Parallel Numerical Calculation on GPU for the 3-Dimensional Mathematical Model in the Walking Beam Reheating Furnace

In this paper, the parallel numerical simulations of 3-dimensional (3D) mathematical model for the walking-beam type reheating furnace have been developed and implemented on the graphics processing unit (GPU) architecture. First, the detailed heat transfer processes in the furnace are described and categorized when building the 3D mathematical model. They consist of the radiative heat exchange into the slab, the heat conduction between the stationary beams and the slabs, the heat convection between the gas flow and slab surfaces, and the heat conduction inside the slabs. Moreover, the proposed 3D mathematical model also accounts for the temperature-dependent material parameters, which is ignored by most published mathematical models. Second, the explicit finite difference method is used to discretize the proposed model to a straightforward parallel computation problem. A detailed analysis of the 3D boundary conditions for the proposed model is introduced and presented. The parallel computing problem is realized by programming on GPU via the platform CUDA in Tesla P100. Finally, the proposed model is verified with industry measurements and the comparison between the GPU-implementation model and the CPU-implementation model is also given to validate the great acceleration. The experimental results prove that the proposed GPU-implementation model declines the computation time from hours to seconds. It is not only orders of magnitude faster but also highly accurate.