A Numerical Study of the Conjugate Conduction-Convection Heat Transfer Problem

This study investigates some of the basic aspects of conjugate, or coupled, heat transfer problems. The ultimate interest is in the improvement of an existing computational fluid dynamics (CFD) code by the inclusion of such a coupling capability. Many CFD codes in the past have treated the thermal boundary conditions of a bounding solid as the simple cases of either a surface across which there is no heat flux, or as a surface along which the temperature is a constant with respect to both space and time. These conditions are acceptable for some applications, but many real-world problems require a more-realistic treatment of the thermal wall condition. A thermal coupling may be accomplished by maintaining a continuous heat flux and temperature across the fluid-solid boundary. A heat flux is calculated on the fluid-side of the interface, and this is used as a boundary condition for a heat-conduction solver to calculate the temperature field within the solid and return an interface temperature to the fluid. This process is executed for each time-step iteration of the code, and, therefore, the temperature field of the solid and the fluid-solid interface temperature are allowed to evolve with time and space. A new heat-conduction solver is developed and coupled with an existing flow solver. For this reason, some of the study is devoted to the testing of the accuracy of the new heat-conduction solver on simple problems for which there exist analytical solutions. Additional coverage is devoted to the possibility of thermal communication between solid grid blocks. This is due to the fact that multiple grid blocking of the solid may be required for more complex geometries. For such cases, a similar procedure as that described for the fluid-solid interface is used to accomplish the solid-solid block-to-block communication. Relatively simple test cases of fluid-solid and solid-solid coupling are conducted; these cases are limited to two-dimensional grids. Other limitations include: the assumption of constant thermophysical properties for the solid, no consideration for thermal expansion of the solid, and no consideration for the radiation mode of heat transfer. The results indicate that the heat-conduction/flow solver shows potential