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Entropy generation in two phase model for simulating flow and heat transfer of carbon nanotubes between rotating stretchable disks with cubic autocatalysis chemical reaction

  • Noor Saeed KhanEmail author
  • Samina Zuhra
  • Qayyum Shah
Original Article
  • 14 Downloads

Abstract

Entropy generation in two phase model for simulating flow and heat transfer of carbon nanotubes in water based fluid in rotating system with the effects of magnetic field, joule heating, thermal radiation, convective boundary conditions and homogeneous–heterogeneous reactions with cubic autocatalysis is examined. The governing equations of the problem are transformed into nonlinear ordinary differential equations by introducing the appropriate similarity transformations which are solved analytically by the homotopy analysis method (HAM). The effects of active parameters are depicted graphically and illustrated. Validation of the present results are shown through Table 2. The study furnishes an overview of the modifications, how they can be detected and quantified using parameters and how this information provides insight into their role in other sciences.

Keywords

Lorentz forces Entropy generation Two phase model SWCNTs/MWCNTs Convective boundary conditions Joule heating Cubic autocatalysis Homogeneous–heterogeneous reactions Homotopy analysis method 

Notes

Acknowledgements

All the comments and valuable suggestions of the reviewer are highly appreciated. The reviewer’s diplomatic and professional transformation of crude to refine mind in the realm of research and academics is noticed and highly appreciated.

The authors are thankful to the Higher Education Commission (HEC) Pakistan for providing the technical and financial support.

Compliance with ethical standards

Conflict of interests

The authors declare that they have no actual or potential conflict of interests including any financial, personal, or other relationship with other people or organization.

References

  1. Bejan A (1980) Second law analysis in heat transfer. Energy 5:720–732CrossRefGoogle Scholar
  2. Choi SUS (1995) Enhancing thermal conductivity of fluids with nanoparticles. In: International mechanical engineering congress and exposition, San Francisco, USA, ASME, FED 231/MD, vol 66, pp 99–105Google Scholar
  3. Hayat T, Farooq M, Alsaedi A (2015) Homogeneous-heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heatings. AIP Adv 5:027130CrossRefGoogle Scholar
  4. Hayat T, Qayyum S, Khan MI, Alsaedi A (2017) Current progresses about probable error and statistical declaration for radiative two phase flow using \(\text{AG-H}_{2}\text{O}\) and \(\text{Cu-H}_{2}\text{O}\) nanomaterials. Int J Hydrogen Energy 42:29107–29120.  https://doi.org/10.1016/j.ijhydene.2017.09.124 CrossRefGoogle Scholar
  5. Imtiaz M, Hayat T, Alsaedi A, Ahmad B (2016) Convective flow of carbon nanotubes between rotating stretchable disks with thermal radiation effects. Int J Heat Mass Transf 101:948–957.  https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.114 CrossRefGoogle Scholar
  6. Karman TV (1921) Uber laminare and turbulente Reibung. J Appl Math Mech 1:233–252Google Scholar
  7. Khan NS (2018) Bioconvection in second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms. Braz J Phys 43(4):227–241.  https://doi.org/10.1007/s13538-018-0567-7 CrossRefGoogle Scholar
  8. Khan NS, Gul T, Islam S, Khan W (2017a) Thermophoresis and thermal radiation with heat and mass transfer in a magnetohydrodynamic thin film second-grade fluid of variable properties past a stretching sheet. Eur Phys J Plus 132:11.  https://doi.org/10.1140/epjp/i2017-11277-3 CrossRefGoogle Scholar
  9. Khan NS, Gul T, Islam S, Khan W, Khan I, Ali L (2017b) Thin film flow of a second-grade fluid in a porous medium past a stretching sheet with heat transfer. Alex Eng J 57:1019–1031.  https://doi.org/10.1016/j.aej.2017.01.036 CrossRefGoogle Scholar
  10. Khan NS, Gul T, Islam S, Khan A, Shah Z (2017c) Brownian motion and thermophoresis effects on MHD mixed convective thin film second-grade nanofluid flow with Hall effect and heat transfer past a stretching sheet. J Nanofluids 6(5):812–829.  https://doi.org/10.1166/jon.2017.1383 CrossRefGoogle Scholar
  11. Khan NS, Gul T, Islam S, Khan I, Alqahtani AM, Alshomrani AS (2017d) Magnetohydrodynamic nanoliquid thin film sprayed on a stretching cylinder with heat transfer. J Appl Sci 7:271CrossRefGoogle Scholar
  12. Khan NS, Gul T, Khan MA, Bonyah E, Islam S (2017e) Mixed convection in gravity-driven thin film non-Newtonian nanofluids flow with gyrotactic microorganisms. Results Phys 7:4033–4049.  https://doi.org/10.1016/j.rinp.2017.10.017 CrossRefGoogle Scholar
  13. Khan NS, Zuhra S, Shah Z, Bonyah E, Khan W, Islam S (2018a) Slip flow of Eyring-Powell nanoliquid film containing graphene nanoparticles. AIP Adv 8:115302CrossRefGoogle Scholar
  14. Khan MI, Hayat T, Qayyum S, Khan MI, Alsaedi A (2018b) Entropy generation (irreversibility) associated with flow and heat transport mechanism in Sisko nanomaterial. Phys Lett A 382:2343–2353.  https://doi.org/10.1016/j.physleta.2018.05.047 CrossRefGoogle Scholar
  15. Khan NS, Zuhra S, Shah Z, Bonyah E, Khan W, Islam S (2019a) Hall current and thermophoresis effects on magnetohydrodynamic mixed convective heat and mass transfer thin film flow. J Phys Commun 3:035009.  https://doi.org/10.1088/2399-6528/aaf830 CrossRefGoogle Scholar
  16. Khan NS, Shah Z, Islam S, Khan I, Alkanhal TA, Tlili I (2019b) Entropy generation in MHD mixed convection non-Newtonian second-grade nanoliquid thin film flow through a porous medium with chemical reaction and stratification. Entropy 21:139.  https://doi.org/10.3390/e21020139 CrossRefGoogle Scholar
  17. Liao SJ (2012) Homotopy analysis method in nonlinear differential equations. Higher Education Press, Springer, BerlinCrossRefGoogle Scholar
  18. Makind OD, Animasaun IL (2016) Bioconvection in MHD nanofluid flow with nonlinear thermal radiation and quartic autocatalysis chemical reaction past an upper surface of a paraboloid of revolution. Int J Therm Sci 109:159–171.  https://doi.org/10.1016/j.ijthermalsci.2016.06.0043 CrossRefGoogle Scholar
  19. Murshed SMS, Nieto de Castro CA, Lourenco MJV, Lopes MLM, Santos FJV (2011) A review of boiling and convective heat transfer with nanofluids. Renew Sustain Energy Rev 15(5):2342–2354CrossRefGoogle Scholar
  20. Palwasha Z, Islam S, Khan NS, Ayaz H (2018) Non-Newtonian nanoliquids thin film flow through a porous medium with magnetotactic microorganisms. Appl Nanosci.  https://doi.org/10.1007/s13204-018-0834-5 Google Scholar
  21. Palwasha Z, Khan NS, Shah Z, Islam S, Bonyah E (2018) Study of two-dimensional boundary layer thin film fluid flow with variable thermo-physical properties in three dimensions space. AIP Adv 8:105318.  https://doi.org/10.1063/1.5053808 CrossRefGoogle Scholar
  22. Qayyum S, Imtiaz M, Alsaedi A, Hayat T (2018) Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganisms for rotating disk of variable thickness. Chin J Phys 106:127–134.  https://doi.org/10.1016/j.cjph.2018.06.020 Google Scholar
  23. Sheikholeslami M (2018) Finite element method for PCM solidification in existence of CuO nanoparticles. J Mol Liquids 265:347–355.  https://doi.org/10.1016/j.molliq.2018.05.132 CrossRefGoogle Scholar
  24. Sheikholeslami M (2018) Solidification of NEPCM under the effect of magnetic field in a porous thermal energy storage enclosure using CuO nanoparticle. J Mol Liquids 263:303–315.  https://doi.org/10.1016/j.molliq.2018.04.144 CrossRefGoogle Scholar
  25. Sheikholeslami M (2018) Influence of magnetic field on \(\text{AL}_{2}\text{O}_{3}\) nanofluid forced convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM. J Mol Liquids 263:472–488.  https://doi.org/10.1016/j.molliq.2018.04.111 CrossRefGoogle Scholar
  26. Sheikholeslami M (2018) Application of Darcy law for nanofluid flow in a porous cavity under the impact of Lorentz forces. J Mol Liquids 266:495–503.  https://doi.org/10.1016/j.molliq.2018.06.083 CrossRefGoogle Scholar
  27. Sheikholeslami M (2019) Numerical approach for MHD \(\text{Al}_{2}\text{O}_{3}\)-water nanofluid transportation inside a permeable medium using innovative computer method. Comput Methods Appl Mech Eng 344:306–318.  https://doi.org/10.1016/j.cma.2018.09.042 CrossRefGoogle Scholar
  28. Sheikholeslami M (2019) New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Comput Methods Appl Mech Eng 344:319–333.  https://doi.org/10.1016/j.cma.2018.09.044 CrossRefGoogle Scholar
  29. Sheikholeslami M, Li Z, Shafee A (2018) Lorentz forces effect on NEPCM heat transfer during solidification in a porous energy storage system. Int J Heat Mass Transf 127:665–674.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.087 CrossRefGoogle Scholar
  30. Sheikholeslami M, Saleem S, Li Z, Shafee A, Jiang Y (2018) Nanofluid heat transfer augmentation and exergy loss inside a pipe equipped with innovative turbulators. Int J Heat Mass Transf 126:156–163.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.128 CrossRefGoogle Scholar
  31. Sheikholeslami M, Shehzad SA, Li Z (2018) Water based nanofluid free convection heat transfer in a three dimensional porous cavity with hot sphere obstacle in existence of Lorentz forces. Int J Heat Mass Transf 125:375–386.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.076 CrossRefGoogle Scholar
  32. Sheikholeslami M, Jafaryar M, Li Z (2018) Second analysis for nanofluid turbulent flow inside a circular duct in presence of twisted tape turbulators. J Mol Liquids 263:489–500CrossRefGoogle Scholar
  33. Sheikholeslami M, Shehzad SA, Li Z, Shafee A (2018) Numerical modeling for alumina nanofluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law. Int J Heat Mass Transf 127:614–622.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.07.013 CrossRefGoogle Scholar
  34. Sheikholeslami M, Gerdroodbary MB, Moradi R, Shafee A, Li Z (2019) Application of neural network for estimation of heat transfer treatment of \(\text{Al}_{2}\text{O}_{3}\text{-H}_{2}\text{O}\) nanofluid through a channel. Comput Methods Appl Mech Eng 344:1–12.  https://doi.org/10.1016/j.cma.2018.09.025 CrossRefGoogle Scholar
  35. Sheikholeslami M, Rizwan-ul Haq, Ahmad Shafee, Zhixiong Li (2019) Heat transfer behavior of nanoparticle enhanced PCM solidification through an enclosure with V shaped fins. Int J Heat Mass Transf 130:1322–1342.  https://doi.org/10.1016/j.ijheatmasstransfer.2018.11.020 CrossRefGoogle Scholar
  36. Zuhra S, Khan NS, Khan MA, Islam S, Khan W, Bonyah E (2018) Flow and heat transfer in water based liquid film fluids dispensed with graphene nanoparticles. Result Phys 8:1143–1157.  https://doi.org/10.1016/j.rinp.2018.01.032 CrossRefGoogle Scholar
  37. Zuhra S, Khan NS, Islam S (2018) Magnetohydrodynamic second grade nanofluid flow containing nanoparticles and gyrotactic microorganisms. Comput Appl Math 37:6332–6358.  https://doi.org/10.1007/s40314-018-0683-6 CrossRefGoogle Scholar

Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.Department of MathematicsAbdul Wali Khan UniversityMardanPakistan
  2. 2.Department of MathematicsAbasyn UniversityPeshawarPakistan
  3. 3.Department of Basic Sciences and IslamiyatUniversity of Engineering and TechnologyPeshawarPakistan

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