Skip to main content
SpringerLink
Log in

Arrhenius Activation and Zero Mass Flux Conditions on Nonlinear Convective Jeffrey Fluid over an Electrically Conducting and Radiated Sheet

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The forthright intention of the present investigation is to analyze the up-to-date progress in Jeffrey nanofluid flow past an electromagnetic sheet by utilizing the properties of nonlinear convection, radiation, convective boundary condition, zero mass flux condition and Arrhenius activation energy. The flow equations are transformed by applying appropriate transformations into a pair of self-similarity equations. Further similarity equivalences are numerically solved through Runge–Kutta-based shooting method. Graphs and tables are structured to analyze the behavior of sundry influential variables. The results acquired showed good agreement with the previous notable works. Through this study we observed that improvement in Lorentz force in the positive x-direction strengthens the momentum, which intensifies the transfer of heat energy from the boundary, resulting in reduced fluid temperature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig.2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Abbreviations

\(x,y,z\) :

Cartesian coordinate system (m)

\(u,v,w\) :

Velocity components of fluid phase in \(\,\,x,y,z\) directions (m/s)

\(u_{\infty }\) :

Ambient fluid velocity (m/s)

\(T\) :

Temperature of the nanofluid (K)

\(C\) :

Nanoparticle concentration (kg/m3)

\(T_{\infty }\) :

Free stream temperature (K)

\(T_{{\text{f}}}\) :

Convective surface temperature (K)

\(k_{{\text{f}}}\) :

Thermal conductivity of base fluid (W/mK)

\(h_{{\text{f}}}\) :

Heat transfer coefficient associated with the convection fluid (W/m2K)

\(\upsilon_{{\text{f}}}\) :

Kinematic viscosity of the base fluid (m2/s)

\(g\) :

Acceleration due to gravity (m/s2)

\(j_{0}\) :

Current density (A/m2)

\(M_{0}\) :

Magnetization of permanent magnets (A/m)

\(p\) :

Width of magnets and electrodes (m)

\(\beta_{1}\) :

Linear thermal expansions coefficients (K)

\(\beta_{2}\) :

Nonlinear thermal expansions coefficients (K)

\(\lambda_{1}\) :

Ratio of relaxation to retardation times

\(\lambda_{2}\) :

Retardation time (s)

\(D_{{\text{B}}}\) :

Brownian diffusion coefficient (m2/s)

\(D_{{\text{T}}}\) :

Thermophoretic diffusion coefficient

\(\rho_{{{\text{nf}}}}\) :

Density of the nanofluid (kg/m3)

\(\rho_{{\text{f}}}\) :

Density of the base fluid (kg/m3)

\(\rho_{{\text{s}}}\) :

Density of the nanoparticle (kg/m3)

\(\mu_{{\text{f}}}\) :

Dynamic viscosity of the base fluid (Ns/m2)

\(\mu_{{{\text{nf}}}}\) :

Dynamic viscosity of the nanofluid (Ns/m2)

\(c_{{p{\text{f}}}}\) :

Specific heat capacity at constant pressure of the fluid (J/kgK)

\(k_{{{\text{nf}}}}\) :

Thermal conductivity (W/mK)

\((\rho c_{{\text{p}}} )_{{\text{f}}}\) :

Effective heat capacity of the fluid (kg/m3K)

\((\rho c_{{\text{p}}} )_{{\text{p}}}\) :

Effective heat capacity of the nanoparticle material (kg/m3K)

\(\alpha_{{\text{f}}}\) :

Thermal diffusivity of the base fluid (m2/s)

\(\tau\) :

Ratio of effective heat capacity of the nanoparticle material to that of the base fluid

\(Z\) :

Modified Hartman Number

\(\gamma\) :

Nonlinear convection parameter due to temperature

\(Pr\) :

Prandtl number

\(Sc\) :

Schmidt number

\(R\) :

Radiation parameter

\(q_{{\text{r}}}\) :

Radiative heat flux

\(\beta\) :

Deborah number

\({\text{Nb}}\) :

Brownian motion parameter

\({\text{Nt}}\) :

Thermophoresis parameter

\(\lambda\) :

Mixed convection or buoyancy parameter

\(\varepsilon\) :

Width of magnets and electrodes

\(\delta\) :

Velocity ratio parameter

\(E\) :

Activation energy

\(\Omega\) :

Temperature relative parameter

\(\sigma^{*}\) :

Stefan Boltzmann constant

\(k^{*}\) :

Mean absorption coefficient

\(Bi\) :

Biot number

\(\zeta\) :

Similarity variable

\(C_{{\text{f}}}\) :

Skin-friction coefficient

\(Nu_{x}\) :

Local Nusselt number

\(Re_{x}\) :

Local Reynolds number

References

  1. MamathaUpadhya, S.; Raju, C.S.K.; Shehzad, S.A.; Abbasi, F.M.: Flow of Eyring-Powell dusty fluid in a deferment of aluminum and ferrous oxide nanoparticles with Cattaneo-Christov heat flux. Powder Technol. 340, 68–76 (2018)

    Article  Google Scholar 

  2. Raju, C.S.K.; Saleem, S.; Al-Qarni, M.M.; Mamatha, S.U.: Unsteady nonlinear convection on Eyring-Powell radiated flow with suspended graphene and dust particles. Microsyst. Technol. 25(4), 1321–1331 (2019)

    Article  Google Scholar 

  3. Saleem, S.; Nadeem, S.; Rashidi, M.M.; Raju, C.S.K.: An optimal analysis of radiated nanomaterial flow with viscous dissipation and heat source. Microsyst. Technol. 25(2), 683–689 (2019)

    Article  Google Scholar 

  4. Santhosh, H.B.; Raju, S.S.K.; Raju, C.S.K.: Comparative study on MHD CARREAU fluid due to stretching/shrinking surface in suspension of dust and graphene nanoparticles. BioNanoScience. 9(2), 483–494 (2019)

    Article  Google Scholar 

  5. Zaib, A.; Haq, R.U.; Chamkha, A.J.; Rashidi, M.M.: Impact of partial slip on mixed convective flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles. Int. J. Numer. Meth. Heat Fluid Flow 29(5), 1647–1662 (2019)

    Article  Google Scholar 

  6. Raju, C.S.K.; Saleem, S.; Mamatha, S.U.; Iqtadar, H.: Heat and mass transport phenomena of radiated slender body of three revolutions with saturated porous: Buongiorno's model. Int. J. Therm. Sci. 132, 309–315 (2018)

    Article  Google Scholar 

  7. Rashid, M.; Khan, M.I.; Hayat, T.; Khan, M.I.; Alsaedi, A.: Entropy generation in flow of ferromagnetic liquid with nonlinear radiation and slip condition. J. Mol. Liq. 276, 441–452 (2019)

    Article  Google Scholar 

  8. Buongiorno, J.: Convective transport in nanofluids. ASME J. Heat Transf. 128, 240–250 (2006)

    Article  Google Scholar 

  9. Narahari, M.; Soorapuraju, S.K.R.; Pendyala, R.; Pop, I.: Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model. Int. J. Numer. Meth. Heat Fluid Flow 27(1), 23–47 (2017)

    Article  Google Scholar 

  10. Reddy, J.R.; Sugunamma, V.; Sandeep, N.: Thermophoresis and Brownian motion effects on unsteady MHD nanofluid flow over a slendering stretching surface with slip effects. Alexandria Eng. J. 57(4), 2465–2473 (2018)

    Article  Google Scholar 

  11. Khan, M.I.; Hayat, T.; Waqas, M.; Alsaedi, A.; Khan, M.I.: Effectiveness of radiative heat flux in MHD flow of Jeffrey-nanofluid subject to Brownian and thermophoresis diffusions. J. Hydrodyn. 31, 1–8 (2019)

    Article  Google Scholar 

  12. Sultan, F.; Khan, W.A.; Ali, M.; Shahzad, M.; Irfan, M.; Khan, M.: Theoretical aspects of thermophoresis and Brownian motion for three-dimensional flow of the cross fluid with activation energy. Pramana 92(2), 21 (2019)

    Article  Google Scholar 

  13. Khan, M.I.; Qayyum, S.; Hayat, T.; Waqas, M.; Khan, M.I.; Alsaedi, A.: Entropy generation minimization and binary chemical reaction with Arrhenius activation energy in MHD radiative flow of nanomaterial. J. Mol. Liq. 259, 274–283 (2018)

    Article  Google Scholar 

  14. Irfan, M.; Khan, W.A.; Khan, M.; Gulzar, M.M.: Influence of Arrhenius activation energy in chemically reactive radiative flow of 3D Carreau nanofluid with nonlinear mixed convection. J. Phys. Chem. Solids 125, 141–152 (2019)

    Article  Google Scholar 

  15. Kumar, R.K.; Kumar, G.V.; Raju, C.S.K.; Shehzad, S.A.; Varma, S.V.K.: Analysis of Arrhenius activation energy in magnetohydrodynamic Carreau fluid flow through improved theory of heat diffusion and binary chemical reaction. J. Phys. Commun. 2(3), 035004 (2018)

    Article  Google Scholar 

  16. Hayat, T.; Aziz, A.; Muhammad, T.; Alsaedi, A.: Effects of binary chemical reaction and Arrhenius activation energy in Darcy-Forchheimer three-dimensional flow of nanofluid subject to rotating frame. J. Thermal Anal. Calorim. 136(4), 1769–1779 (2019)

    Article  Google Scholar 

  17. Rashid, S.; Khan, M.I.; Hayat, T.; Ayub, M.; Alsaedi, A.: Numerical treatment for rotating Maxwell nanomaterial flow with Arrhenius energy. Appl. Nanosci. (2019). https://doi.org/10.1007/s13204-019-00998-3

    Article  Google Scholar 

  18. Dhlamini, M.; Kameswaran, P.K.; Sibanda, P.; Motsa, S.; Mondal, H.: Activation energy and binary chemical reaction effects in mixed convective nanofluid flow with convective boundary conditions. J. Comput. Design Eng. 6(2), 149–158 (2019)

    Article  Google Scholar 

  19. Ram, R.C.; Rao, C.: Numerical study for mixed convective flow of a radiative nanofluid over the vertical frustum of a cone with Arrhenius activation energy and binary chemical reaction. Adv. Sci. Eng. Med. 10(9), 952–960 (2018)

    Article  Google Scholar 

  20. Umar, M.; Akhtar, R.; Sabir, Z.; Wahab, H.A.; Zhiyu, Z.; Imran, A.; Raja, M.A.Z.: Numerical treatment for the three-dimensional Eyring-Powell fluid flow over a stretching sheet with velocity slip and activation energy. Adv. Math. Phys. 2019, 9860471 (2019). https://doi.org/10.1155/2019/9860471

    Article  MathSciNet  MATH  Google Scholar 

  21. Gailitis, A.K.; Lielausis, O.A.: On the possibility of drag reduction of a flat plate in an electrolyte. Appl. Magnetohydrodyn. Trudy Inst. FisikyAN Latvia SSR 12, 143 (1961)

    Google Scholar 

  22. Ahmad, R.; Mustafa, M.; Turkyilmazoglu, M.: Buoyancy effects on nanofluid flow past a convectively heated vertical Riga-plate: a numerical study. Int. J. Heat Mass Transf. 111, 827–835 (2017)

    Article  Google Scholar 

  23. Nayak, M.K.; Oyelakin, I.S.; Mondal, S.; Sen, S.S.: Impact of the Cattaneo-Christov thermal and solutal diffusion models on the stagnation point slip flow of Walters' B nanofluid past an electromagnetic sheet. Heat Transf. Asian Res. 48(2), 713–726 (2019)

    Article  Google Scholar 

  24. Hakeem, A.K.; Nayak, M.K.; Makinde, O.D.: Effect of exponentially variable viscosity and permeability on Blasius flow of Carreau Nano fluid over an electromagnetic plate through a porous medium. J. Appl. Comput. Mech. 5(2), 390–401 (2019)

    Google Scholar 

  25. Qayyum, S.; Hayat, T.; Shehzad, S.A.; Alsaedi, A.: Effect of a chemical reaction on magnetohydrodynamic (MHD) stagnation point flow of Walters-B nanofluid with Newtonian heat and mass conditions. Nuclear Eng. Technol. 49(8), 1636–1644 (2017)

    Article  Google Scholar 

  26. Shafiq, A.; Hammouch, Z.; Turab, A.: Impact of radiation in a stagnation point flow of Walters’ B fluid towards a Riga plate. Thermal Sci. Eng. Prog. 6, 27–33 (2018)

    Article  Google Scholar 

  27. Najib, N.; Bachok, N.; Arifin, N.; Ali, F.: Stability analysis of Stagnation-Point flow in a Nanofluid over a stretching/shrinking sheet with second-order slip, Soret and Dufour effects, a revised model. Appl. Sci. 8(4), 642 (2018)

    Article  Google Scholar 

  28. Ansari, M.S.; Magagula, V.M.; Trivedi, M.: Jeffrey nanofluid flow near a Riga plate: spectral quasilinearization approach. Heat Transf. Asian Res. (2020). https://doi.org/10.1002/htj.21673

    Article  Google Scholar 

  29. Hayat, T.; Qayyum, S.; Imtiaz, M.; Alsaedi, A.: Impact of Cattaneo-Christov heat flux in Jeffrey fluid flow with homogeneous-heterogeneous reactions. PLoS One 11(2), e0148662 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the Deanship of Scientific Research at King Faisal University for the financial support under Nasher Track (Grant No. 186307).

Author information

Authors and Affiliations

  1. Department of Mathematics, Kristu Jayanti College, Autonomous, PO, K. Narayanapura, Kothanur, Bengalore, Karnataka, 560077, India

    S. Mamatha Upadhya

  2. Department of Mathematics and Statistics, College of Science, King Faisal University, Al Hufuf, 31982, Saudi Arabia

    S. Suresh Kumar Raju & Chokri Mnasri

  3. Department of Mathematics, GITAM Deemed to be University, Bengaluru-Campus, Nagadenahalli, Bengalore, Karnataka, 562163, India

    C. S. K. Raju

Authors
  1. S. Mamatha Upadhya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Suresh Kumar Raju
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. S. K. Raju
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chokri Mnasri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Suresh Kumar Raju.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Upadhya, S.M., Raju, S.S.K., Raju, C.S.K. et al. Arrhenius Activation and Zero Mass Flux Conditions on Nonlinear Convective Jeffrey Fluid over an Electrically Conducting and Radiated Sheet. Arab J Sci Eng 45, 9095–9109 (2020). https://doi.org/10.1007/s13369-020-04687-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-020-04687-0

Keywords

Search

Navigation