Arabian Journal for Science and Engineering

, Volume 44, Issue 1, pp 579–589 | Cite as

Interpretation of Chemical Reactions and Activation Energy for Unsteady 3D Flow of Eyring–Powell Magneto-Nanofluid

  • A. S. AlshomraniEmail author
  • M. Zaka Ullah
  • S. S. Capizzano
  • W. A. Khan
  • M. Khan
Research Article - Physics


Refrigeration of electronic instruments, in view of environmental concern and energy security, is one of the main challenges of the new generation technology. The miniaturization of electronic devices has benefits, but in such situations, the heat dissipated per unit area rises in an uncontrolled manner. This can be done by either improving the characteristics of secondary and primary working liquids or by modifying the system. In this article, we present a comprehensive detail of unsteady 3D flow of Eyring–Powell nanofluid with convective heat and mass flux conditions. The effects of heat source–sink and nonlinear thermal radiations are considered in the Eyring–Powell nanofluid model. Additionally, chemical mechanism responsible for the mass transfer such as activation energy is accounted in the current relation. Moreover, suitable transformations are betrothed to obtain coupled nonlinear ordinary differential equations (ODEs) from the system of highly nonlinear coupled partial differential equations and numerical solution of system of coupled ODEs is obtained by means of bvp4c scheme. Our findings demonstrate that heat flux at the wall declines by uplifting the chemical reaction rate constant. The concentration of Eyring–Powell nanofluid is directly affected by activation energy of chemical process, and a trend of thermophoretic force on magneto-nanofluid is qualitative, contradictory to that of Brownian motion.


Unsteady 3D flow Eyring–Powell model Nanoparticles Nonlinear thermal radiation New mass flux boundary conditions 



Velocity components


Space coordinates


Kinematics viscosity

\(\beta ,d_1 \)

Liquid parameters


Fitted rate constant

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

Heat capacity of fluid


Temperature of fluid


Thermal conductivity

\(\alpha _1 \)

Thermal diffusivity

\(\tau \)

Effective heat capacity ratio

\(D_\mathrm{B} \)

Brownian diffusion coefficient

\(D_\mathrm{T} \)

Thermophoresis diffusion coefficient

\(T_\infty \)

Ambient fluid temperature


Nanoparticles concentration

\(Q_0 \)

Heat generation/absorption parameter

\(C_\infty \)

Ambient nanoliquid concentration

\(E_\mathrm{a} \)

Activation energy



\(h_\mathrm{t} \)

Wall heat transfer coefficients


Positive constants

\(\sigma ^{*}\)

Stefan–Boltzmann constant


Mean absorption coefficient

\(\beta _1 \)

Dimensional unsteadiness parameter

\(U_w (x,t), V_w (x,t)\)

Stretching velocities

\(q_\mathrm{r} \)

Radiative heat flux

\(k_\mathrm{c} \)

Rate of chemical reaction

\(C_\mathrm{c} \)

Concentration of the heated fluid

\(h_\mathrm{c} \)

Mass transfer coefficient


Boltzmann constant

\(\eta \)

Dimensionless variable

\(\varepsilon ,\delta _1 ,\delta _2\)

s The Eyring–Powell fluid parameters


Unsteadiness parameter


Prandtl number

\(\lambda >0\)

Heat generation parameter

\(\lambda <0\)

Heat absorption parameter

\(N_\mathrm{b} \)

Brownian motion parameter

\(N_\mathrm{t} \)

Thermophoresis parameter

\(R_d \)

Radiation parameter


Lewis number

\(\alpha \)

Ratio of stretching rates parameter


Magnetic parameter

\(\gamma \)

Thermal Biot number

\(\gamma _1 \)

Concentration Biot number

\(\sigma \)

Chemical reaction parameter

\(\delta \)

Temperature difference parameter

\(\theta _f \)

Temperature ratio parameter


Activation energy parameter


Dimensionless velocities

\(\theta \)

Dimensionless temperature

\(\phi \)

Dimensionless concentration

\(Nu_x \)

Local Nusselt number

\(Re_x \)

Local Reynolds number

\(Sh_x \)

Local Sherwood number


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This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (RG-8-130-38). The authors, therefore, acknowledge with thanks the DSR’s technical and financial support.


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • A. S. Alshomrani
    • 1
    Email author
  • M. Zaka Ullah
    • 1
  • S. S. Capizzano
    • 2
  • W. A. Khan
    • 3
  • M. Khan
    • 4
  1. 1.NAAM Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Science and High TechnologyUniversity of InsubriaComoItaly
  3. 3.Department of Mathematics and StatisticsHazara UniversityMansehraPakistan
  4. 4.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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