Skip to main content
SpringerLink
Log in

Numerical simulation for Arrhenius activation energy on the nanofluid dissipative flow by a curved stretching sheet

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

In this paper, we have analysed a binary chemical nanofluid dissipative flow (in two cases i.e., 50% EG \( + \) 50% water/silica and 50% EG \( + \) 50% water/graphene oxide) due to a curved stretching sheet with activation energy. Appropriate transformations yield the nonlinear ordinary differential system. Shooting procedure (R-K 4th order based) is executed to solve the resultant equations. Graphical illustrations thoroughly demonstrate the features of the involved pertinent parameters. We have deliberated the behaviour of the alike parameters on the rate of transfers (heat and mass) and surface drag force (skin friction coefficient) by means of tables. This investigation reveals that (a) reaction rate parameter and temperature difference parameter are helpful to ameliorate the mass transfer rate (b) concentration enhances for higher estimation of activation energy variable (c) increasing the volume fraction of nanoparticles reflects an escalation in temperature (d) heat transfer rate enhancement is recognized for the influence of heat transfer Biot number. At the end this study, we came to know that the EG-Water \( + \) Graphene Oxide mixture has more heat transfer rate compared to EG-Water \( + \) Silica mixture. This outcome helps to conclude that, whenever the more heat transport required in manufacturing and industries, we can take the EG-Water \( + \) Graphene Oxide mixture.

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

Similar content being viewed by others

Abbreviations

u, v :

Velocity components in s, r directions (ms\(^{{-1}}\))

p :

Dimensional pressure (Kg m\(^{-1}\)s\(^{-2}\))

\( \rho \) :

Density (Kgm\(^{-3}\))

\( \mu \) :

Dynamic viscosity (Kg m\(^{-1}\)s\(^{-1}\))

\( \sigma \) :

Electrical conductivity (Sm\(^{-1}\))

\( B_{0} \) :

Magnetic field strength (T)

T :

Dimensional temperature of fluid (K)

k :

Thermal conductivity (Wm\(^{-1}\)K\(^{-1}\))

\( C_\mathrm{p}\) :

Specific heat capacity (JKgK\(^{-1}\))

Q :

Temperature dependent volumetric rate of heat source (J)

C :

Dimensional concentration (mol m\(^{-3}\))

\( D_\mathrm{m}\) :

Molecular diffusivity (m\(^{2}\)s\(^{-1}\))

\(k_\mathrm{r} \) :

Chemical reaction rate (mol L\(^{-1}\)s\(^{-2}\))

\( E_\mathrm{a}\) :

Activation energy (KJ mol\(^{-1}\))

\(k*\) :

Boltzmann constant (8.314 J/mol K)

n :

Fitted rate constant (W m\(^{-2}\)K\(^{-1}\))

\(\upsilon \) :

Kinematic viscosity (m\(^{2}\)s\(^{-1}\))

\(T_\mathrm{w}\) :

Temperature at the surface (K)

\(T_{\infty } \) :

Temperature at free stream (K)

\(C_{\infty }\) :

Concentration at the free stream (mol m\(^{-3}\))

\(C_\mathrm{w}\) :

Concentration at the surface (mol m\(^{-3}\))

P :

Dimensionless pressure

\( \eta \) :

Similarity variable

f :

Stream function

\( f' \) :

Dimensionless velocity

\( \theta \) :

Dimensionless temperature of fluid

\(\Phi \) :

Dimensionless concentration of fluid

K :

Dimensionless curvature parameter

M :

Dimensionless magnetic field

\(\Pr \) :

Prandtl number

S :

Dimensionless heat source parameter

Ec:

Eckert number

Sc:

Schmidt number

\( \Lambda \) :

Dimensionless chemical reaction rate parameter

\( \gamma \) :

Temperature difference parameter

E :

Dimensionless activation energy Parameter

Bi :

Heat transfer Biot number

f:

Fluid

nf:

Nanofluid

References

  1. J.C. Maxwell, A treatise on electricity and magnetism, vol. I (Clarendon Press, Oxford, 1881)

    MATH  Google Scholar 

  2. S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, No. ANL/MSD/CP-84938; CONF-951135-29, Argonne National Lab., IL (United States) (1995)

  3. L. Gosselin, A.K. da Silva, Combined “heat transfer and power dissipation” optimization of nanofluid flows. Appl. Phys. Lett. 85(18), 4160–4162 (2004)

    Article  ADS  Google Scholar 

  4. J. Koo, C. Kleinstreuer, Laminar nanofluid flow in microheat-sinks. Int. J. Heat Mass Transf. 48, 2652–2661 (2005)

    Article  Google Scholar 

  5. F. Talebi, A.H. Mahmoudi, M. Shahi, Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid. Int. Commun. Heat Mass Transf. 37, 79–90 (2010)

    Article  Google Scholar 

  6. P.K. Kameswaran, S. Shaw, P. Sibanda, P.V.S.N. Murthy, Homogeneous-heterogeneous reactions in a nanofluid flow due to a porous stretching sheet. Int. J. Heat Mass Transf. 57, 465–472 (2013)

    Article  Google Scholar 

  7. M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technol. 239, 259–265 (2013)

    Article  Google Scholar 

  8. M. Turkyilmazoglu, Nanofluid flow and heat transfer due to a rotating disk. Comput. Fluids 94, 139–146 (2014)

    Article  MathSciNet  Google Scholar 

  9. S. Das, R.N. Jana, Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate. Alexandria Eng. J. 54, 55–64 (2015)

    Article  Google Scholar 

  10. M. Jayachandra Babu, N. Sandeep, 3D MHD slip flow of a ferrofluid over a slendering stretching sheet with thermophoresis and Brownian motion effects. J. Mol. Liq. 222, 1003–1009 (2016)

    Article  Google Scholar 

  11. Z. Abbas, M. Naveed, M. Sajid, Hydromagnetic slip flow of nanofluid over a curved stretching surface with heat generation and thermal radiation. J. Mol. Liq. 215, 756–762 (2016)

    Article  Google Scholar 

  12. M. Jayachandra Babu, N. Sandeep, Three-dimensional MHD slip flow of a nanofluid over a slendering stretching sheet with thermophoresis and Brownian motion effects. Adv. Powder Technol. 27(5), 2039–2050 (2016)

    Article  Google Scholar 

  13. T. Hayat, M.I. Khan, M. Farooq, T. Yasmeen, A. Alsaedi, Water-carbon nanofluid flow with variable heat flux by a thin needle. J. Mol. Liq. 224, 786–791 (2016)

    Article  Google Scholar 

  14. N. Sandeep, Effect of aligned magnetic field on liquid thin film flow of magnetic-nanofluids embedded with graphene nanoparticles. Adv. Powder Technol. 28(3), 865–875 (2017)

    Article  Google Scholar 

  15. M.H. Bahmani, G. Sheikhzadeh, M. Zarringhalam, O.A. Akbari, A.A.A.A. Alrashed, G.A.S. Shabani, M. Goodarzi, Investigation of turbulent heat transfer and nanofluid flow in a double pipe heat exchanger. Adv. Powder Technol. 29(2), 273–282 (2018)

    Article  Google Scholar 

  16. I. Waini, A. Ishak, I. Pop, Transpiration effects on hydrid nanofluid flow and heat transfer over a stretching/shrinking sheet with uniform shear flow. Alexandria Eng. J. 59(1), 91–99 (2020)

    Article  Google Scholar 

  17. M.R. Zangooee, Kh Hosseinzadeh, D.D. Ganji, Hydrothermal analysis of MHD nanofluid ( \( TiO_{2} -GO) \) flow between two radiative stretchable rotating disks using AGM. Case Stud. Therm. Eng. 14, 100460 (2019)

    Article  Google Scholar 

  18. N. Muhammad, S. Nadeem, A. Issakhov, Finite volume method for mixed convection flow of \( Ag \) - ethylene glycol nanofluid flow in a cavity having thin central heater. Phys. A 537, 122738 (2020)

    Article  MathSciNet  Google Scholar 

  19. L. Yang, J. Huang, M. Mao, W. Ji, Numerical assessment of Ag–water nano-fluid flow in two new microchannel heatsinks: Thermal performance and thermodynamic considerations. Int. Commun. Heat Mass Transf. 110, 104415 (2020)

    Article  Google Scholar 

  20. Kh.A. Maleque, Effects of exothermic/endothermic chemical reactions with Arrhenius activation energy on MHD free convection and mass transfer flow in presence of thermal radiation. J. Thermodyn. 2013 (2013)

  21. KhA Maleque, A binary chemical reaction on unsteady free convective boundary layer heat and mass transfer flow with Arrhenius activation energy and heat generation/absorption. Latin Am. Appl. Res. 44, 97–104 (2014)

    Google Scholar 

  22. F.G. Awad, S. Motsa, M. Khumalo, Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy. PloS One 9(9) (2014)

  23. M. Mustafa, A. Mushtaq, T. Hayat, A. Alsaedi, Numerical study of MHD viscoelastic fluid flow with binary chemical reaction and Arrhenius activation energy. Int. J. Chem. React. Eng. 15(1) (2017)

  24. Z. Shafique, M. Mustafa, A. Mushtaq, Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy. Res. Phys. 6, 627–633 (2016)

    Google Scholar 

  25. M. Ramzan, N. Ullah, J.D. Chung, D. Lu, U. Farooq, Buoyancy effects on the radiative magneto micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction. Sci. Rep. 7(1), 1–15 (2017)

    Article  Google Scholar 

  26. M. Monica, J. Sucharitha, Ch. Kishore, Effects of exothermic chemical reaction with Arrhenius activation energy, non-uniform heat source/sink on MHD stagnation point flow of a Casson fluid over a nonlinear stretching sheet with variable fluid properties and slip conditions. J. Niger. Math. Soc. 36, 163–190 (2017)

    MathSciNet  Google Scholar 

  27. R.V.M.S.S.Kiran Kumar, G.Vinod Kumar, C.S.K. Raju, S.A. Shehzad, S.V.K. Varma, 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 

  28. M.I. Khan, S. Qayyum, T. Hayat, M. Waqas, M.I. Khan, A. Alsaedi, 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 

  29. M. Irfan, M. Khan, W.A. Khan, L. Ahmad, Influence of binary chemical reaction with Arrhenius activation energy in MHD nonlinear radiative flow of unsteady Carreau nanofluid: dual solutions. Appl. Phys. A 125(3), 179 (2019)

    Article  ADS  Google Scholar 

  30. S.R.R. Reddy, P. Bala Anki Reddy, A.M. Rashad, Activation energy impact on chemically reacting Eyring-Powell nanofluid flow over a stretching cylinder. Arab. J. Sci. Eng. 1–16 (2020)

  31. M. Ijaz, M. Yousaf, A.M.E.I. Shafey, Arrhenius activation energy and Joule heating for Walter—B fluid with Cattaneo–Christov double-diffusion model. J. Therm. Anal. Calorimetry, 1–12 (2020)

  32. M. Alghamdi, Significance of Arrhenius activation energy and binary chemical reaction in mixed convection flow of nanofluid due to a rotating disk. Coatings 10(1), 86 (2020)

    Article  MathSciNet  Google Scholar 

  33. M.M. Bhatti, E.E. Michaelides, Study of Arrhenius activation energy on the thermo-bioconvection nanofluid flow over a riga plate. J. Therm. Anal. Calorimetry, 1–10 (2020)

  34. Yixin Xu, Kehui Sun, Shaobo He, Limin Zhang, Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method. Eur. Phys. J. Plus 131(6), 1–12 (2016)

    Article  Google Scholar 

  35. Deog-Hee Doh, M. Muthtamilselvan, B. Swathene, E. Ramya, Homogeneous and heterogeneous reactions in a nanofluid flow due to a rotating disk of variable thickness using HAM. Math. Comput. Simul. 168, 90–110 (2020)

    Article  MathSciNet  Google Scholar 

  36. A. Renuka, M. Muthtamilselvan, Deog-Hee Doh, Gyeong-Rae Cho, Effects of homogeneous-heterogeneous reactions in flow of nanofluid between two stretchable rotating disks. Eur. Phys. J. Spec. Top. 228(12), 2661–2676 (2019)

    Article  Google Scholar 

  37. A.-A. Fahad, M. Muthtamilselvan, Stagnation point flow of nanofluid containing micro-organisms. Case Stud. Therm. Eng. 100656 (2020)

  38. M.R. Zangooee, Kh Hosseinzadeh, D.D. Ganji, Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM. Case Stud. Therm. Eng. 14, 100460 (2019)

    Article  Google Scholar 

  39. S.F.A. Talib, W.H. Azmi, I. Zakaria, W.A.N.W. Mohamed, A.M.I. Mamat, H. Ismail, W.R.W. Daud, Thermophysical properties of silicon dioxide (\( SiO_{2}\)) in ethylene glycol/water mixture for proton exchange membrane fuel cell cooling application. Energy Procedia 79, 366–371 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Gokaraju Rangaraju Institute of Engineering and Technology, Bachupally, Hyderabad, 500 090, India

    Gadamsetty Revathi

  2. Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, 522502, India

    Venkata Subrahmanyam Sajja

  3. Department of Mathematics, GITAM School of Science, Bengaluru, Karnataka, India

    C. S. K. Raju

  4. Department of Mathematics, S.V.A. Government College, Srikalahasti, Andhra Pradesh, 517644, India

    M. Jayachandra Babu

Authors
  1. Gadamsetty Revathi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Venkata Subrahmanyam Sajja
    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. M. Jayachandra Babu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Miss. GR is responsible for Conceptualization and Methodology. Prof. VSS is responsible for the Formal analysis. Dr MJB, is responsible for Writing—Original Draft, Resources and Project administration. Dr CSKR, Data Curation,—Review and Editing, Visualization and Supervision.

Corresponding author

Correspondence to C. S. K. Raju.

Ethics declarations

Conflict of interest

The authors declare that no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Revathi, G., Sajja, V.S., Raju, C.S.K. et al. Numerical simulation for Arrhenius activation energy on the nanofluid dissipative flow by a curved stretching sheet . Eur. Phys. J. Spec. Top. 230, 1283–1292 (2021). https://doi.org/10.1140/epjs/s11734-021-00048-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00048-6

Search

Navigation