Investigation on the effect of conductivity ratio on a conjugate heat transfer for a steady flow around a cylinder by using the hybridizable discontinuous Galerkin method

Conjugate heat transfer (CHT) problem of flow around a fixed cylinder is examined by using a high-order method which is based on the hybridizable discontinuous Galerkin (HDG) method. The present numerical method based on HDG discretization produces a system of equations in which the energy equation of fluid is coupled with that of solid while the continuity of heat-flux at the fluid-solid interface is automatically satisfied. We Investigate the effect of the conductivity ratio on the temperature distribution inside the cylinder and more importantly, the constraint of heat-flux continuity at the fluid-solid interface. The present high-order solutions are compared with low-order solutions by finite volume method of ANSYS, especially in terms of the constraint of heat-flux continuity at the interface. We show that the present high-order method provides accurate solutions and satisfies the constraint of heat-flux continuity better than ANSYS even with the use of a coarse grid. Furthermore, we have derived a numerical correlation between the Nusselt and the Reynolds number by using the fact that the surface temperature of the cylinder is nearly constant when conductivity ratio is larger than order of hundred. The proposed numerical correlation was found to be close to that from the exiting experiment.