Skip to main content
SpringerLink
Log in

Energy dissipation and Hall effect on MHD convective flow of nanofluid within an asymmetric channel with arbitrary wall thickness and conductance

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The current study examines the consequences of viscous and Joule dissipations, and Hall current on steady buoyancy-driven MHD flow of Ti6Al4V-H2O-based nanofluid within an asymmetric channel with arbitrary wall thickness and conductance in the presence of a highly intense magnetic field. The boundary conditions for the induced magnetic field are also derived. The closed-form solutions for velocity field, induced magnetic field, temperature field, surface skin friction, mass flow rate and critical Grashof number are extracted from non-dimensional flow model analytically, while the numerical values of heat transport rate are obtained by mathematical computations using MATLAB software. The results of the study are thoroughly discussed with the assistance of graphs and tables. Such study has great importance in analyzing the heat transport behavior of the highly electrically conducting nanofluids. A special feature observed from this investigation is that, on incrementing the wall electrical conductivity, the fluid velocity reduces due to induction of magnetic drag. On raising the volumetric concentration of nanoparticles in the fluid, the fluid temperature raises and hence the fluid velocity rises due to generation of more thermal buoyancy force. The viscous dissipation leads to rise the fluid temperature due to rise in internal energy of the system.

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
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Similar content being viewed by others

Abbreviations

\(C_{p}\) :

Specific heat at constant pressure

\(\vec{E}\) :

Electric field

\({\text{Er}}\) :

Eckert number

\(g\) :

Acceleration due to gravity

\(g_{\Theta }\) :

Thermal Grashof number

\({\text{Gc}}\) :

Critical Grashof number

\(\vec{h}\) :

Magnetic field vector

\({\text{Hc}}\) :

Hall current parameter

\(H_{0}\) :

Applied magnetic field

\(\left( {h_{1} ,\,\,h_{2} ,\,\,\,h_{3} } \right)\) :

Components of induced magnetic field along the coordinate axes

\(\vec{J}\) :

Current density

\(k\) :

Thermal conductivity

\(M\) :

Mass flow rate

\({\text{Mg}}\) :

Magnetic parameter

\(\Pr\) :

Prandtl number

\({\text{Ro}}\) :

Rotation parameter

\(\vec{u}\) :

Fluid velocity

\(\left( {u_{1} ,\,\,u_{2} ,\,\,u_{3} } \right)\) :

Components of velocity along the coordinate axes

\(w\) :

Thickness of the wall of the channel

\(w_{0}\) :

Separation of the walls of the channel

\(\left( {x_{1} ,x_{2} ,x_{3} } \right)\) :

Rectangular Cartesian coordinate

\(\beta\) :

Volumetric thermal expansion coefficient

\(\mu\) :

Dynamic viscosity

\(\mu_{e}\) :

Magnetic permeability

\(\upsilon\) :

Coefficient of viscosity

\(\vec{\Omega }\) :

Angular velocity of the gyration

\(\phi\) :

Wall conductance constants

\(\rho\) :

Fluid density

\(\sigma\) :

Electrical conductivity

\(\theta\) :

Fluid temperature

\(\Theta\) :

Non-dimensional fluid temperature

\(\tau\) :

Non-dimensional skin friction

\(\vartheta\) :

Volume fraction constant of nanofluid

\(f\) :

Quantities for base fluid

\(l\) :

Quantities at the lower wall of the channel

\({\text{nf}}\) :

Quantities for nanofluid

\(s\) :

Quantities for suspended nanoparticles

\(u\) :

Quantities at the upper wall of the channel

References

  1. Jul. Hartmann, Hg-DYNAMICS I-Theory of the Laminar flow of an electric-ally conductive liquid in a Homogeneous magnetic field, Det Kgl. Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser, XV, 6 (1937)

  2. J.C.R. Hunt, J. Fluid Mech. 21, 577 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  3. C.C. Chang, J.T. Yen, ZAMP 13(3), 266 (1962)

    ADS  Google Scholar 

  4. W.T. Snyder, J. Heat Transf. 86(4), 552 (1964)

    Article  Google Scholar 

  5. R.R. Gold, AIAA J. 5(3), 266 (1967)

    Article  Google Scholar 

  6. B.S. Mazumdar, Acta Mech. 28(1), 85 (1977)

    Article  ADS  Google Scholar 

  7. M. Tezer-Sezgin, S. Dost, Appl. Math. Model. 18(8), 429 (1994)

    Article  Google Scholar 

  8. T. Nagy, Z. Demendy, Acta Mech. 113(1), 77 (1995)

    Article  Google Scholar 

  9. M.S. Ansari, G.S. Seth, R. Nandkeolyar, Math. Comput. Model. 54, 765 (2011)

    Article  Google Scholar 

  10. G.S. Seth, J.K. Singh, Appl. Math. Model. 40(4), 2783 (2016)

    Article  MathSciNet  Google Scholar 

  11. G.S. Seth, S. Sarkar, O.D. Makinde, J. Mech. 32(5), 613 (2016)

    Article  Google Scholar 

  12. J.K. Singh, S.G. Begum, G.S. Seth, Phys. Fluids 30, 113602 (2018)

    Article  ADS  Google Scholar 

  13. A. Borrelli, G. Giantesio, M.C. Patria, ASME J. Fluids Eng. 139, 1 (2017)

    Article  Google Scholar 

  14. G.S. Seth, J.K. Singh, N. Mahto, N. Joshi, Math. Sci. Lett. 5, 259 (2016)

    Article  Google Scholar 

  15. J.K. Singh, S. Vishwanath, Int. J. Thermofluid Sci. Technol. 7(4), 070402 (2020)

    Article  Google Scholar 

  16. J.K. Singh, G.S. Seth, S. Vishwanath, Heat Transf. 50(2), 1812 (2021)

    Article  Google Scholar 

  17. B. Kumar, G.S. Seth, R. Nandkeolyar, A.J. Chamkha, Int. J. Therm. Sci. 149, 106101 (2019)

    Article  Google Scholar 

  18. T. Hayat, J. Akram, H. Zahir, A. Alsaedi, Phys. Scr. 94, 105201 (2019)

    Article  ADS  Google Scholar 

  19. M. Rashid, K. Ansar, S. Nadeem, Phys. A Stat. Mech. Appl. 553, 123979 (2020)

    Article  Google Scholar 

  20. D. Kumar, A.K. Singh, D. Kumar, Phys. A Stat. Mech. Appl. 544, 123562 (2020)

    Article  Google Scholar 

  21. M. Raza, R. Ellahi, S.M. Sait, M.M. Sarafraz, M.S. Shadloo, I. Waheed, J. Therm. Anal. Calorim. 140, 1277 (2020)

    Article  Google Scholar 

  22. H. Sato, J. Phys. Soc. Jpn. 16, 1427 (1961)

    Article  ADS  Google Scholar 

  23. O.A. Beg, J. Zueco, H.S. Takhar, Commun. Nonlinear Sci. Numer. Simul. 14, 1082 (2009)

    Article  ADS  Google Scholar 

  24. B.K. Jha, C.A. Apere, Appl. Math. Mech. 33, 399 (2012)

    Article  Google Scholar 

  25. S. Siddiqa, M.A. Hossain, R.S.R. Int, J. Therm. Sci. 71, 196 (2013)

    Article  Google Scholar 

  26. O.D. Makinde, T. Iskander, F. Mabood, W.A. Khan, M.S. Tshehla, J. Mol. Liq. 221, 778 (2016)

    Article  Google Scholar 

  27. J.K. Singh, N. Joshi, S.G. Begum, Int. J. Heat Technol. 34, 89 (2016)

    Article  Google Scholar 

  28. R. Tripathi, G.S. Seth, M.K. Mishra, Adv. Powder Technol. 28, 2630 (2017)

    Article  Google Scholar 

  29. I. Tlili, N.N. Hamadneh, W.A. Khan, S. Atawneh, J. Therm. Anal. Calorim. 132, 1899 (2018)

    Article  Google Scholar 

  30. D. Kumar, A.K. Singh, D. Kumar, Eur. Phys. J. Plus 133, 207 (2018)

    Article  Google Scholar 

  31. B.K. Jha, P.B. Malgwi, B. Aina, Proc .IMechE Part N J. Nanomater. Nanoeng. Nanosyst. 233, 73 (2019)

    Google Scholar 

  32. J.K. Singh, G.S. Seth, N. Joshi, C.T. Srinivasa, Bulg. Chem. Commun. 52(1), 147 (2020)

    Google Scholar 

  33. B. Mahanthesh, B.J. Gireesha, G.T. Thammanna, T. Hayat, A. Alsaedi, In: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, 1224 (2018)

  34. A.J. Chamkha, A.S. Dogonchi, D.D. Ganji, AIP Adv. 9(2), 025103 (2019)

    Article  ADS  Google Scholar 

  35. A.T. Akinshilo, BioNanoScience 9, 740 (2019)

    Article  Google Scholar 

  36. J.K. Singh, G.S. Seth, S. Vishwanath, P. Rohidas, Heat Transf. 49(8), 4370 (2020)

    Article  Google Scholar 

  37. S. Nandi, B. Kumbhakar, Therm. Sci. Eng. Progress 19, 100561 (2020)

    Article  Google Scholar 

  38. M. Shoaib, M.A.Z. Raja, M.T. Sabir, S. Islam, Z. Shah, P. Kumam, H. Alrabaiah, Sci. Rep. 10, 18533 (2020)

    Article  Google Scholar 

  39. C.-H. Chen, J. Heat Transf. 132(6), 064503 (2010)

    Article  Google Scholar 

  40. D. Gopal, N. Kishan, C.S.K. Raju, Inf. Med. Unlocked 9, 154 (2017)

    Article  Google Scholar 

  41. K. Ramesh, Propuls. Power Res. 7, 329 (2018)

    Article  Google Scholar 

  42. S.M. Atif, S. Hussain, M. Sagheer, J. Braz. Soc. Mech. Sci. Eng. 41, 189 (2019)

    Article  Google Scholar 

  43. M.D. Shamshuddin, P.V. Satya Narayana, Indian J. Phys. 94, 1385 (2020)

    Article  ADS  Google Scholar 

  44. B.K. Swain, B.C. Parida, S. Kar, N. Senapati, Heliyon 6(10), e05338 (2020)

    Article  Google Scholar 

  45. S.U.S. Choi, ASME Publ. Fed. 231, 99 (1995)

    Google Scholar 

  46. S. Lee, S.U.S. Choi, S. Li, J. A. J. Heat Transfer. 121(2), 280 (1999). https://doi.org/10.1115/1.2825978

    Article  Google Scholar 

  47. C.H. Chon, K.D. Kihm, Appl. Phys. Lett. 87, 153107 (2005)

    Article  ADS  Google Scholar 

  48. A.A. Hussein, M.Z. Abdullah, M.A. Al-Nimr, Appl. Energy 164, 733 (2016)

    Article  Google Scholar 

  49. Z. Li, M. Sheikholeslami, A.J. Chamkha, Z.A. Raizah, S. Saleem, Comput. Methods Appl. Mech. Eng. 338, 618 (2018)

    Article  ADS  Google Scholar 

  50. M. Sheikholeslami, Comput. Methods Appl. Mech. Eng. 344, 306 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  51. Z.Z. Rashed, S.E. Ahmed, M.A. Sheremat, J. Mech. 35(4), 563 (2019)

    Article  Google Scholar 

  52. U. Khan, A. Zaib, I. Khan, K.S. Nisar, J. Mater. Res. Tech. 9(1), 188 (2020)

    Article  Google Scholar 

  53. M. Ramzan, H. Gul, J.D. Chung, S. Kadry, Y.M. Chu, Sci. Rep. 10, 18342 (2020)

    Article  ADS  Google Scholar 

  54. J.K. Singh, K. Suneetha, S. Vishwanath, Heat Transf. 50, 5793 (2021)

    Article  Google Scholar 

  55. S. Das, B. Tarafdar, R.N. Jana, O.D. Makinde, Spec. Top. Rev. Porous Media Int. J. 10, 357 (2019)

    Article  Google Scholar 

  56. B.K. Jha, G. Samaila, SN Appl. Sci. 2, 1321 (2020)

    Article  Google Scholar 

  57. N. Askari, H. Salmani, M.H. Taheri, M. Masoumnezhad, M.A. Kazemi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 235, 1966 (2021)

    Article  Google Scholar 

  58. G.W. Sutton, A. Sherman, Engineering Magnetohydrodynamics (Dover Publications Inc., New York, 2006)

    Google Scholar 

  59. K.R. Cramer, S.I. Pai, Magnetofluiddynamics for Engineers and Applied Physicists (MacGraw-Hill, New York, 1973)

    Google Scholar 

  60. R. Aris, Vectors, Tensors, and the Basic Equations of Fluid Mechanics (Prentice Hall, Englewood Cliffs, NJ, 1962)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Vijayanagara Sri Krishnadevaraya University, Ballari, 583105, India

    Jitendra Kumar Singh & Suneetha Kolasani

  2. Department of Mathematics, Ballari Institute of Technology and Management, Ballari, 583105, India

    Suneetha Kolasani

Authors
  1. Jitendra Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suneetha Kolasani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jitendra Kumar Singh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, J.K., Kolasani, S. Energy dissipation and Hall effect on MHD convective flow of nanofluid within an asymmetric channel with arbitrary wall thickness and conductance. Eur. Phys. J. Plus 136, 1074 (2021). https://doi.org/10.1140/epjp/s13360-021-02022-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-02022-6

Search

Navigation