Theoretical analysis of thermal entrance problem for blood flow: An extension of classical Graetz problem for Casson fluid model using generalized orthogonality relations

2019 ◽  
Vol 109 ◽  
pp. 104314 ◽  
Author(s):  
Muhammad Waris Saeed Khan ◽  
Nasir Ali
Keyword(s):  
Blood Flow ◽  
Theoretical Analysis ◽  
Fluid Model ◽  
Casson Fluid ◽  
Graetz Problem ◽  
Casson Fluid Model ◽  
Orthogonality Relations ◽  
Thermal Entrance

scholarly journals Mechanics of non-Newtonian blood flow in an artery having multiple stenosis and electroosmotic effects

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110316
Author(s):  
Salman Akhtar ◽  
Luthais B McCash ◽  
Sohail Nadeem ◽  
Salman Saleem ◽  
Alibek Issakhov
Keyword(s):  
Blood Flow ◽  
Flow Problem ◽  
Fluid Model ◽  
Casson Fluid ◽  
Viscous Effects ◽  
Heating Effects ◽  
Casson Fluid Model ◽  
Flow Through ◽  
Mathematical Equations ◽  
Mathematica Software

The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as [Formula: see text]. The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter [Formula: see text] and flow rate [Formula: see text]. The trapping declines in size with incrementing [Formula: see text], for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

scholarly journals The Effects of Magnetic Casson Blood Flow in an Inclined Multi-stenosed Artery by using Caputo-Fabrizio Fractional Derivatives

2021 ◽  
Vol 82 (2) ◽  
pp. 28-38
Author(s):  
Dzuliana Fatin Jamil ◽  
Salah Uddin ◽  
Muhamad Ghazali Kamardan ◽  
Rozaini Roslan
Keyword(s):  
Blood Flow ◽  
Fractional Derivatives ◽  
Magnetic Particles ◽  
Hartmann Number ◽  
Fluid Model ◽  
Casson Fluid ◽  
Medical Problems ◽  
Casson Fluid Model ◽  
Stenosed Artery ◽  
Fractional Differential

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under the influence of a uniformly distributed magnetic field and an oscillating pressure gradient. The blood is modelled using the non-Newtonian Casson fluid model. The governing fractional differential equations are expressed by using the fractional Caputo-Fabrizio derivative without singular kernel. Exact analytical solutions are obtained by using the Laplace and finite Hankel transforms for both velocities. The velocities of blood flow and magnetic particles are graphically presented. It shows that the velocity increases with respect to the Reynolds number and the Casson parameter. Meanwhile, the velocity decreases as the Hartmann number increases. These results are useful for the diagnosis and treatment of certain medical problems.

scholarly journals Nonlinear Analysis for Shear Augmented Dispersion of Solutes in Blood Flow through Narrow Arteries

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
D. S. Sankar ◽  
Nurul Aini Binti Jaafar ◽  
Yazariah Yatim
Keyword(s):  
Blood Flow ◽  
Circular Tube ◽  
Fluid Model ◽  
Nonlinear Differential Equations ◽  
Outer Region ◽  
Casson Fluid ◽  
Flat Plates ◽  
Axial Diffusivity ◽  
Casson Fluid Model ◽  
Relative Diffusivity

The shear augmented dispersion of solutes in blood flow (i) through circular tube and (ii) between parallel flat plates is analyzed mathematically, treating blood as Herschel-Bulkley fluid model. The resulting system of nonlinear differential equations are solved with the appropriate boundary conditions, and the expressions for normalized velocity, concentration of the fluid in the core region and outer region, flow rate, and effective axial diffusivity are obtained. It is found that the normalized velocity of blood, relative diffusivity, and axial diffusivity of solutes are higher when blood is modeled by Herschel-Bulkley fluid rather than by Casson fluid model. It is also noted that the normalized velocity, relative diffusivity, and axial diffusivity of solutes are higher when blood flows through circular tube than when it flows between parallel flat plates.

scholarly journals Heat and mass transfer analysis on MHD blood flow of Casson fluid model due to peristaltic wave

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2439-2448 ◽  
Author(s):  
Mohammad Rashidi ◽  
Zhigang Yang ◽  
Muhammad Bhatti ◽  
Munawwar Abbas
Keyword(s):  
Mass Transfer ◽  
Blood Flow ◽  
Heat And Mass Transfer ◽  
Fluid Model ◽  
Pressure Rise ◽  
Casson Fluid ◽  
Peristaltic Wave ◽  
Friction Forces ◽  
Casson Fluid Model ◽  
The Impact

In this article, heat and mass transfer analysis on MHD blood flow of Casson fluid model due to peristaltic wave has been investigated. The governing equations of blood flow for Casson fluid model, temperature, and energy equation have been solved by taking the assumption of long wavelength and neglecting the inertial forces. The resulting coupled differential equations have been solved analytically and the exact solutions are presented. The impact of various pertinent parameters is plotted and discussed. It is found that the influence of magnetic field and fluid parameter shows similar behavior on velocity profile while its behavior is opposite for pressure rise and pressure gradient profile. Trapping phenomena have also taken into account by sketching the streamlines. The expression for pressure rise and friction forces are evaluated numerically.

scholarly journals Exact Solutions for Unsteady Free Convection Flow of Casson Fluid over an Oscillating Vertical Plate with Constant Wall Temperature

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Asma Khalid ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Fluid Model ◽  
Casson Fluid ◽  
Convection Flow ◽  
Constant Wall Temperature ◽  
Transform Method ◽  
Casson Fluid Model

The unsteady free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature has been studied. The Casson fluid model is used to distinguish the non-Newtonian fluid behaviour. The governing partial differential equations corresponding to the momentum and energy equations are transformed into linear ordinary differential equations by using nondimensional variables. Laplace transform method is used to find the exact solutions of these equations. Expressions for shear stress in terms of skin friction and the rate of heat transfer in terms of Nusselt number are also obtained. Numerical results of velocity and temperature profiles with various values of embedded flow parameters are shown graphically and their effects are discussed in detail.

An approximate Casson fluid model for tube flow of blood1

Biorheology ◽  
1975 ◽  
Vol 12 (2) ◽  
pp. 111-119 ◽  
Author(s):  
Walter P. Walawender ◽  
Te Yu Chen ◽  
David F. Cala
Keyword(s):  
Fluid Model ◽  
Casson Fluid ◽  
Tube Flow ◽  
Casson Fluid Model

scholarly journals Analysis of Blood Flow in Arterial Stenosis Using Casson and Power-Law Fluid Model

2013 ◽  
Vol 14 (2) ◽  
pp. 73
Author(s):  
Riri Jonuarti
Keyword(s):  
Blood Flow ◽  
Power Law ◽  
Fluid Model ◽  
Blood Flow Rate ◽  
Casson Fluid ◽  
Arterial Stenosis ◽  
Fluid Models ◽  
Power Law Fluid ◽  
Pass Through ◽  
Flow Power

Simulation of blood flow behaviour in the arteries and in arterial stenosis has been made and will be discussed in this paper. This simulation uses pulsatile flow and blood flow in artery without stenosis is considered as a dynamic fluid, compressed and condensed. Whereas, in the case of arterial stenosis has been used Casson and Power-law fluid models. In the arteries without stenosis, blood flow velocity profiles show the same pattern for each Womersley number, but with different speed value. In the case of arterial stenosis, blood flow rate decreases with increasing stenosis position away from axis of blood vessels. Resistances to flow are increases with increasing the size (height and length) of stenosis, both for the Casson and Power-law fluid models. If resistance to flow increases, it is more difficult for the blood to pass through an artery, result the flow decreases and heart has to work harder to maintain adequate circulation.Keywords : Artery, blood flow, power-law fluid, Casson fluid, stenosis  

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