TY - JOUR T1 - Unified Solution of Conjugate Fluid and Solid Heat Transfer – Part I. Solid Heat Conduction AU - Li , Shujie AU - Ju , Lili JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 814 EP - 830 PY - 2023 DA - 2023/02 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0359 UR - https://global-sci.org/intro/article_detail/aamm/21451.html KW - Conjugate heat transfer, solid heat conduction, compressible Navier-Stokes, exponential time integration, discontinuous Galerkin. AB -

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.