A Mathematical Model of Blood Flow in a Catheterized artery with multiple stenoses

2020 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
B. Basu Mallik ◽  
Saktipada Nanda
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Stress Distribution ◽  
Flow Resistance ◽  
Wall Stress ◽  
Symmetric Flow ◽  
Catheterized Artery ◽  
Impedance Wall ◽  
Analytical Expressions ◽  
Insight Into

A mathematical model is developed in this investigation for studying the axi-symmetric flow of blood through a catheterized artery with multiple stenoses. Consideration of Newtonian character of blood is described following the report of Young (1968) and Srivastava (2009) with the appropriate constitutive equation governing the flow. The boundary conditions appropriate to the problem under study are the standard no slip conditions at the artery and the catheter wall. Analytical expressions for impedance (flow resistance), the wall stress distribution in the stenotic region and the shear stress at the stenosis throat in their non dimensional form are derived by using the model. The derived expressions are computed numerically and the results are presented graphically for different values of the rheological and other parameters. The study provides an insight into the effects of catheter radius and stenosis height on impedance, wall stress distribution in the stenotic region and the shear stress at the stenotic throat.

Contact Stress Analysis of Multilayered Strands

2011 ◽  
Vol 130-134 ◽  
pp. 1230-1233 ◽  
Author(s):  
Xin Ze Zhao ◽  
Wei Peng ◽  
Shao Qing Zhang ◽  
Ming Song Yang
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Contact Zone ◽  
Contact Stress ◽  
Contact Surface ◽  
Gaussian Quadrature ◽  
Arbitrary Point ◽  
Fretting Wear ◽  
Adjacent Layer ◽  
Analytical Expressions

The calculation method of contact force in contact-zone between adjacent layer wires has been analyzed. The principal radii of curvatures of wires were taken into consideration while obtaining the analytical expressions for contact stesses and sizes of contact surface. Meanwhile, a formular for shear stress of arbitrary point in half-space under contact-zone was derived on basis of the Boussinesq problem and it was simplified by using Gaussian quadrature. According to the results, the stress distribution could be unsderstood more thoroughly and the results is of great importance for studying looseness, fatigue and fretting wear of multilayered strands.

A Mathematical Model for a Vibrating Human Head

2010 ◽  
Vol 1 (2) ◽  
pp. 29-42
Author(s):  
J. C. Misra ◽  
S. Dandapat ◽  
S. Adhikary
Keyword(s):  
Mathematical Model ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Laplace Transformation ◽  
Human Head ◽  
General Function ◽  
Numerical Techniques ◽  
Analytical Expressions ◽  
Inviscid Compressible Fluid ◽  
Translational Acceleration

In this paper, a mathematical model has been formulated to study the vibration of the human head. In the mathematical analysis of the model, the skull is considered as an anisotropic spherical shell and brain matter is represented as an inviscid compressible fluid. Also, in the model, the translational acceleration is considered as a general function of time. The authors use the method of Laplace transformation to achieve the analytical solution of the problem, while the analytical expressions have been used to compute the stress distribution in the system by resorting to numerical techniques.

FLOW OF MICROPOLAR FLUID THROUGH CATHETERIZED ARTERY — A MATHEMATICAL MODEL

2012 ◽  
Vol 05 (02) ◽  
pp. 1250019 ◽  
Author(s):  
D. SRINIVASACHARYA ◽  
D. SRIKANTH
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Micropolar Fluid ◽  
Outer Wall ◽  
Shear Stresses ◽  
Closed Form Solutions ◽  
Catheterized Artery ◽  
Wall Shear ◽  
Coupling Number

In this paper, the flow of blood through catheterized artery with mild constriction at the outer wall is considered. The closed form solutions are obtained for velocity and microrotation components. The impedance (resistance to the flow) and wall shear stress are calculated. The effects of catheterization, coupling number, micropolar parameter, and height of the stenosis on impedance and wall shear stresses are discussed.

scholarly journals Mathematical model to determine the surface stress acting on the tooth of gear

2010 ◽  
Vol 37 (2) ◽  
pp. 97-110
Author(s):  
J. Hinojosa-Torres ◽  
J.L. Hernández-Anda ◽  
J.M. Aceves-Hernández
Keyword(s):  
Mathematical Model ◽  
Shear Stress ◽  
Stress Distribution ◽  
Surface Stress ◽  
Gear Tooth ◽  
Maximum Shear Stress ◽  
Contact Problems ◽  
Failure Criteria ◽  
Shear Stresses ◽  
Alternative Expression

Surface stress on the surface contact of gear tooth calculated by the Buckingham equation constitutes the basis for The American Gear Manufacturers Association (AGMA) pitting resistance formula, which is based on a normal stress that does not cause failure since the yielding in contact problems is caused by shear stresses. An alternative expression based on the maximum-shear-stress is proposed in this paper. The new expression is obtained by using the maximum-shear-stress distribution and the Tresca failure criteria in order to know the maximum-shear-stress value and its location beneath the contact surface. Remarkable differences between the results using the proposed equation and those when the AGMA equation is applied are found.

ROLE OF SLIP VELOCITY IN BLOOD FLOW THROUGH STENOSED ARTERIES: A NON-NEWTONIAN MODEL

2007 ◽  
Vol 07 (03) ◽  
pp. 337-353 ◽  
Author(s):  
J. C. MISRA ◽  
G. C. SHIT
Keyword(s):  
Blood Flow ◽  
Skin Friction ◽  
Flow Rate ◽  
Slip Velocity ◽  
Flow Resistance ◽  
Volumetric Flow Rate ◽  
Flow Through ◽  
Analytical Expressions ◽  
Insight Into

A mathematical model is developed in this paper for studying blood flow through a stenosed arterial segment by taking into account the slip velocity at the wall of the artery. Consideration of the non-Newtonian character of blood is made, where a constitutive relation of blood is described by the Herschel–Bulkley equation. The effect of slip at the arterial wall in the presence of mild, moderate, and severe stenosis growth at the lumen of an artery is investigated. Analytical expressions for skin friction, flow resistance, and the flow rate are derived by using the model. The derived expressions are computed numerically by considering an illustrative example. The study provides an insight into the effects of slip velocity on the volumetric flow rate of blood, flow resistance, and skin friction.

Effect of mobility conditions on the throughput of the Wireless Body Area Network

2020 ◽  
Vol 10 ◽  
Author(s):  
Shilpa Shinde ◽  
Santosh Sonavane
Keyword(s):  
Mathematical Model ◽  
Wireless Body Area Network ◽  
Data Rate ◽  
Hand Movements ◽  
Body Area Network ◽  
Area Network ◽  
Mobility Patterns ◽  
Body Area ◽  
Insight Into ◽  
Leg Movements

Background and objective: In the Wireless Body Area Network (WBAN) sensors are placed on the human body; which has various mobility patterns like seating, walking, standing and running. This mobility typically assisted with hand and leg movements on which most of the sensors are mounted. Previous studies were largely focused on simulations of WBAN mobility without focusing much on hand and leg movements. Thus for realistic studies on performance of the WBAN, it is important to consider hand and leg movements. Thus, an objective of this paper is to investigate an effect of the mobility patterns with hand movements on the throughput of the WBAN. Method: The IEEE 802.15.6 requirements are considered for WBAN design. The WBAN with star topology is used to connect three sensors and a hub. Three types of mobility viz. standing, walking and running with backward and forward hand movements is designed for simulation purpose. The throughput analysis is carried out with the three sets of simulations with standing, walking and running conditions with the speed of 0 m/s, 0.5 m/s and 3 m/s respectively. The data rate was increased from 250 Kb to 10000 Kb with AODV protocol. It is intended to investigate the effect of the hand movements and the mobility conditions on the throughput. Simulation results are analyzed with the aid of descriptive statistics. A comparative analysis between the simulated model and a mathematical model is also introduced to get more insight into the data. Results: Simulation studies showed that as the data rate is increased, throughput is also increased for all mobility conditions however, this increasing trend was discontinuous. In the standing (static) position, the throughput is found to be higher than mobility (dynamic) condition. It is found that, the throughput is better in the running condition than the walking condition. Average values of the throughput in case of the standing condition were more than that of the dynamic conditions. To validate these results, a mathematical model is created. In the mathematical model, a same trend is observed. Conclusion: Overall, it is concluded that the throughput is decreased due to mobility of the WBAN. It is understood that mathematical models have given more insight into the simulation data and confirmed the negative effect of the mobility conditions on throughput. In the future, it is proposed to investigate effect of interference on the designed network and compare the results.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

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