Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part I. Solid Heat Conduction (Advances in Applied Mathematics and Mechanics, 2023)
A unified solution framework is proposed for efficiently solving conjugatefluid and solid heat transfer problems. The unified solution is solely governed by thecompressible Navier-Stokes (N-S) equations in both fluid and solid domains. Suchmethod 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 heattransfer. This paper serves as Part I of the proposed unified solution framework andaddresses the handling of solid heat conduction with the nondimensional N-S equations. Specially, a parallel, adaptive high-order discontinuous Galerkin unified solverhas been developed and applied to solve solid heat transfer problems under variousboundary conditions.