Skip to main content
SpringerLink
Log in

On the Use of Wavelets for Analysis of Nanofluid Flow and Thermal Transmission Through Asymmetric Porous Channel

  • Scientific Research Paper
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

The present work analyses the unsteady nanofluid flow and thermal transmission through an asymmetric porous channel using wavelet collocation method. The nanofluid considered herein is water mixed with Cu-nanoparticles. These types of problems have been solved by Galerkin and least square methods. The main aim of this work is to overcome the limitations of these methods via scale-3 Haar wavelets-based method. Using similarity transformation, the two-dimensional nanofluid flow problem has been transformed into coupled non-linear ordinary differential equations (ODEs), which have been solved employing wavelet collocation method. The wavelets are chosen to be uniform scale-3 Haar wavelets. The influence of various emerging parameters on velocity and temperature profile has been analysed. For some special cases, the results obtained have been compared with exact solutions. An excellent agreement shows the accuracy and versatility of the present method.

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

Similar content being viewed by others

Abbreviations

\(s\) :

Solid

\(f\) :

Base Fluid

\(nf\) :

Nanofluid

References

  1. Majdalani J, Zhou C, Dawson CA (2002) Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. J Biomech 35:1399–1403

    Article  Google Scholar 

  2. Dauenhauer EC, Majdalani J (2003) Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls. Phys Fluids 15:1485–1495

    Article  MathSciNet  MATH  Google Scholar 

  3. Dinarvand S, Rashidi MM (2010) A reliable treatment of a Homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls. Nonlinear Anal Real World Appl 11:1502–1512

    Article  MathSciNet  MATH  Google Scholar 

  4. Khan NA, Mahmood A, Ara A (2010) Approximate solution of couple stress fluid with expanding or contracting porous channel. Eng Comput: I J Comput Aided Eng Softw 30:399–408

    Article  Google Scholar 

  5. Kandelousi MS (2014) KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel. Phys Lett A 378:3331–3339

    Article  MATH  Google Scholar 

  6. Sheikholeslami M, Abelman S, Ganji DD (2014) Numerical simulation of MHD nanofluid flow and heat transfer considering viscous dissipation. Int J Heat Mass Transf 79:212–222

    Article  Google Scholar 

  7. Sheikholeslami M, Hatami M, Ganji DD (2013) Analytical investigation of MHD nanofluid flow in a semi-porous channel. Powder Technol 246:327–336

    Article  Google Scholar 

  8. Hatami M, Sheikholeslami M, Ganji DD (2014) Nanofluid flow and heat transfer in an asymmetric porous channel with expanding or contracting wall. J Mol Liq 195:230–239

    Article  Google Scholar 

  9. Akbar MZ, Ashraf M, Iqbal MF, Ali K (2016) Heat and mass transfer analysis of unsteady MHD nanofluid flow through a channel with moving porous walls and medium. AIP Adv 6:045222

    Article  Google Scholar 

  10. Das K (2015) Nanofluid flow over a non-linearpermeable stretching sheet with partial slip. J Egypt Math Soc 23(2):451–456

    Article  MATH  Google Scholar 

  11. Elgazery NS (2019) Nanofluids flow over a permeable unsteady stretching surface with non-uniform heat source/sink in the presence of inclined magnetic field. Elgazery J Egypt Math Soc 27:9

    Article  MathSciNet  MATH  Google Scholar 

  12. Jusoh R, Nazar R, Pop I (2018) Three-dimensional flow of a nanofluid over a permeable stretching/shrinking surface with velocity slip: a revised model. Phys Fluids 30:033604

    Article  Google Scholar 

  13. Mohyud-Din STH, Hamid M, Usman M, Kanwal A, Zubair T, Wang W, Nazir A (2019) Rotating flow of nanofluid due to exponentially stretching surface: an optimal study. J Algorithms Comput Technol 13:1–14

    Article  MathSciNet  Google Scholar 

  14. Khan NA, Sultan F, Shaikh A, Ara A, Rubbab Q (2016) Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid. AIP Adv 6:115102

    Article  Google Scholar 

  15. Soomro FA, Usman M, Haq R, Wang W (2018) Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: modified Legendre wavelets approach. Phys E: Low-dimens Syst Nanostruct 104:130–137

    Article  Google Scholar 

  16. Aznam SM, Ghani NAC, Chowdhury MSH (2019) A numerical solution for nonlinear heat transfer of fin problems using the quasilinearization method. Results Phys 14:102393

    Article  Google Scholar 

  17. Islam S, Sarler B, Aziz I, Haq F (2011) Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems. Int J Therm Sci 5:686–697

    Article  Google Scholar 

  18. Mittal RC, Pandit S (2017) Numerical simulation of unsteady squeezing nanofluid and heat flow between two parallel plates using wavelets. Int J Therm Sci 118:410–422

    Article  Google Scholar 

  19. Uchida S, Aoki H (1977) Unsteady flows in a semi-infinite contracting or expanding pipe. J Fluid Mech 82:371–387

    Article  MathSciNet  MATH  Google Scholar 

  20. Chui CK, Lian JA (1995) Construction of compactly supported symmetric and anti-symmetric orthonormal wavelets with scale-3. Appl Comput Harmon Anal 2:21–51

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The work is supported by University Grant Commission under D. S. Kothari Postdoctoral Fellowship scheme with grant No. MA/18-19/0013 (S-78).

Author information

Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147001, India

    Sapna Pandit

  2. Department of Mathematics and Statistics, Gurukul Kangri, Vishwavidyalaya, Hardwar, (U.K.), 249404, India

    Seema Sharma

Authors
  1. Sapna Pandit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Seema Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sapna Pandit.

Additional information

Publisher's Note

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

Research Statement: Investigation of the influence of various emerging parameters, such as expansion ratio, Reynolds number, nanoparticle volume fraction and temperature power index on thermal transmission and nanofluid flow through an asymmetric porous channel is analysed. Governing PDEs have been transformed in system of ODEs using similarity transformation. Then, wavelet collocation method has been employed to compute the solutions of coupled non-linear ODEs. Validation of wavelet method has been demonstrated through numerical results as well as graphs.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pandit, S., Sharma, S. On the Use of Wavelets for Analysis of Nanofluid Flow and Thermal Transmission Through Asymmetric Porous Channel. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 92, 571–583 (2022). https://doi.org/10.1007/s40010-022-00773-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-022-00773-0

Keywords

Search

Navigation