Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part I. Solid Heat Conduction

Abstract

A unified solution framework is proposed for efficiently solving conjugate fluid and solid heat transfer problems. The unified solution is solely governed by the compressible Navier-Stokes (N-S) equations in both fluid and solid domains. Such method not only provides the computational capability for solid heat transfer simulations with existing successful N-S flow solvers, but also can relax time-stepping restrictions often imposed by the interface conditions for conjugate fluid and solid heat transfer. This paper serves as Part I of the proposed unified solution framework and addresses the handling of solid heat conduction with the nondimensional N-S equations. Specially, a parallel, adaptive high-order discontinuous Galerkin unified solver has been developed and applied to solve solid heat transfer problems under various boundary conditions.