Skip to main content

Advertisement

Springer Nature Link
Log in

Modeling and analysis of unsteady second-grade nanofluid flow subject to mixed convection and thermal radiation

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This article addresses the flow over an unsteady slendering stretching sheet considering second-grade nanofluid with mixed convection. By taking the features of non-linear thermal radiation, thermophoresis and Brownian diffusion effects are scrutinized. The flow is induced by a non-linear stretching surface of variable thickness. Essential features of combined zero mass flux and convective conditions are analyzed. The use of appropriate transformations results in the non-linear ODEs. Computations for the convergent series solutions are provided. Graphical illustrations assign the interpretations to quantities of physical interest. Nusselt number and skin friction are analyzed as well. By observing these results, it is evident that the attributes of nanoparticles and non-linear thermal radiation increase the temperature distribution.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Abbas SZ, Khan WA, Sun H, Ali M, Waqas M, Irfan M, Ahmad S (2019a) Modeling and analysis of von Kármán swirling flow for Oldroyd-B nanofluid featuring chemical processes. J Braz Soc Mech Sci Eng 41(12):556

    Article  Google Scholar 

  • Abbas SZ, Khan WA, Sun H, Irfan M, Khan MI, Waqas M (2019b) Von Kármán swirling analysis for modeling Oldroyd-B nanofluid considering cubic autocatalysis. Phys Scr 95(1):015206

    Article  Google Scholar 

  • Abbas SZ, Khan WA, Waqas M, Irfan M, Asghar Z (2020a) Exploring the features for flow of Oldroyd-B liquid film subjected to rotating disk with homogeneous/heterogeneous processes. Comput Methods Programs Biomed 189:105323

    Article  Google Scholar 

  • Abbas SZ, Khan WA, Gulzar MM, Hayt T, Waqas M, Asghar Z (2020b) Magnetic field influence in three-dimensional rotating micropolar nanoliquid with convective conditions. Comput Methods Programs Biomed 189:105324

    Article  Google Scholar 

  • Acharya N, Das K, Kundu PK (2016) Framing the effects of solar radiation on magneto-hydrodynamics bioconvection nanofluid flow in presence of gyrotactic microorganisms. J Mol Liq 222:28–37

    Article  Google Scholar 

  • Ali W, Mahmood S, Chammam W, Haq WU, Khan WA, Abbas SZ Mathematical modeling and chemical conduct considering non- 2 Newtonian nanofluid by utilizing heat flux features. Soft Comput https://doi.org/10.1007/s00500-020-05072-7

  • Alsaedi A, Awais M, Hayat T (2012) Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions. Commun Non-Linear Sci Numer Simul 17:4210–4223

    Article  MathSciNet  Google Scholar 

  • Sakiadis BC (1961) Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 7:2628

    Google Scholar 

  • Buongiorno J (2006) Convective transport in nanofluids. J Heat Transfer Trans AsME 128:240

    Article  Google Scholar 

  • Choi SUS, Eastman JA (1995) Enhancing thermal conductivity of fluids with nanoparticles. In: The Proceedings of the 1995 AsME International Mechanical Engineering Congress and Exposition, san Francisco, UsA, AsME, FED 231/MD, 66:99–105

  • Cortell R (2008) Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 372:631–636

    Article  Google Scholar 

  • Hayat T, Waqas M, Shehzad SA, Alsaedi A (2016) A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid. J Mol Liq 215:704–710

    Article  Google Scholar 

  • Hayat T, Khan WA, Abbas SZ, Nadeem S, Ahmad S Impact of induced magnetic field on second-grade nanofluid flow past a convectively heated stretching sheet. Appl Nanosci 1–9

  • Imtiaz M, Hayat T, Alsaedi A (2016) Mixed convection flow of Casson nanofluid over a stretching cylinder with convective boundary conditions. Adv Powder Tech 27:2245–2256

    Article  Google Scholar 

  • Jackson JD, Cotton MA, Axcell BP (1989) studies of mixed convection in vertical tubes. Int J Heat Fluid Flow 10:2–15

    Article  Google Scholar 

  • Khan M, Irfan M, Khan WA, Ahmad L (2017) Modeling and simulation for 3D magneto Eyring-Powell nanomaterial subject to non-linear thermal radiation and convective heating. Res Phys 7:1899–1906

    Google Scholar 

  • Khan WA, Waqas M, Kadry S, Asghar Z, Abbas SZ, Irfan M (2020) On the evaluation of stratification based entropy optimized hydromagnetic flow featuring dissipation aspect and Robin conditions. Comput Methods Programs Biomed 190:105347

    Article  Google Scholar 

  • Kuhn S, Rudolf von Rohr P (2008) Experimental study of heat flux in mixed convective flow over solid waves. Exp Fluids 44:973–984

    Article  Google Scholar 

  • Martínez-suastegui L, Trevino C (2007) Particle image velocimetry measurements for opposing flow in a vertical channel with a differential and asymmetric heating condition. Exp Therm Fluid Sci 32:262–275

    Article  Google Scholar 

  • Mohammadi K, Khorasanizadeh H (2015) A review of solar radiation on vertically mounted solar surfaces and proper azimuth angles in six Iranian major cities. Renew Sustain Energy Rev 47:504–518

    Article  Google Scholar 

  • Nield DA, Kuznetsov AV (2009) The Cheng-Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid. Int J Heat Mass Transfer 52:5792–5795

    Article  Google Scholar 

  • Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int J Heat Fluid Flow 29:1326–1336

    Article  Google Scholar 

  • Pashiardis S, Kalogirou SA, Pelengaris A (2017) statistical analysis for the characterization of solar energy utilization and inter-comparison of solar radiation at two sites in Cyprus. Appl Energy 190:1138–1158

    Article  Google Scholar 

  • Shehzad A, Hayat T, Alsaedi A, Chen B (2016) A useful model for solar radiation. Energy Ecol Environ 1:30–38

    Article  Google Scholar 

  • Song Y, Wang X, Bi S, Wu J, Huang S (2017) Effects of solar radiation, terrestrial radiation and lunar interior heat flow on surface temperature at the nearside of the Moon: based on numerical calculation and data analysis. Adv Space Res 60:938–947

    Article  Google Scholar 

  • Tiwari RJ, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int J Heat Mass Transfer 50:2002–2018

    Article  Google Scholar 

  • Zubair M, Waqas M, Hayat T, Ayub M, Alsaedi A (2017) The onset of modified Fourier and Fick’s theories in temperature-dependent conductivity flow of micropolar liquid. J Res Phys 7:3145–3152

    Google Scholar 

  • Zubair M, Waqas M, Hayat T, Ayub M, Alsaedi A (2018a) Simulation of non-linear convective thixotropic liquid with Cattaneo-Christov heat flux. J Res Phys 8:1023–1027

    Google Scholar 

  • Zubair M, Waqas M, Hayat T, Alsaedi A, Ayub M (2018b) Stagnation point flow of third grade liquid due to variable thickness a useful application to non-Fourier heat flux approach. J Res Phys 8:1010–1016

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank Deanship of Scientific Re- search at Majmaah University for supporting this work under Project Number No. R-2021-263. Any source or any organization did not support this study.

Author information

Authors and Affiliations

  1. Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan Jiangsu, 215316, China

    S. Z. Abbas

  2. NUTECH School of Applied Sciences and Humanities, National University of Technology, Islamabad, 44000, Pakistan

    M. Waqas

  3. Department of Computer Science and Information, College of Science at Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia

    A. Thaljaoui

  4. Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif, Azad Kashmir, 12010, Pakistan

    M. Zubair & W. A. Khan

  5. Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah, 11952, Saudi Arabia

    A. Riahi

  6. Department of Mathematics, Huzhou University, Huzhou, 313000, People’s Republic of China

    Y. M. Chu

  7. Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, People’s Republic of China

    Y. M. Chu

Authors
  1. S. Z. Abbas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Waqas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Thaljaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Zubair
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Riahi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Y. M. Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. W. A. Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. M. Chu.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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

Abbas, S.Z., Waqas, M., Thaljaoui, A. et al. Modeling and analysis of unsteady second-grade nanofluid flow subject to mixed convection and thermal radiation. Soft Comput 26, 1033–1042 (2022). https://doi.org/10.1007/s00500-021-06575-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-021-06575-7

Keywords