Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan.
School of Mathematics & Acturial Science, University of Leicester, Leicester, LE1 7RH, UK.
Sci Rep. 2021 Mar 24;11(1):6718. doi: 10.1038/s41598-021-86051-2.
The blood flow inside a tube with multi-thromboses is mathematically investigated. The existence of these multiple thromboses restricts the blood flow in this tube and the flow is revamped by using a catheter. This non-Newtonian blood flow problem is modeled for Jeffrey fluid. The energy equation includes a notable effect of viscous dissipation. We have calculated an exact solution for the developed mathematical governing equations. These mathematical equations are solved directly by using Mathematica software. The graphical outcomes are added to discuss the results in detail. The multiple thromboses with increasing heights are evident in streamline graphs. The sinusoidally advancing wave revealed in the wall shear stress graphs consists of crest and trough with varying amplitude. The existence of multi-thrombosis in this tube is the reason for this distinct amplitude of crest and trough. Further, the viscous dissipation effects come out as a core reason for heat production instead of molecular conduction.
对带有多处血栓的管内血流进行了数学研究。这些多处血栓的存在限制了管内的血流,通过使用导管来改变血流。使用 Jeffrey 流体对这个非牛顿血流问题进行建模。能量方程包括粘性耗散的显著影响。我们已经为所开发的数学控制方程找到了精确解。这些数学方程直接使用 Mathematica 软件求解。添加图形结果来详细讨论结果。流线图中明显显示了高度增加的多处血栓。壁面剪切应力图中显示的正弦推进波由波峰和波谷组成,幅度不断变化。管内存在多处血栓是波峰和波谷幅度变化的原因。此外,粘性耗散效应是产生热量而不是分子传导的核心原因。