Skip to main content
SpringerLink
Log in

Thermal analysis of radiative water- and glycerin-based carbon nanotubes past a Riga plate with stratification and non-Fourier heat flux theory

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

The impact of thermal stratification and thermally radiative flow of carbon nanotubes on a Riga plate with injection/suction and heat generation/consumption is investigated. The two varieties of base fluids, like, water and glycerin with single-wall nanotubes and multi-wall carbon nanotubes, are incorporated in this investigation. Cattaneo–Christov heat flux theory is utilized to frame the energy equation. The controlling PDEs are remodeled into ODEs using the appropriate variables. The obtained ODEs are analytically solved by applying the HAM procedure and numerically solved by using the BVP4c scheme. The consequences of the physical parameters on fluid velocity, fluid temperature, skin friction coefficients and local Nusselt number are explained through tables, graphs and charts. It is detected that the fluid velocity in both directions diminishes when raising the suction/injection and velocity slip parameters. The fluid temperature downturns when enhancing the suction/injection and stratification parameters. The surface shear stress suppresses when increasing the Forchheimer number. The radiation parameter leads to strengthening the heat transfer gradient.

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

\(\alpha\) :

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

\({a_1,b_1,d_1,d_2}\) :

Positive constants (\(\text {s}^{-1}\))

\(a_\text {n}\) :

Magnets positioned in the interval separating the electrodes

\(CF_{\text {x}}\sqrt{Re}\)  &:

\(CF_{\text {y}}\sqrt{Re}\) Skin friction coefficient’s

\(c_\text {p}\) :

Capacity of specific heat (\(\text {m}^{2} \text {s}^{-2}\text {K}^{-1}\))

F:

Inertia coefficient of the porous medium

\(J_0\) :

Current density applied to the electrodes (\(\text {Am}^{-2}\))

\(k^{*}\) :

Thermal conductivity

\(\Lambda _{0}\) :

Molecular mean free path

M:

Magnetic property of the permanent magnets that are organized on top of the plate surface \(\left( {{\text{kgs}}^{{ - 2}} {\text{A}}^{{ - 1}} } \right)\)

nf,f:

Subscript represents the nanofluid and base fluid

\({\nu }\) :

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

Q:

Heat consumption/generation coefficient (\(\text {W m}^{-3} \text {K}^{-1}\))

\(\rho\) :

Fluid density (\(\text {kg m}^{-3}\))

\(\sigma ^{*}\) :

Stefan-Boltzmann constant

\(\Sigma _{\nu }\) :

Coefficient of tangential momentum accommodation

T:

 Fluid temperature (K)

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

Surface temperature (K)

\(T_{\infty }\) :

Ambient temperature (K)

\(\tau _{\text {w}}\) :

Surface shear stress

\({\Theta }\) :

Dimensionless temperature

u,v,w:

Velocity components

\(U_\text {w}, V_\text {w}\) :

Surface stretching velocities (\(\text {m}^{2} \text {s}^{-1}\))

x,y,z:

Cartesian coordinates (m)

\(\beta\) :

Dimensionless parameter

Fr:

Forchheimer number

fw:

Suction/injection parameter

\(\Gamma\) :

Thermal relaxation time parameter

Ha:

Modified Hartmann number

Hg:

Heat consumption/generation parameter

K:

Slip parameter

\(\Lambda\) :

Porosity parameter

Pr:

Prandtl number

Rd:

Radiation parameter

Re:

Local Reynolds number

\(S_{1}\) :

Thermal stratification parameter

CNTs:

Carbon nanotubes

HAM:

Homotopy analysis method

ODE:

Ordinary differential equations

MHD:

Magnetohydrodynamics

MWCNTs:

Multi-wall carbon nanotubes

PDE:

Partial differential equations

SS:

Stretching sheet

SWCNTs:

Single-wall carbon nanotubes

References

  1. Iijima S. Helical microtubules of graphitic carbon. Nature. 1991;354:56–68.

    Article  CAS  Google Scholar 

  2. Bhattacharyya A, Seth GS, Kumar R, Chamkha AJ. Simulation of Cattaneo–Christov heat flux on the flow of single and multi-walled carbon nanotubes between two stretchable coaxial rotating disks. J Therm Anal Calorim. 2020;139:1655–70.

    Article  CAS  Google Scholar 

  3. Anuar NS, Bachok N, Pop I. A stability analysis of solutions in boundary layer flow and heat transfer of carbon nanotubes over a moving plate with slip effect. Energies. 2018;11:3243.

    Article  CAS  Google Scholar 

  4. Gul T, Khan MA, Noman W, Khan I, Alkanhal TA, Tlili I. Fractional order forced convection carbon nanotube nanofluid flow passing over a thin needle. Symmetry. 2019;11(3):312.

    Article  CAS  Google Scholar 

  5. Saleh H, Alali E, Ebaid A. Medical applications for the flow of carbon-nanotubes suspended nanofluids in the presence of convective condition using Laplace transform. J Assoc Arab Univ Basic Appl Sci. 2017;24:206–12.

    Google Scholar 

  6. Anuar NS, Bachok N, Arifin NM, Rosali H. Role of multiple solutions in flow of nanofluids with carbon nanotubes over a vertical permeable moving plate. Alex Eng J. 2020;59(2):763–73.

    Article  Google Scholar 

  7. Gailitis A, Lielausis O. On possibility to reduce the hydrodynamics resistance of a plate in an electrolyte. Appl Magnetohydrodyn Rep Phys Inst Riga. 1961;12:143–6.

    Google Scholar 

  8. Nagalakshmi PSS, Vijaya N. Three dimensional Boger nanofluid flow explored with carbon nanotubes over a Riga plate. J Nanofluids. 2020;9(2):114–20.

    Article  Google Scholar 

  9. Madhukesh JK, Ramesh GK, Aly EH, Chamkha AJ. Dynamics of water conveying SWCNT nanoparticles and swimming microorganisms over a Riga plate subject to heat source/sink. Alex Eng J. 2022;61(3):2418–29.

    Article  Google Scholar 

  10. Ahmad A, Asghar S, Afzal S. Flow of nanofluid past a Riga plate. J Magn Magn Mater. 2016;402:44–8.

    Article  CAS  Google Scholar 

  11. Ansari MS, Magagula VM, Trivedi M. Jeffrey nanofluid flow near a Riga plate: spectral quasilinearization approach. Heat Transf Res. 2020;49(3):1491–510.

    Article  Google Scholar 

  12. Ramesh GK, Roopa GS, Gireesha BJ, Shehzad SA, Abbasi FM. An electromagnetohydrodynamic flow Maxwell nanoliquid past a Riga plate: a numerical study. J Braz Soc Mech Sci Eng. 2017;39:4547–54.

    Article  CAS  Google Scholar 

  13. Mehmood R, Nayak MK, Akber NS, Makinde OD. Effects of thermal-diffusion and diffusion-thermo on oblique stagnation point flow of couple stress Casson fluid over a stretched horizontal Riga plate with higher-order chemical reaction. J Nanouids. 2019;8(1):94–102.

    Google Scholar 

  14. Berrehal H, Maougal A. Entropy generation analysis for multi-walled carbon nanotube (MWCNT) suspended nanofluid flow over wedge with thermal radiation and convective boundary condition. J Mech Sci Technol. 2019;33(1):459–64.

    Article  Google Scholar 

  15. Fatunmbi EO, Adeosun AT. Nonlinear radiative Eyring-Powell nanofluid flow along a vertical Riga plate with exponential varying viscosity and chemical reaction. Int Commun Heat Mass Transf. 2020;119: 104913.

    Article  CAS  Google Scholar 

  16. Asshaari I, Jedi A, Pati KD. A Weibull distribution: flow and heat transfer of nanofluids containing carbon nanotubes with radiation and velocity slip effects. Math Probl Eng. 2020;2020:9.

    Article  Google Scholar 

  17. Loganathan K, Alessa N, Kayikci S. Heat transfer analysis of 3-D viscoelastic nanofluid flow over a convectively heated porous Riga plate with Cattaneo-Christov double flux. Front Phys. 2021;9:1–12.

    Article  Google Scholar 

  18. Zainal NA, Pop I, Nazar R, Naganthran K. MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation. Int J Numer Methods Heat Fluid Flow. 2020;31(3):858–79.

    Article  Google Scholar 

  19. Yaseen M, Kumar Manoj, Rawat SK. Assisting and opposing flow of a MHD hybrid nanofluid flow past a permeable moving surface with heat source sink and thermal radiation. Partial Differ Equ Appl Math. 2021;4:1–12.

    Google Scholar 

  20. Javed T, Faisal M, Ahmad I. Dynamisms of solar radiation and prescribed heat sources on bidirectional flow of magnetized Eyring-Powell nanofluid. Case Stud Therm Eng. 2020;21: 100689.

    Article  Google Scholar 

  21. Javed T, Faisal M, Ahmad I. Dynamisms of activation energy and convective Nield’s conditions on bidirectional flow of radiative Eyring–Powell nanofluid. Int J Mod Phys. 2020;31(11):2050156.

    Article  CAS  Google Scholar 

  22. Mallawi FOM, Bhuvaneswari M, Sivasankarana S, Eswaramoorthi S. Impact of double-stratification on convective flow of a non-Newtonian liquid in a Riga plate with Cattaneo–Christov double-flux and thermal radiation. Ain Shams Eng J. 2021;12:969–81.

    Article  Google Scholar 

  23. Eswaramoorthi S, Nazek Alessa, Sangeethavaanee M, Ngawang Namgyel. Numerical and analytical investigation for Darcy–Forchheimer flow of a Williamson fluid over a Riga plate with double stratification and Cattaneo–Christov dual flux. Adv Math Phys. 2021;15:46.

    Google Scholar 

  24. Kandasamy R, Dharmalingam R, Prabhu KS. Thermal and solutal stratification on MHD nanofluid flow over a porous vertical plate. Alex Eng J. 2018;57(1):121–30.

    Article  Google Scholar 

  25. Megahed AM, Abbas W. Non-Newtonian Cross fluid flow through a porous medium with regard to the effect of chemical reaction and thermal stratification phenomenon. Case Stud Therm Eng. 2022;29:1–9.

    Article  Google Scholar 

  26. Ahmad I, Khurshid I, Faisal M, Javed T, Abbas Z. Mixed convective flow of an Oldroyd-B nanofuid impinging over an unsteady bidirectional stretching surface with the signifcances of double stratifcation and chemical reaction. SN Appl Sci. 2020;2:1599. https://doi.org/10.1007/s42452-020-03430-6.

    Article  CAS  Google Scholar 

  27. Hayat T, Khan MI, Khan TA, Khan MI, Ahmad S, Alsaedi A. Entropy generation in Darcy–Forchheimer bidirectional flow of water-based carbon nanotubes with convective boundary condition. J Mol Liq. 2018;265:629–38.

    Article  CAS  Google Scholar 

  28. Hayat T, Imtiaz M, Alsaedi A, Kutbi MA. MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation. J Magn Magn Mater. 2015;396(15):31–7.

    Article  CAS  Google Scholar 

  29. Hayat T, Haider F, Muhammad T, Alsaedi A. Darcy–Forchheimer three-dimensional flow of carbon nanotubes with nonlinear thermal radiation. J Therm Anal Calorim. 2020;140:2711–20.

    Article  CAS  Google Scholar 

  30. Loganathan K, Muhiuddin G, Alanazi AM, Alshammari FS, Alqurashi BM, Rajan S. Entropy optimization of third-grade nanofluid slip flow embedded in a porous sheet with zero mass flux and a non-Fourier heat flux model. Front Phys. 2020;8:14.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Bolu Abant Izzet Baysal University, Bolu, Turkey

    Safak Kayikci

  2. Department of Mathematics, Dr. N.G.P. Arts and Science College, Coimbatore, Tamil Nadu, India

    S. Eswaramoorthi

  3. Department of Computer Engineering, Izmir Demokrasi University, Izmir, Turkey

    Seda Postalcioglu

  4. Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan, India

    K. Loganathan

  5. Research and Development Wing, Live4Research, Tiruppur, Tamil Nadu, India

    K. Loganathan

Authors
  1. Safak Kayikci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Eswaramoorthi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Seda Postalcioglu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. Loganathan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to this work. And all the authors have read and approved the final version manuscript.

Corresponding author

Correspondence to S. Eswaramoorthi.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kayikci, S., Eswaramoorthi, S., Postalcioglu, S. et al. Thermal analysis of radiative water- and glycerin-based carbon nanotubes past a Riga plate with stratification and non-Fourier heat flux theory. J Therm Anal Calorim 148, 533–549 (2023). https://doi.org/10.1007/s10973-022-11669-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-022-11669-x

Keywords

Search

Navigation