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

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


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.


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


Velocity vector



\(\nu ,\mu\)

Kinematic and dynamic viscosities

p, T

Fluid pressure and temperature


Extra stress tensor


Relaxation time parameter


Specific heat at constant pressure


Gradient of velocity vector


First Rivlin–Ericksen tensor


Magnetic field strength


Lower disk stretching rate


Upper disk stretching rate


Lower disk rotation rate


Upper disk rotation rate


Lower disk temperature


Upper disk temperature

\(\rho ,C\)

Fluid density and concentration


Magnetic field


Variable thermal conductivity


Dimensionless variable


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


Brownian diffusion coefficient


Thermophoretic diffusion coefficient


Fluid thermal conductivity


Current density


Electrical conductivity


Heat flux


Dimensionless radial velocity


Dimensionless azimuthal velocity


Dimensionless axial velocity


Dimensionless pressure


Dimensionless temperature


Dimensionless concentration


Rotation parameter


Magnetic parameter


Deborah number


Prandtl number


Local Reynolds number


Lower disk stretching parameter


Upper disk stretching parameter


Thermal conductivity parameter


Pressure gradient parameter


Thermophoresis parameter


Brownian motion parameter


Schmidt number


Local Nusselt number at lower disk


Local Nusselt number at upper disk


Local Sherwood number at lower disk


Local Sherwood number at upper disk



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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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