Peristaltic flow of a magnetohydrodynamic nanofluid through a bifurcated channel
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O R I G I NA L PA P E R
Ashfaq Ahmed
Peristaltic flow of a magnetohydrodynamic nanofluid through a bifurcated channel
Received: 9 December 2019 / Revised: 20 March 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A mathematical model with peristalsis for blood flow through a bifurcated artery is presented by taking blood as a nanofluid with magnetic field effects. The arteries pattern of bifurcation is treated to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The equations governing the flow are made non-dimensional, and coordinate transformation is employed to convert the irregular boundary to a regular boundary. The resulting system of equations is solved by Cauchy Euler’s method. The influence of model parameters on blood velocity, pressure difference, pressure gradient, and trapping is investigated, and results are represented graphically.
List of symbols a b c α DB DT F g GrF GrT h k Nb Nt p Pr q Q t T Re u U
Half width of the channel (m) Amplitude of the wave (m) Wave velocity (m/s) Dimensionless bifurcation angle Brownian diffusion coefficient (m2 /s) Thermophoretic diffusion coefficient (m2 /s) Nanoparticle volume fraction Acceleration due to gravity (m/s2 ) Basic-density Grashof number Thermal Grashof number Transverse vibration of the wall (m) Thermal conductivity (W/m K) Brownian motion parameter Thermophoresis parameter Pressure (N/m2 ) Prandtl number Volume flow rate (in wave frame) (m3 /s) Volume flow rate (in laboratory frame) (m3 /s) Time (s) Temperature (K) Reynolds number Axial velocity (in laboratory frame) (m/s) Axial velocity (in wave frame) (m/s)
A. Ahmed (B) Department of Mathematics, Post Graduate College, Mirpur 10250, AJK, Pakistan E-mail: [email protected]
A. Ahmed
v V
Transverse velocity (in laboratory frame) (m/s) Transverse velocity (in wave frame) (m/s)
Greek symbols β δ λ ξ η θ μ (ρ)p (ρc)f ν ρp ψ ρf ρf0
Volumetric expansion coefficient of the fluid Wave number Wavelength (m) Axial coordinate (m) Transverse coordinate (m) Amplitude ratio Dimensionless temperature Fluid viscosity (N s/m2 ) Effective heat capacity of nanoparticle (J/K) Heat capacity of fluid (J/K) Kinematic viscosity (m2 /s) Nanoparticle mass density (kg/m3 ) Rescaled nanoparticle volume fraction Stream function (m2 /s) Fluid density (kg/m3 ) Fluid density at the reference temperature (T ) (kg/m3 ).
1 Introduction The study of blood flow in the bifurcation, which occurred in the aortic artery, is of vast clinical curiosity with respect to the diagnostics of physiological flow of the cardiovascular system. The examination of blood flow through unlike types of geometries under different flow sites is very important for the reason that the primary cause of death in the world by arterial diseases is associated with malaise flow disorders in the blood vessels. The blood flow owing to physical characteristics in the blood vessels is strongly subjected to the attributes of viscosity of blood, size, and shape of the arteries and the
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