We investigate a convective Brinkman--Forchheimer problem coupled with a heat transfer equation. The investigated model considers thermal diffusion and viscosity depending on the temperature. We prove the existence of a solution without restriction on the data and uniqueness when the solution is slightly smoother and the data is suitably restricted. We propose a finite element discretization scheme for the considered model and derive convergence results and a priori error estimates. Finally, we illustrate the theory with numerical examples.

翻译：本文研究了一个与热传导方程耦合的对流Brinkman-Forchheimer问题。所考虑的模型包含依赖于温度的热扩散系数和黏性系数。我们证明了在数据无限制条件下解的存在性，并在解适当光滑且数据满足一定限制时证明了其唯一性。针对该模型提出了有限元离散格式，并推导了收敛性结果及先验误差估计。最后，通过数值算例验证了理论分析。