Skip to main content
SpringerLink
Log in

Heat sink/source and chemical reaction in stagnation point flow of Maxwell nanofluid

  • T.C. : Solar Energy Materials and Applications
  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

A modern progress in fluid dynamics has been emphasizes on nanofluids which maintain remarkable thermal conductivity properties and intensify the transport of heat in fluids. Here, the present-day endeavor progresses a Maxwell nanofluid towards stretched cylinder heated convectively. The addition properties, i.e., MHD, stagnation point, thermal radiation, heat sink/source and chemical reactions are elaborated. The homotopic algorithm has been exploited for solutions of ODEs. Here, it is noted that the temperature field enhances for Biot number and radiation parameter. Additionally, Brownian movement and thermophoretic influences have conflicting performance for nanomaterial concentration. The mass transport rate for constructive–destructive chemical reaction is opposite in nature in response to the thermal Biot number. The ratification of our findings is also addressed via tables and attained noteworthy results.

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

Similar content being viewed by others

Abbreviations

\(u,w\) :

Axial and radial velocity components

\(z,r\) :

Space coordinates

\(\lambda\) :

Relaxation time

\(\nu\) :

Kinematic viscosity

\(\sigma\) :

Electrical conductivity

\(B_{0}\) :

Magnetic field strength

\(\rho_{f}\) :

Fluid density

\(c_{f}\) :

Specific heat of fluid

\(\alpha_{1}\) :

Thermal diffusivity

\((\rho c)_{f}\) :

Heat capacity of fluid

\(k_{1}\) :

Thermal conductivity

\(\tau\) :

Effective heat capacity ratio

\(T\),\(C\) :

Fluid temperature and concentration

\(T_{\infty }\),\(C_{\infty }\) :

Ambient temperature and concentration

\(h_{f}\) :

Heat conversion coefficient

\(T_{f}\) :

Fluid temperature

\(C_{w}\) :

Surface concentration

\(D_{B} ,D_{T}\) :

Brownian and thermophoresis diffusion coefficient

\(q_{r}\) :

Radiative heat flux

\(k^{ * }\) :

Mean absorption coefficient

\(\sigma^{ * }\) :

Stefan-Boltzmann constant

\(Q_{1}\) :

Heat sink/source parameter

\(K_{r}\) :

Reaction rate

\(U_{0} ,U_{\infty }\) :

Reference velocities

\(l\) :

Specific length

\(R\) :

Radius of cylinder

\(U(z,r)\) :

Stretching velocity

\(\eta\) :

Dimensionless variable

\(\alpha\) :

Curvature parameter

\(\beta\) :

Deborah number

\(M\) :

Magnetic parameter

\(A\) :

Velocities ratio parameter

\(N_{b}\) :

Brownian motion parameter

\(N_{t}\) :

Thermophoresis parameter

\(R_{d}\) :

Radiation parameter

\(\Pr\) :

Prandtl number

\(\gamma\) :

Thermal Biot number

\(\delta\) :

Heat sink/source parameter

\(Le\) :

Lewis number

\(C_{R}\) :

Chemical reaction parameter

\(Nu_{z}\) :

Local Nusselt number

\(Sh_{z}\) :

Local Sherwood number

\({\text{Re}}_{z}\) :

Local Reynolds number

\(f\) :

Dimensionless velocity

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Dimensionless concentration

ODEs:

Ordinary differential equations

PDEs:

Partial differential equations

MHD:

Magnetohydrodynamics

HAM:

Homotopy analysis method

References

  1. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles. ASME Int Mech Eng 66, 99–105 (1995)

    Google Scholar 

  2. H. Masuda, A. Ebata, K. Teramae, N. Hishinuma, Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of -Al2O3, SiO2 and TiO2 ultra-fine particles). Netsu Bussei 7, 227–233 (1993)

    Article  Google Scholar 

  3. R.U. Haq, Z.H. Khan, S.T. Hussain, Z. Hammouch, Flow and heat transfer analysis of water and ethylene glycol based Cu nanoparticles between two parallel disks with suction/injection ejects. J Mol Liq 221, 298–304 (2016)

    Article  Google Scholar 

  4. S.S. Nourazar, M. Hatami, D.D. Ganji, M. Mhazayinejad, Thermal-flow boundary layer analysis of nanofluid over a porous stretching cylinder under the magnetic field effect. Powder Tech 317, 310–319 (2017)

    Article  Google Scholar 

  5. M. Khan, M. Irfan, W.A. Khan, Impact of nonlinear thermal radiation and gyrotactic microorganisms on the Magneto-Burgers nanofluid. Int J Mech Sci 130, 375–382 (2017)

    Article  Google Scholar 

  6. P.V. Narayana, S.M. Akshit, J.P. Ghori, B. Venkateswarlu, Thermal radiation effects on an unsteady MHD nanofluid flow over a stretching sheet with non-uniform heat source/sink. J Nanofluids 6, 899–907 (2017)

    Article  Google Scholar 

  7. M. Irfan, M. Khan, W.A. Khan, M. Ayaz, Modern development on the features of magnetic field and heat sink/source in Maxwell nanofluid subject to convective heat transport. Phy Lett A 382, 1992–2002 (2018)

    Article  ADS  Google Scholar 

  8. R.U. Haq, F.A. Soomro, H.F. Öztop, T. Mekkaoui, Thermal management of water-based carbon nanotubes enclosed in a partially heated triangular cavity with heated cylindrical obstacle. Int J Heat Mass Transf 131, 724–736 (2019)

    Article  Google Scholar 

  9. T.A. Alkanhal, M. Sheikholeslami, M. Usman, R.U. Haq, A. Shafee, A.S. Al-Ahmadi, I. Tlili, Thermal management of MHD nanofluid within the porous medium enclosed in a wavy shaped cavity with square obstacle in the presence of radiation heat source. Int J Heat Mass Transf 139, 87–94 (2019)

    Article  Google Scholar 

  10. R.U. Haq, M. Usman, E.A. Algehyne, Natural convection of CuO–water nanofluid filled in a partially heated corrugated cavity: KKL model approach. Commun Theoretical Phy (2020). https://doi.org/10.1088/1572-9494/ab8a2d

    Article  Google Scholar 

  11. H.A. Bafrani, O. Noori-kalkhoran, M. Gei, R. Ahangari, M.M. Mirzaee, On the use of boundary conditions and thermophysical properties of nanoparticles for application of nanofluids as coolant in nuclear power plants; a numerical study. Progress Nuclear Energy 126, 103417 (2020)

    Article  Google Scholar 

  12. R.U. Haq, A. Raza, E.A. Algehyne, I. Tlili, Dual nature study of convective heat transfer of nanofluid flow over a shrinking surface in a porous medium. Int Commun Heat Mass Transf 114, 104583 (2020)

    Article  Google Scholar 

  13. R.G. Villarejo, P. Estell, J. Navas, Boron nitride nanotubes-based nanofluids with enhanced thermal properties for use as heat transfer fluids in solar thermal applications. Solar Energy Mater Solar Cells 205, 110266 (2020)

    Article  Google Scholar 

  14. M. Irfan, K. Rafiq, W.A. Khan, M. Khan, Numerical analysis of unsteady carreau Nanofluid Flow with variable conductivity. Appl Nanosci 10, 3075–3084 (2020)

    Article  Google Scholar 

  15. M. Waqas, S. Jabeen, T. Hayat, S.A. Shehzad, A. Alsaedi, Numerical simulation for nonlinear radiated Eyring-Powell nanofluid considering magnetic dipole and activation energy. Int Commun Heat Mass Transf 112, 104401 (2020)

    Article  Google Scholar 

  16. K. Hiemenz, Grenzschicht an einem in den gleichformigen glussigkeitsstrom einge-tauchten geraden kreiszylinder. Dinglers Polytechnisches J 326, 321–410 (1911)

    Google Scholar 

  17. M.I. Khan, M.I. Khan, M. Waqas, T. Hayat, A. Alsaedi, Chemically reactive flow of Maxwell liquid due to variable thicked surface. Int Commun Heat Mass Transf 86, 231–238 (2017)

    Article  Google Scholar 

  18. J.H. Merkin, I. Pop, Stagnation point flow past a stretching/shrinking sheet driven by Arrhenius kinetics. Appl Math Comput 337, 583–590 (2018)

    MathSciNet  MATH  Google Scholar 

  19. M. Khan, M. Irfan, L. Ahmad, W.A. Khan, Simultaneous investigation of MHD and convective phenomena on time-dependent flow of Carreau nanofluid with variable properties: dual solutions. Phy Lett A 382, 2334–2342 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  20. F.U. Rehman, S. Nadeem, H.U. Rehman, R.U. Haq, Thermophysical analysis for three-dimensional MHD stagnation-point flow of nano-material influenced by an exponential stretching surface. Res Phys 8, 316–323 (2018)

    Google Scholar 

  21. B. Mahanthesh, B.J. Gireesha, Dual solutions for unsteady stagnation-point flow of Prandtl nanofluid past a stretching/shrinking plate. Def Diffusion Forum 388, 124–134 (2018)

    Article  Google Scholar 

  22. M. Irfan, M. Khan, W.A. Khan, M. Alghamdi, M. Zaka Ullah, Influence of thermal-solutal stratifications and thermal aspects of non-linear radiation in stagnation point Oldroyd-B nanofluid flow. Int Commun Heat Mass Transf 116, 104636 (2020)

    Article  Google Scholar 

  23. A. Mahdy, A.J. Chamkha, H.A. Nabwey, Entropy analysis and unsteady MHD mixed convection stagnation-point flow of Casson nanofluid around a rotating sphere. Alex Eng J 59, 1693–1703 (2020)

    Article  Google Scholar 

  24. M. Irfan, M. Khan, W.A. Khan, M.S. Alghamdi, Magnetohydrodynamic stagnation point flow of a Maxwell nanofluid with variable conductivity. Commun Theor Phys 71, 1493–1500 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Khan, M. Irfan, W.A. Khan, Heat transfer enhancement for Maxwell nanofluid flow subject to convective heat transport. Pramana J Phy (2018). https://doi.org/10.1007/s12043-018-1690-2

    Article  Google Scholar 

  26. M. Khan, M. Irfan, W.A. Khan, Impact of heat source/sink on radiative heat transfer to Maxwell nanofluid subject to revised mass flux condition. Res Phy 9, 851–857 (2018)

    Google Scholar 

  27. M. Rashid, A. Alsaedi, T. Hayat, B. Ahmed, Magnetohydrodynamic flow of Maxwell nanofluid with binary chemical reaction and Arrhenius activation energy. Appl Nanosci 10, 2951–2963 (2020)

    Article  Google Scholar 

  28. M.S. Abel, J.V. Tawade, M.M. Nandeppanavar, MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet. Meccanica 47, 385–393 (2012)

    Article  MathSciNet  Google Scholar 

  29. A.M. Megahed, Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity. Chin Phys B 22, 094701 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University, Islamabad, 44000, Pakistan

    M. Irfan & M. Khan

  2. Department of Mathematical Sciences Federal, Urdu University of Arts Sciences and Technology, Islamabad, 44000, Pakistan

    M. Irfan

  3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    W. A. Khan

Authors
  1. M. Irfan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. A. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Irfan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Irfan, M., Khan, M. & Khan, W.A. Heat sink/source and chemical reaction in stagnation point flow of Maxwell nanofluid. Appl. Phys. A 126, 892 (2020). https://doi.org/10.1007/s00339-020-04051-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00339-020-04051-x

Keywords

Search

Navigation