Modeling a poiseuille flow through a rectangular pipe in a floor slab (PSD)

What is it about?

This study was devoted to the modeling of a laminar fluid flow in a pipe of the rectangular section located in a floor slab. This theme was raised because of its relevance in the large business sector as well as in the areas of energy saving and storage at the residential scale. The equations of motion quantity and heat transport are the classical equations of forced convection. However, to describe the movement amount within the heating slab pipeline, Prandtl simplified model was most appropriate. In addition, this model retains the most important terms for a laminar regime flow. In addition, the modeling of fluid flow conservation in the pipeline was taken into account in the equation system. To achieve the abovementioned objective, a numerical resolution was made for the system resolution of the Navier-Stokes equations that govern this fluid flow. These equations were discretized by an implicit finite difference method. The system of algebraic equations as well as obtained was solved by the algorithm of Gauss and the algorithm of Thomas. The results obtained such as: the evolution of the fluid velocity profile within the slab according to pipeline to the Reynolds number variation, the fluid temperature have clearly demonstrated the Poiseuille effect on fluid flow. Moreover, the stabilization of the Gauss algorithm and the Thomas algorithm in this numerical modeling was well verified against the tricks that were taken into consideration. The result of this study was that Thomas algorithm and Gauss algorithm are the best in this type of numerical modeling.

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Photo by Benjamin Voros on Unsplash

Photo by Benjamin Voros on Unsplash

Why is it important?

The results obtained were very convincing from a scientific and mathematical point of view, because the iterative algorithms used to study the flow of Poiseuille fluid were stable and fairly accurate in the values obtained. Gauss’s algorithm and Thomas' algorithm are the most appropriate for this type of numerical studies given the importance of the results obtained;

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