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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
  • 25 Downloads

Abstract

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.

Keywords

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

List of symbols

\(u,v\)

Velocity components

\(x,r\)

Cylindrical coordinates

\(\rho\)

Fluid density

\(m\)

Fitted rate constant

\(D_{B}\)

Brownian diffusion coefficient

a, c

Constants

\(\varGamma\)

Material parameter

\(T\)

Temperature of fluid

\(T_{w}\)

Surface temperature

\(T_{\infty }\)

Ambient fluid temperature

\(C\)

Concentration of nanofluid

\(n\)

Power law index

\(\mu\)

Generalized Newtonian viscosity

\(c_{p}\)

Specific heat

\(C_{w}\)

Surface concentration

\(u_{w}\)

Stretching velocity

\(\nu\)

Kinematic viscosity

\(\mu_{0}\)

Shear viscosity

\(D_{T}\)

Thermophoretic force

\(\tau\)

Ratio parameter

\(C_{\infty }\)

Ambient nanoparticle concentration

\(k^{*}\)

Mean absorption coefficient

\(\beta_{0}\)

Magnetic field strength

\(\alpha_{m}\)

Thermal conductivity

\(\sigma^{*}\)

Stefan Boltzmann

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

Capacity of heat for base liquid

\(\tau_{w}\)

Surface shear stress

\(\eta\)

Non-dimensional variable

\(\psi\)

Stream function

\({\text{We}}\)

Local Weissenberg number

\(M\)

Parameter for magnetic field

\(\gamma\)

Curvature parameter

\({ \Pr }\)

PRANDTL number

\(\sigma\)

Reaction rate parameter

\(A\)

Time-dependent parameter

\(E\)

Parameter for activation energy

\(N_{t}\)

Thermophoresis parameter

\(\delta\)

Temperature difference parameter

\(N_{b}\)

Parameter of Brownian moment

\(\theta_{f}\)

Temperature ratio parameter

\(N_{R}\)

Radiation parameter

\(\gamma_{\text{1}}\)

Biot number

\({\text{Re}}\)

Local Reynolds number

\(f\)

Non-dimensional velocity

θ

Temperature

ϕ

Concentration

\(\tau_{rx}\)

Wall shear stress

\(q_{w}\)

Wall heat flux

\({\text{Nu}}\)

Local Nusselt number

\(C_{f}\)

Drag force

\({\text{Sc}}\)

Schmidt number

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

Temperature-dependent/space dependent heat sink/source coefficients

\(Q^{'''}\)

Non-uniform heat sink/source

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

Dimensionless space–time dependent heat sink/source

Notes

Acknowledgements

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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