Spectral element simulations of three dimensional convective heat transfer

This paper presents new formulation for simulating three-dimensional convective heat transfer by incorporating the complete viscous dissipation function in the energy equation to account for viscous heating and adopting the Boussinesq approximation for the thermal buoyancy term in the Navier-Stokes equations. In addition, new implementation of fourth order Stiffly Stable Schemes was achieved and tested for time integration. In order to provide dual-level mesh refinement, the hp-refinement, for flexible spatial resolutions, a modal spectral element method was used to solve these equations in three dimensions. Simulation results were compared with exact solutions or higher order solutions and good agreement were accomplished. This demonstrates that the new formulation and implementation are accurate enough for investigating convective heat transfer with viscous heating subject to complex thermal and flow boundary conditions in three dimensional irregular domains using the high order version of finite element method.