A note on activation energy and magnetic dipole aspects for Cross nanofluid subjected to cylindrical surface

  • W. A. KhanEmail author
  • M. AliEmail author
  • M. Shahzad
  • F. Sultan
  • M. Irfan
  • Z. Asghar
Original Article


Our main emphasis in this manuscript was to scrutinize the aspects of activation energy for magnetized Cross nanofluid subjected to cylindrical surface. Formulation for energy expression is developed through heat sink-source phenomenon. More specifically, Velocity of Cross liquid is deliberated by considering infinite shear rate viscosity and Lorentz’s force. The considered Cross nanoliquid expression (Buongiorno relation) comprises thermophoretic and Brownian movement mechanisms. Moreover, Chemical processes are deliberated subjected to appliance of activation energy. Bvp4c algorithm is implemented to tackle the nonlinear structure. Outcomes for Sherwood number, Nusselt number, skin fraction, temperature, concentration and velocity are presented in this manuscript. Our results revealed that temperature of Cross nanoliquid intensifies for larger thermophoretic parameter. Moreover, nanoliquid concentration dwindles for greater estimation of activation energy parameter.


Non-uniform heat absorption-generation Nanofluid Non-Newtonian fluid Activation energy 

List of symbols


Velocity components


Cylindrical coordinates


Fluid density


Fitted rate constant


Brownian diffusion coefficient

a, c



Material parameter


Temperature of fluid


Surface temperature

\(T_{\infty }\)

Ambient fluid temperature


Concentration of nanofluid


Power law index


Generalized Newtonian viscosity


Specific heat


Surface concentration


Stretching velocity


Kinematic viscosity


Shear viscosity


Thermophoretic force


Ratio parameter

\(C_{\infty }\)

Ambient nanoparticle concentration


Mean absorption coefficient


Magnetic field strength


Thermal conductivity


Stefan Boltzmann

\(\left( {\rho c} \right)_{f}\)

Capacity of heat for base liquid


Surface shear stress


Non-dimensional variable


Stream function


Local Weissenberg number


Parameter for magnetic field


Curvature parameter

\({ \Pr }\)

PRANDTL number


Reaction rate parameter


Time-dependent parameter


Parameter for activation energy


Thermophoresis parameter


Temperature difference parameter


Parameter of Brownian moment


Temperature ratio parameter


Radiation parameter


Biot number


Local Reynolds number


Non-dimensional velocity






Wall shear stress


Wall heat flux


Local Nusselt number


Drag force


Schmidt number

\(\left( {h,h^{*} } \right)\)

Temperature-dependent/space dependent heat sink/source coefficients


Non-uniform heat sink/source

\(\left( {\delta_{1} ,\delta_{2} } \right)\)

Dimensionless space–time dependent heat sink/source



This project was funded by the postdoctoral international exchange program for incoming postdoctoral students, at Beijing Institute of Technology, Beijing, China.


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Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Department of MathematicsMohi-ud-Din Islamic UniversityNerian SharifPakistan
  3. 3.Department of Mathematics and StatisticsHazara UniversityMansehraPakistan
  4. 4.Department of MathematicsQuaid-I-Azam UniversityIslamabadPakistan
  5. 5.NUTECH School of Applied Sciences and HumanitiesNational University of TechnologyIslamabadPakistan

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