Abstract
The purpose of this paper is to advance a mathematical model for reviewing to simulate biological flows such as blood flow in arteries or veins, flow of urine in urethras and air flow in the bronchial airways. They can also be used to study and prediction of many diseases, as the lung disease (asthma and emphysema), or the cardiovascular diseases (heart stroke), Makinde (2005). In this work, laminar flow of an incompressible viscous fluid through a collapsible tube of circular cross section is considered. Collapsible tubes are easily deformed by negative transmural pressure owing to marked reduction of rigidity. Thus, they show a considerable nonlinearity and reveal various complicated phenomena Our objectives are to study the effect of temperature along the tube as the fluid Prandtl number and Reynolds number increases. We launch the mathematical formulation of the problem. The problem is solved by using power series and perturbation techniques with help of boundary conditions and results are displayed graphically for different flow characteristics, velocity profile.
Highlights
In human body, all the channels are malleable and collapsible
We observed that the fluid axial velocity profile is parabolic with maximum value at centerline and minimum at the plates
It is interesting to Axial velocity profile during tube con-traction (R > 0)
Summary
All the channels are malleable and collapsible. That is, when the exterior pressure exceeds the interior pressure, the tube cross-sectional area can be deliberately shortened, if not fully reduced. A mathematical model to simulate biological fluid flow in a collapsible tube is presented. High cholesterol could contribute to the stenosis of an artery when it accumulates on the inner wall of the artery This accretion, referred to as atherosclerosis, can build up within the artery to the point where it reduces blood flow to organs of the body. Muhammad Zeeshan Ashraf et al.: Mathematical Modeling to Simulate Biological Fluid Flow in a Collapsible Tube models, by reducing the spatial dimension of the problem, which involve a number of ad-hoc assumptions e.g., Contrad (1969), Grotberg (1971), Flaherty et al (1972), Cowley (1982), Bonis & Ribreau (1987), etc. The inertia and resistance of the fluid in the supporting rigid tubes have an important influence on the system’s overall dynamics This experiment forms the basis for most recent theoretical investigations due to its three-dimensional nature. The chief merit of this new method is its ability to reveal the dominant singularity in the flow field together with solution branches of the underlying problem in addition to the one represented by the original series
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