Advertisement

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

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

Abstract

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.

Keywords

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

Nomenclature

uvw

Velocity components

xyz

Space coordinates

v

Kinematics viscosity

\(\beta ,d_1 \)

Liquid parameters

m

Fitted rate constant

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

Heat capacity of fluid

T

Temperature of fluid

k

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

C

Nanoparticles concentration

\(Q_0 \)

Heat generation/absorption parameter

\(C_\infty \)

Ambient nanoliquid concentration

\(E_\mathrm{a} \)

Activation energy

t

Time

\(h_\mathrm{t} \)

Wall heat transfer coefficients

ab

Positive constants

\(\sigma ^{*}\)

Stefan–Boltzmann constant

\(k^{*}\)

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

K

Boltzmann constant

\(\eta \)

Dimensionless variable

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

s The Eyring–Powell fluid parameters

S

Unsteadiness parameter

Pr

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

Le

Lewis number

\(\alpha \)

Ratio of stretching rates parameter

M

Magnetic parameter

\(\gamma \)

Thermal Biot number

\(\gamma _1 \)

Concentration Biot number

\(\sigma \)

Chemical reaction parameter

\(\delta \)

Temperature difference parameter

\(\theta _f \)

Temperature ratio parameter

E

Activation energy parameter

fg

Dimensionless velocities

\(\theta \)

Dimensionless temperature

\(\phi \)

Dimensionless concentration

\(Nu_x \)

Local Nusselt number

\(Re_x \)

Local Reynolds number

\(Sh_x \)

Local Sherwood number

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

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.

References

  1. 1.
    Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles, p. 231. ASME, FED (1995)Google Scholar
  2. 2.
    Oztop, H.F.; Abu-Nada, E.: Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow 29, 1326–1336 (2008)CrossRefGoogle Scholar
  3. 3.
    Khan, W.A.; Khan, M.; Malik, R.: Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption. PLoS ONE 9(8), e10510 (2014)Google Scholar
  4. 4.
    Sheikholeslami, M.; Ellahi, R.: Three-dimensional mesoscopic simulation of magnetic field effect on natural convection of nanofluid. Int. J. Heat Mass Transf. 89, 799–808 (2015)CrossRefGoogle Scholar
  5. 5.
    Akbar, N.S.; Raza, M.; Ellahi, R.: Influence of induced magnetic field and heat flux with the suspension of carbon nanotubes for the peristaltic flow in a permeable channel. J. Mag. Mag. Mat. 381, 405–415 (2015)CrossRefGoogle Scholar
  6. 6.
    Sandeep, N.; Kumar, B.R.; Kumar, M.S.J.: A comparative study of convective heat and mass transfer in non-Newtonian nanofluid flow past a permeable stretching sheet. J. Mol. Liq. 212, 585–591 (2015)CrossRefGoogle Scholar
  7. 7.
    Rehman, S.; ul Haq, R.; Khan, Z.H.; Lee, C.: Entropy generation analysis for non-Newtonian nanofluid with zero normal flux of nanoparticles at the stretching surface. J. Taiwan Inst. Chem. Eng. 63, 226–235 (2016)CrossRefGoogle Scholar
  8. 8.
    Haq, R.; Khan, Z.H.; Hussain, S.T.; Hammouch, Z.: Flow and heat transfer analysis of water and ethylene glycol-based Cu nanoparticles between two parallel disks with suction/injection effects. J. Mol. Liq. 221, 298–304 (2016)CrossRefGoogle Scholar
  9. 9.
    Rahman, S.U.; Ellahi, R.; Nadeem, S.; Zia, Q.M.Z.: Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis. J. Mol. Liq. 218, 484–493 (2016)CrossRefGoogle Scholar
  10. 10.
    Hayat, T.; Rashid, M.; Imtiaz, M.; Alsaedi, A.: Nanofluid flow due to rotating disk with variable thickness and homogeneous–heterogeneous reactions. Int. J. Heat Mass Transf. 113, 96–105 (2017)CrossRefGoogle Scholar
  11. 11.
    Hayat, T.; Javed, M.; Imtiaz, M.; Alsaedi, A.: Double stratification in the MHD flow of a nanofluid due to a rotating disk with variable thickness. Eur. Phys. J. Plus 132, 146 (2017).  https://doi.org/10.1140/epjp/i2017-11408-x CrossRefGoogle Scholar
  12. 12.
    Sandeep, N.: Effect of aligned magnetic field on liquid thin film flow of magnetic-nanofluids embedded with graphene nanoparticles. Adv. Powder. Technol. 28, 865–875 (2017)CrossRefGoogle Scholar
  13. 13.
    Ramzan, M.; Ullah, N.; Chung, J.D.; Lu, D.; Farooq, U.: Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction. Sci Rep. 7(12901), 12901 (2017).  https://doi.org/10.1038/s41598-017-13140-6 CrossRefGoogle Scholar
  14. 14.
    Ramzan, M.; Bilal, M.; Chung, J.D.: Radiative flow of Powell–Eyring magneto-nanofluid over a stretching cylinder with chemical reaction and double stratification near a stagnation point. PLoS ONE 12(1), e0170790 (2016)CrossRefGoogle Scholar
  15. 15.
    Shafique, Z.; Mustafa, M.; Mushtaq, A.: Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Results Phys. 6, 627–633 (2016)CrossRefGoogle Scholar
  16. 16.
    Khan, W.A.; Alshomrani, A.S.; Khan, M.: Assessment on characteristics of heterogeneous-homogeneous processes in three-dimensional flow of Burgers fluid. Results Phys. 6, 772–779 (2016)CrossRefGoogle Scholar
  17. 17.
    Khan, W.A.; Irfan, M.; Khan, M.; Alshomrani, A.S.; Alzahrani, A.K.; Alghamdi, M.S.: Impact of chemical processes on magneto nanoparticle for the generalized Burgers fluid. J. Mol. Liq. 234, 201–208 (2017)CrossRefGoogle Scholar
  18. 18.
    Mustafa, M.; Khan, J.A.; Hayat, T.; Alsaedi, A.: Buoyancy effects on the MHD nanofluid flow past a vertical surface with chemical reaction and activation energy. Int. J. Heat Mass Transf. 108, 1340–1346 (2017)CrossRefGoogle Scholar
  19. 19.
    Khan, M.; Irfan, M.; Khan, W.A.: Impact of nonlinear thermal radiation and gyrotactic microorganisms on the magneto-Burgers nanofluid. Int. J. Mech. Sci. 130, 375–382 (2017)CrossRefGoogle Scholar
  20. 20.
    Ali, F.; Sheikh, N.A.; Saqib, M.; Khan, A.: Hidden phenomena of an MHD unsteady flow in porous medium with heat transfer. Nonlinear Sci. Lett. A 8(1), 101–116 (2017)Google Scholar
  21. 21.
    Bhatti, M.M.; Zeeshan, A.; Ellahi, R.: Heat transfer with thermal radiation on MHD particle-fluid suspension induced by metachronal wave. Pramana J. Phys. 89(3), 48 (2017).  https://doi.org/10.1007/s12043-017-1444-6 CrossRefGoogle Scholar
  22. 22.
    Khan, M.; Ahmad, L.; Khan, W.A.: Numerically framing the impact of radiation on magneto-nanoparticle for 3D Sisko fluid flow. J. Braz. Soc. Mech. Sci. Eng. 39, 4475–4487 (2017)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  • A. S. Alshomrani
    • 1
  • 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

Personalised recommendations