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Swirling flow of Maxwell nanofluid between two coaxially rotating disks with variable thermal conductivity

  • Jawad AhmedEmail author
  • Masood Khan
  • Latif Ahmad
Technical Paper
  • 16 Downloads

Abstract

The main concern of this article is to study the Maxwell nanofluid flow between two coaxially parallel stretchable rotating disks subject to axial magnetic field. The heat transfer process is studied with the characteristics of temperature-dependent thermal conductivity. The Brownian motion and thermophoresis features due to nanofluids are captured with the Buongiorno model. The upper and lower disks rotating with different velocities are discussed for the case of same as well as opposite direction of rotations. The von Kármán transformations procedure is implemented to obtain the set of nonlinear ordinary differential equations involving momentum, energy and concentration equations. A built-in numerical scheme bvp4c is executed to obtain the solution of governing nonlinear problem. The graphical and tabular features of velocity, pressure, temperature and concentration fields are demonstrated against the influential parameters including magnetic number, stretching parameters, Deborah number, Reynolds number, Prandtl number, thermal conductivity parameter, thermophoresis and Brownian motion parameters. The significant outcomes reveal that stretching action causes to reverse the flow behavior. It is noted that the effect of Deborah number is to reduce the velocity and pressure fields. Further, the impact of thermophoresis and thermal conductivity parameters is to increase the temperature profile. Moreover, the fluid concentration is reduced with the stronger action of Schmidt number.

Keywords

Maxwell nanofluid Coaxially rotating disks Variable thermal conductivity Magnetic field Numerical solutions 

List of symbols

u, v, w

Velocity components

\(r,\varphi ,z\)

Cylindrical coordinate system

V

Velocity vector

\(\nabla\)

Nabla

\(\nu ,\mu\)

Kinematic and dynamic viscosities

p, T

Fluid pressure and temperature

S

Extra stress tensor

λ1

Relaxation time parameter

cp

Specific heat at constant pressure

L

Gradient of velocity vector

A1

First Rivlin–Ericksen tensor

B0

Magnetic field strength

s1

Lower disk stretching rate

s2

Upper disk stretching rate

Ω1

Lower disk rotation rate

Ω2

Upper disk rotation rate

T1

Lower disk temperature

T2

Upper disk temperature

\(\rho ,C\)

Fluid density and concentration

B

Magnetic field

k(T)

Variable thermal conductivity

η

Dimensionless variable

d

Vertical distance between disks

\(\left( {\rho c_{p} } \right)_{f}\)

Specific heat of the base fluid

\(\left( {\rho c_{p} } \right)_{p}\)

Heat capacity of the nanofluid

DB

Brownian diffusion coefficient

DT

Thermophoretic diffusion coefficient

k

Fluid thermal conductivity

J

Current density

σ

Electrical conductivity

q

Heat flux

f′

Dimensionless radial velocity

g

Dimensionless azimuthal velocity

f

Dimensionless axial velocity

P

Dimensionless pressure

θ

Dimensionless temperature

ϕ

Dimensionless concentration

Ω

Rotation parameter

M

Magnetic parameter

β1

Deborah number

Pr

Prandtl number

Re

Local Reynolds number

S1

Lower disk stretching parameter

S2

Upper disk stretching parameter

ε

Thermal conductivity parameter

\(\varLambda\)

Pressure gradient parameter

Nt

Thermophoresis parameter

Nb

Brownian motion parameter

Sc

Schmidt number

Nur1

Local Nusselt number at lower disk

Nur2

Local Nusselt number at upper disk

Shr1

Local Sherwood number at lower disk

Shr2

Local Sherwood number at upper disk

Notes

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan
  2. 2.Department of Basic SciencesUniversity of Engineering and TechnologyTaxilaPakistan
  3. 3.Department of MathematicsShaheed Benazir Bhutto UniversitySheringal, Upper DirPakistan

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