Solution Of Mathematical Equations Research Articles

Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall

Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique (We2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_e^2$$\\end{document} as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.

Investigation of Erying–Powell fluid flow in the elliptical multi‐stenosed artery: Application of perturbation method via polynomial solutions

AbstractIn the current work, we analyzed the non‐Newtonian rheology of blood through a multi‐stenosed artery with a cross‐section of elliptical shape. The blood is regarded as Erying–Powell fluid, and flow is considered to have no slip at the stenotic wall. The mathematical model is processed to a non‐dimensional form, and conditions of mild stenosis are utilized to decrease its nonlinearity. The resulting equations are solved by applying the perturbation technique by considering the fluid characteristic parameter as the perturbation parameter. The solution is completed by using the polynomial of degree four. The solutions of mathematical equations are deeply examined by graphical analysis. The non‐Newtonian impacts are predominant in the surrounding of the stenosed wall along the minor axis of the elliptical artery. The height of stenosis affects the pressure rise and flow resistance. The shear stress at the arterial wall is very high in the stenotic region and has more potent effects in the neighboring boundary point on the minor axis. Progressive stenosis causes a reduction in the blood flow velocity surrounding the arterial wall due to higher resistance to the flow. However, the velocity improves near the center line of the artery. Further, the fluid's velocity is very high in the constricted (stenotic zone) region.

Analysis of pulsatile flow of Rabinowitsch fluid in the multi-stenosed inclined artery under the influence of external body acceleration

The stenosis builds up and its progression in the artery causes serious damages, which may lead to death. This research aims to investigate the non-Newtonian properties of the pulsatile blood flow through the multi-stenotic inclined artery. The effect of external body acceleration is considered, and blood is taken as Rabinowitsch fluid in this work. The mathematical model representing the proposed problem is transformed into a dimensionless form by applying the assumption for mild stenosis. The dimensionless mathematical equations are solved using the perturbation method. The solutions of mathematical equations are investigated graphically to analyze the impacts of various physical constraints. We find that strong non-Newtonian effects lead to an increase in flow velocity and wall shear stress. The stenosis’s presence and progression in the artery reduces the flow velocity. The stenotic artery (diseased artery) is found to have less flow rate than the healthy artery. It is noted that the vertically held conduit effectively has a larger flow velocity and wall shear stress than the horizontal one. External body acceleration is noted to have an impact that raises velocity and wall shear stress.

Uncertainty Management in Computational Simulations of Medical Devices1

Uncertainty Management in Computational Simulations of Medical Devices1

The solution of mathematical equations in chemical problems

The solution of mathematical equations in chemical problems