BEM) — radial basis integral equation (RBIE) method is derived to solve conjugate heat transfer (CHT) problems. The BEM is used to solve the heat transfer in the solid region, while the fluid region is solved by using the RBIE. The capability of the RBIE to calculate the potential and the spatial gradients, while advantageous when knowledge of the spatial gradients is of primary importance, can lead to unnecessary increases in the computational cost when solving CHT problems due to the additional equations imposed per node. By using the BEM to solve the heat transfer in the solids, a significant reduction in the size of the system matrix compared to the case of using the RBIE for both the heat transfer in the solid and fluid regions can be achieved. A case study that examines the CHT inside the human eye is solved using the derived hybrid BEM–RBIE method.