Skip to main content
SpringerLink
Log in

Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular porous channel

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

In the present work, the characteristics of physical model unsteady nanofluid flow and heat transfer in an asymmetric porous channel are analyzed numerically using wavelet collocation method. Using similarity transformation, unsteady two-dimensional flow model of nanofluid in a porous channel through expanding or contracting walls has been transformed into a system of nonlinear ordinary differential equations (ODEs). Then, the obtained nonlinear system of ODEs is solved via wavelet collocation method. The effect of various emerging parameters, such as nanoparticle volume fraction, Reynolds number (Re), and expansion ratio have been analyzed on velocity and temperature profiles. Numerical results have been presented in form of figures and tables. For some special cases, the obtained numerical results are compared with exact one and found that the results are good in agreement with exact solutions.

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.

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

Similar content being viewed by others

Abbreviations

\( \hat{u} \) :

Velocity component in \( \hat{x} \) direction

\( \hat{v} \) :

Velocity component in \( \hat{y} \) direction

\( \varphi \) :

Nanoparticle volume fraction

T :

Temperature

R:

Re

Pr:

Prandtl number

p :

Pressure

ρ :

Density

µ :

Viscosity

\( C_{\text{p}} \) :

Specific heat in constant pressure

\( k \) :

Thermal conductivity

\( a \) :

Distance between parallel plates

\( \alpha \) :

Expansion and Contraction ratio

\( {\text{Nu}} \) :

Nusselt Number

t :

Time

\( \nu \) :

Kinematic viscosity

f:

Base Fluid

nf:

Nanofluid

w:

Wall

l:

Lower wall

u:

Upper wall

References

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

    Article  Google Scholar 

  2. Ahmed N, Erturk VS, Khan U, Mohyud-Din S, Bin-Mohsin B (2017) MHD flow of a viscous fluid between dilating and squeezing porous walls. Iran J Sci Technol Trans A 41:951–956

    Article  MathSciNet  Google Scholar 

  3. Ahmed N, Mohyud-Din ST, Hassan SM (2016) Flow and heat transfer of nanofluid in an asymmetric channel with expanding and contracting walls suspended by carbon nanotubes: a numerical investigation. Aerosp Sci Technol 48:53–60

    Article  Google Scholar 

  4. 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 

  5. Khan U, Ahmed N, Mohyud-Din ST, Sikander W (2018) Flow of carbon nanotubes suspended nanofluid in stretchable non-parallel walls. Neural Comput Appl 30:2859–2871

    Article  Google Scholar 

  6. Khan U, Ahmed N, Mohyud-Din ST (2017) Heat transfer effects on carbon nanotubes suspended nanofluid flow in a channel with non-parallel walls under the effect of velocity slip boundary condition: a numerical study. Neural Comput Appl 28:37–46

    Article  Google Scholar 

  7. 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 

  8. 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 

  9. Khan NA, Mahmood A, Ara A (2013) Approximate solution of couple stress fluid with expanding or contracting porous channel. Eng Comput 30:399–408

    Article  Google Scholar 

  10. 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. https://doi.org/10.1063/1.1567719

    Article  MathSciNet  MATH  Google Scholar 

  11. Xinhui S, Liancun Z, Xinxin Z, Jianhong Y (2011) Homotopy analysis method for the heat transfer in a asymmetric porous channel with an expanding or contracting wall. Appl Math Model 35:4321–4329

    Article  MathSciNet  Google Scholar 

  12. Baharifard F, Parand K, Rashidi MM (2019) Novel solution for heat and mass transfer of a MHD micropolar fluid flow on a moving plate with suction and injection. Eng Comput. https://doi.org/10.1007/s00366-020-01026-7

    Article  Google Scholar 

  13. Rosa MA, Lippiello M, Tomasiello S (2018) Differential quadrature solutions for the nonconservative instability of a class of single-walled carbon nanotubes. Eng Comput 35(1):251–267

    Article  Google Scholar 

  14. Ahmed N, Khan U, Mohyud-Din ST, Bin-Mohsin B (2018) A finite element investigation of the flow of a Newtonian fluid in dilating and squeezing porous channel under the influence of nonlinear thermal radiation. Neural Comput Appl 29:501–508

    Article  Google Scholar 

  15. Khan SI, Mohyud-Din ST, Bin-Mohsin B (2017) Thermo-diffusion and Diffuso-thermo effects on MHD squeezing flow between parallel disks. Surf Rev Lett. https://doi.org/10.1142/s0218625x17500226

    Article  Google Scholar 

  16. Mohyud-Din ST, Ahmed N, Khan U (2017) Flow of a radioactive Casson fluid through a deformable asymmetric porous channel. Int J Numer Methods Fluid Flow 27:2115–2130

    Article  Google Scholar 

  17. Khan U, Ahmed N, Mohyud-Din ST (2018) Analysis of magnetohydrodynamic flow and heat transfer of Cu-water nanofluid between parallel plates for different shapes of nanoparticles. Neural Comput Appl 29:695–703

    Article  Google Scholar 

  18. Mohyud-Din ST, Yildirim A, Demirli G (2011) Analytical solution of wave system in with coupling controllers. Int J Numer Methods Heat Fluid Flow 21:198–205

    Article  MathSciNet  Google Scholar 

  19. Lijima AV, Amadi EV, Chen Y, Papadopoulos C (2019) Carbon nanotube assembly and integration for applications. Nanoscale Res Lett. https://doi.org/10.1186/s11671-019-3046-3

    Article  Google Scholar 

  20. Srinivas S, Subramanyam Reddy A, Ramamohan TR (2012) A study on thermal-diffusion and diffusion-thermo effects in a two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability. Int J Heat Mass Transf 55:3008–3020

    Article  Google Scholar 

  21. Mittal RC, Pandit S (2018) Sensitivity analysis of shock wave Burgers’ equation via a novel algorithm based on scale-3 Haar wavelets. Int J Comput Math 95(3):601–625

    Article  MathSciNet  Google Scholar 

  22. Pandit S, Kumar M, Mohapatra RN, Alshomrani AS (2017) Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets. Int J Numer Methods Heat Fluid Flow 27(8):1814–1850

    Article  Google Scholar 

  23. Kumar M, Pandit S (2014) A composite scheme for the numerical simulation of coupled Burgers’ equation. Comput Phys Commun 185:809–817

    Article  MathSciNet  Google Scholar 

  24. Mittal RC, Pandit S (2019) A numerical algorithm to capture spin patterns of fractional bloch NMR flow models. J Comput Nonlinear Dyn. https://doi.org/10.1115/1.4043565

    Article  Google Scholar 

  25. Jiwari R (2015) A hybrid numerical scheme for the numerical solution of the Burgers’ equation. Comput Phys Commun 188:59–67

    Article  MathSciNet  Google Scholar 

  26. Jiwari R (2012) Haar wavelet quasilinearization approach for numerical simulation of Burgers’ equation. Comput Phys Commun 183:2413–2423

    Article  MathSciNet  Google Scholar 

  27. Oruç O, Esen A, Bulut F (2019) A haar wavelet approximation for two–dimensional time fractional reaction-subdiffusion equation. Eng Comput 35:75–86

    Article  Google Scholar 

  28. Iqbal MA, Mohyud-Din ST, Bin-Mohsin B (2016) Modified Legendre wavelets technique for nonlinear biochemical reaction model. Int J Biomath. https://doi.org/10.1142/s1793524516500716

    Article  MATH  Google Scholar 

  29. Syed MT, Muhammad H, Muhammad U, Afshan K, Tamour Z, Wei W, Aqsa N (2019) Rotating flow of nanofluid due to exponentially stretching surface: an optimal study. J Algorithms Comput Technol. https://doi.org/10.1177/1748302619881365

    Article  MathSciNet  Google Scholar 

  30. 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. https://doi.org/10.1063/1.4967212

    Article  Google Scholar 

  31. 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 104:130–137

    Article  Google Scholar 

  32. 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 

  33. 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 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Mathematics, Gurukula Kangri Vishwavidyalaya, Haridwar, UK, 249404, India

    Sapna Pandit & 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.

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. Wavelet strategy for flow and heat transfer in CNT-water based fluid with asymmetric variable rectangular porous channel. Engineering with Computers 38 (Suppl 1), 93–103 (2022). https://doi.org/10.1007/s00366-020-01139-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01139-z

Keywords

Search

Navigation