Skip to main content
SpringerLink
Log in

Effect of zero mass flux condition on heat and mass transfer analysis of nanofluid flow inside a cavity with magnetic field

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

Abstract

The present paper examines steady natural convection of Buongiorno’s model nanofluid flow in a square cavity with enhanced mass flux boundary condition numerically. The impact of magnetic field, Brownian motion, radiation and thermophoresis is also considered in this analysis. The governing equations are represented in terms of stream function, temperature and concentration which are solved by utilizing finite difference method of second-order accuracy. The results are presented in the form of streamlines, temperature lines, concentration lines, local Nusselt number and Sherwood number for various values of influenced parameters, such as, Rayleigh number \( \left( {100 \le {\text{Ra}} \le 10^{3} } \right) \), Magnetic parameter \( \left( {0.1 \le {\text{M}} \le 0.5} \right) \), Buoyancy ratio parameter \( \left( {0.1 \le {\text{Nr}} \le 1.0} \right) \), Radiation number \( \left( {0.1 \le {\text{R}} \le 1.0} \right) \), Brownian motion number \( \left( {0.1 \le {\text{Nb}} \le 0.7} \right) \), Thermophoresis number \( \left( {0.1 \le {\text{Nt}} \le 1.0} \right) \) and Lewis number \( \left( {10 \le {\text{Le}} \le 20} \right) \) are represented through graphs. The outcomes indicate that noticeable intensification in rate of heat transfer is perceived after suspending nanoparticles. Furthermore, increasing the values of both thermophoresis and Brownian motion parameters augments the values of Nusselt number inside the cavity.

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
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36

Similar content being viewed by others

Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

Abbreviations

g:

Gravitational acceleration

\( k_{\text{f}} \) :

Thermal conductivity of basefluid

\( {\text{Nt}} \) :

Thermophoretic Parameter

\( C_{0} \) :

Nanoparticle volume fraction reference value

\( T_{\text{c}} \) :

Temperature of the cooled wall

T :

Fluid temperature

C :

Nanoparticle volume fraction

\( \overline{{{\text{Nu}}_{1} }} \) :

Average Nusselt Number

\( K^{*} \) :

Mean absorption coefficient

\( {\text{Sh}}_{1} \) :

Sherwood number

\( \left( {u,v} \right) \) :

Velocity components in x- and y-axis

Le:

Lewis number

\( D_{\text{m}} \) :

Diffusion coefficient

\( \left( {x, y} \right) \) :

Direction along and perpendicular to the cylinder

Nr:

Buoyancy ratio parameter

M:

Magnetic parameter

Nb:

Brownian motion parameter

\( {\text{Nu}}_{1} \) :

Nusselt number

\( {\text{Ra}} \) :

Local Rayleigh number

H:

Height of the cavity

\( T_{\text{h}} \) :

Temperature of the hot wall

\( D_{\text{B}} \) :

Brownian diffusion coefficient

\( D_{\text{T}} \) :

Thermophoretic diffusion coefficient

\( {\text{Nu}}_{1} \) :

Nusselt number

\( \sigma^{*} \) :

Stephan–Boltzmann constant

Pr:

Prandtl number

\( R \) :

Radiation parameter

\( \overline{{{\text{Sh}}_{1} }} \) :

Average Sherwood number

Le:

Lewis number

L:

Square cavity size

\( B_{0} \) :

Strength of electrical conductivity

\( \alpha_{\text{m}} \) :

Thermal diffusivity of base fluid

\( \mu \) :

Fluid viscosity

\( \phi \) :

Dimensionless nanoparticle volume fraction

\( \beta \) :

Volumetric expansion coefficient of the fluid

\( \left( {\rho c_{\text{p}} } \right)_{\text{nf}} \) :

Heat capacitance of the nanofluid

Ψ :

Dimensionless stream function

\( \nu \) :

Kinematic viscosity

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

Nanoparticle mass density

\( \theta \) :

Dimensionless temperature

\( \rho_{\text{f}} \) :

Fluid density

\( (\rho c_{\text{p}} )_{\text{p}} \) :

Heat capacitance of the fluid

References

  1. S.U.S. Choi, Z.G. Zhang, W. Yu, F.E. Lockwood, E.A. Grulke, Anomalous thermal conductivity enhancement in nanotube suspensions. Appl. Phys. 79, 2252–2254 (2001)

    ADS  Google Scholar 

  2. M. Ghalambaz, A. Behseresht, J. Behseresht, A.J. Chamkha, Effects of nanoparticles diameter and concentration on natural convection of the Al2O3–water nanofluids considering variable thermal conductivity around a vertical cone in porous media. Adv. Powder Technol. 26, 224–235 (2015)

    Article  Google Scholar 

  3. M. Ghalambaz, A. Doostani, A.J. Chamkha, M.A. Ismael, Melting of nanoparticles-enhanced phase-change materials in an enclosure: effect of hybrid nanoparticles. Int. J. Mech. Sci. 134, 85–97 (2017)

    Article  Google Scholar 

  4. P. Sreedevi, K.V. Suryanarayana Rao, P. Sudarsana Reddy, A.J. Chamkha, Heat and Mass transfer flow over a vertical cone through nanofluid saturated porous medium under convective boundary condition with suction/injection. J. Nanofluids 6, 476–486 (2017)

    Article  Google Scholar 

  5. P. Sudarsana Reddy, P. Sreedevi, A.J. Chamkha, MHD boundary layer heat and mass transfer characteristics of nanofluid over a vertical cone under convective boundary condition. Propolsion Power Res. 7, 308–319 (2018)

    Article  Google Scholar 

  6. B. Prabhavathi, P. Sudarsana Reddy, R. Bhuvana Vijaya, Heat and mass transfer enhancement of SWCNTs and MWCNTs based Maxwell nanofluid flow over a vertical cone with slip effects. Powder Technol. 340, 253–263 (2018)

    Article  Google Scholar 

  7. P. Sudarsana Reddy, K. Jyothi, M. Suryanarayana Reddy, Flow and heat transfer analysis of carbon nanotubes based Maxwell nanofluid flow driven by rotating stretchable disks with thermal radiation. J. Braz. Soc. Mech. Sci. Eng. 40, 576 (2018)

    Article  Google Scholar 

  8. P. Sreedevi, P. Sudarsana Reddy, A.J. Chamkha, Heat and mass transfer analysis of unsteady hybrid nanofluid flow over a stretching sheet with thermal radiation. SN Appl. Sci. 2, 1222 (2020)

    Article  Google Scholar 

  9. K. Jyothi, P. Sudarsana Reddy, M. Suryanarayana Reddy, Carreau nanofluid heat and mass transfer flow through wedge with slip conditions and nonlinear thermal radiation. J. Braz. Soc. Mech. Sci. Eng. 41, 415 (2019)

    Article  Google Scholar 

  10. P. Sreedevi, P. Sudarsana Reddy, Combined influence of Brownian motion and thermophoresis on Maxwell three dimensional nanofluid flow over stretching sheet with chemical reaction and thermal radiation. J. Porous Media 23(4), 327–340 (2020)

    Article  Google Scholar 

  11. A. Noghrehabadi, A. Samimi Behbahan, I. Pop, Thermophoresis and Brownian effects on natural convection of nanofluids in a square enclosure with two pairs of heat source/sink. Int. J. Numer. Methods Heat Fluid Flow 25(5), 1030–1046 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. H.M. Elshehabey, S.E. Ahmed, MHD mixed convection in a lid-driven cavity filled by a nanofluid with sinusoidal temperature distribution on the both vertical walls using Buongiorno’s nanofluid model. Int. J. Heat Mass Transf. 88, 181–202 (2015)

    Article  Google Scholar 

  13. M.A. Sheremet, I. Pop, A. Shenoy, Unsteady free convection in a porous open wavy cavity filled with a nanofluid using Buongiorno’s mathematical model. Int. Commun. Heat Mass Transf. 67, 66–72 (2015)

    Article  Google Scholar 

  14. M.A. Sheremet, I. Pop, M.M. Rahman, Three-dimensional natural convection in a porous enclosure filled with a nanofluid using Buongiorno’s mathematical model. Int. J. Heat Mass Transf. 82, 396–405 (2015)

    Article  Google Scholar 

  15. M.A. Sheremet, I. Pop, N.C. Roşca, Magnetic field effect on the unsteady natural convection in a wavy-walled cavity filled with a nanofluid: Buongiorno’s mathematical model. J. Taiwan Inst. Chem. Eng. 61, 211–222 (2016)

    Article  Google Scholar 

  16. M. Ghalambaz, M. Sabour, I. Pop, Free convection in a square cavity filled by a porous medium saturated by a nanofluid: viscous dissipation and radiation effects. Eng. Sci. Technol. Int. J. 19(3), 1244–1253 (2016)

    Google Scholar 

  17. G.H.R. Kefayati, H. Tang, Simulation of natural convection and entropy generation of MHD non-Newtonian nanofluid in a cavity using Buongiorno’s mathematical model. Int. J. Hydrog. Energy 42(27), 17284–17327 (2017)

    Article  Google Scholar 

  18. G.H.R. Kefayati, N.A. Che Sidik, Simulation of natural convection and entropy generation of non-Newtonian nanofluid in an inclined cavity using Buongiorno’s mathematical model (Part II, entropy generation). Powder Technol. 305, 679–703 (2017)

    Article  Google Scholar 

  19. B. Chandra Sekhar, N. Kishan, C. Haritha, Convection in nanofluid-filled porous cavity with heat absorption/generation and radiation. J. Thermophys. Heat Transf. 31(3), 549–562 (2017)

    Article  Google Scholar 

  20. E. Khalili, A. Saboonchi, M. Saghafian, Experimental study of nanoparticles distribution in natural convection of Al2O3–water nanofluid in a square cavity. Int. J. Therm. Sci. 112, 82–91 (2017)

    Article  Google Scholar 

  21. F. Selimefendigil, H.F. Öztop, Modeling and optimization of MHD mixed convection in a lid-driven trapezoidal cavity filled with alumina–water nanofluid: effects of electrical conductivity models. Int. J. Mech. Sci. 136, 264–278 (2018)

    Article  Google Scholar 

  22. N.S. Bondareva, M.A. Sheremet, H.F. Öztop, N. Abu-Hamdeh, Transient natural convection in a partially open trapezoidal cavity filled with a water-based nanofluid under the effects of Brownian diffusion and thermophoresis. Int. J. Numer. Methods Heat Fluid Flow 28(3), 606–623 (2018). https://doi.org/10.1108/hff-04-2017-0170

    Article  Google Scholar 

  23. Z.A.S. Raizah, A.M. Aly, S.E. Ahmed, Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media. Int. J. Mech. Sci. 140, 376–393 (2018)

    Article  Google Scholar 

  24. Q. Yu, H. Xu, S. Liao, Analysis of mixed convection flow in an inclined lid-driven enclosure with Buongiorno’s nanofluid model. Int. J. Heat Mass Transf. 126, 221–236 (2018)

    Article  Google Scholar 

  25. M.S. Astanina, E. Abu-Nada, M.A. Sheremet, Combined effects of thermophoresis, brownian motion, and nanofluid variable properties on Cuo–water nanofluid natural convection in a partially heated square cavity. J. Heat Transf. (2018). https://doi.org/10.1115/1.4039217

    Article  Google Scholar 

  26. S.A.M. Mehryan, M. Ghalambaz, M. Izadi, Conjugate natural convection of nanofluids inside an enclosure filled by three layers of solid, porous medium and free nanofluid using Buongiorno’s and local thermal non-equilibrium models. J. Therm. Anal. Calorim. 135(2), 1047–1067 (2018)

    Article  Google Scholar 

  27. M.H. Sun, G.B. Wang, X.R. Zhang, Rayleigh–Bénard convection of non-Newtonian nanofluids considering Brownian motion and thermophoresis. Int. J. Therm. Sci. 139, 312–325 (2019)

    Article  Google Scholar 

  28. C.S. Balla, C. Haritha, K. Naikoti, A.M. Rashad, Bioconvection in nanofluid-saturated porous square cavity containing oxytactic microorganisms. Int. J. Numer. Methods Heat Fluid Flow 29(4), 1448–1465 (2019)

    Article  Google Scholar 

  29. A.I. Alsabery, T. Armaghani, A.J. Chamkha, I. Hashim, Two-phase nanofluid model and magnetic field effects on mixed convection in a lid-driven cavity containing heated triangular wall. Alex. Eng. J. 59(1), 129–148 (2020)

    Article  Google Scholar 

  30. A.I. Alsabery, M. Ghalambaz, T. Armaghani, A. Chamkha, I. Hashim, M. Saffari Pour, Role of rotating cylinder toward mixed convection inside a wavy heated cavity via two-phase nanofluid concept. Nanomaterials 10(6), 1138 (2020)

    Article  Google Scholar 

  31. M. Ghalambaz, S.A.M. Mehryan, I. Zahmatkesh, A. Chamkha, Free convection heat transfer analysis of a suspension of nano–encapsulated phase change materials (NEPCMs) in an inclined porous cavity. Int. J. Therm. Sci. 157, 106503 (2020)

    Article  Google Scholar 

  32. M. Ghalambaz, S.A.M. Mehryan, A. Tahmasebi, A. Hajjar, Non-Newtonian phase-change heat transfer of nano-enhanced octadecane with mesoporous silica particles in a tilted enclosure using a deformed mesh technique. Appl. Math. Model. 85, 318–337 (2020)

    Article  MathSciNet  Google Scholar 

  33. M. Izadi, M. Ghalambaz, S.A.M. Mehryan, Location impact of a pair of magnetic sources on melting of a magneto-Ferro phase change substance. Chin. J. Phys. 65, 377–388 (2020)

    Article  MathSciNet  Google Scholar 

  34. R.S.R. Gorla, S. Siddiqa, A.A. Hasan, T. Salah, A.M. Rashad, MHD mixed convection in copper-water nanofluid filled lid-driven square cavity containing multiple adiabatic obstacles with discrete heating. Int. J. Appl. Mech. Eng. 25(2), 57–74 (2020)

    Article  Google Scholar 

  35. A.J. Chamkha, R. Yassen, M.A. Ismael, A.M. Rashad, T. Salah, H.A. Nabwey, MHD free convection of localized heat source/sink in hybrid nanofluid-filled square cavity. J. Nanofluids 9(1), 1–12 (2020)

    Article  Google Scholar 

  36. A.M. Rashad, S.E. Ahmed, M.A. Mansour, T. Salah, H.A. Nabwey, Impact of heat corners on magneto-nanofluids natural convection flow in a square porous cavity with elliptical blocks. J. Porous Media 23(8), 805–820 (2020)

    Article  Google Scholar 

  37. T. Armaghani, A. Chamkha, A.M. Rashad, M.A. Mansour, Inclined magneto convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09449-6

    Article  Google Scholar 

  38. F.M. Azizul, A.I. Alsabery, I. Hashim, A.J. Chamkha, Heat line visualization of mixed convection inside double lid-driven cavity having heated wavy wall. J. Therm. Anal. Calorim. (2020). https://doi.org/10.1007/s10973-020-09806-5

    Article  Google Scholar 

  39. M.A. Sheremet, D.S. Cimpean, I. Pop, Thermogravitational convection of hybrid nanofluid in a porous chamber with a central heat-conducting body. Symmetry 12(4), 593 (2020)

    Article  Google Scholar 

  40. E.V. Shulepova, M.A. Sheremet, H.F. Oztop, N. Abu-Hamdeh, Mixed convection of Al2O3–H2O nanoliquid in a square chamber with complicated fin. Int. J. Mech. Sci. 165, 105192 (2020)

    Article  Google Scholar 

  41. S.M. Hashem Zadeh, S.A.M. Mehryan, M. Ghalambaz, M. Ghodrat, J. Young, A. Chamkha, Hybrid thermal performance enhancement of a circular latent heat storage system by utilizing partially filled copper foam and Cu/GO nano-additives. Energy 213, 118761 (2020)

    Article  Google Scholar 

  42. M. Ghalambaz, S.A.M. Mehryan, A. Hajjar, A. Veismoradi, Unsteady natural convection flow of a suspension comprising Nano-Encapsulated Phase Change Materials (NEPCMs) in a porous medium. Adv. Powder Technol. 31(3), 954–966 (2020)

    Article  Google Scholar 

  43. S.A.M. Mehryan, M. Ghalambaz, L. Sasani Gargari, A. Hajjar, M. Sheremet, Natural convection flow of a suspension containing nano-encapsulated phase change particles in an eccentric annulus. J. Energy Storage 28, 101236 (2020)

    Article  Google Scholar 

  44. S.M. Hashem Zadeh, S.A.M. Mehryan, M. Sheremet, M. Ghodrat, M. Ghalambaz, Thermo-hydrodynamic and entropy generation analysis of a dilute aqueous suspension enhanced with nano-encapsulated phase change material. Int. J. Mech. Sci. 178, 105609 (2020)

    Article  Google Scholar 

  45. A.I. Alsabery, I. Hashim, A. Hajjar, M. Ghalambaz, S. Nadeem, M. Saffari Pour, Entropy generation and natural convection flow of hybrid nanofluids in a partially divided wavy cavity including solid blocks. Energies 13(11), 2942 (2020)

    Article  Google Scholar 

  46. M. Sheremet, T. Grosan, I. Pop, MHD free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms. Int. J. Numer. Methods Heat Fluid Flow 29(12), 4642–4659 (2019)

    Article  Google Scholar 

  47. M.A. Sheremet, I. Pop, Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno’s mathematical model. Int. J. Heat Mass Transf. 79, 137–145 (2014)

    Article  Google Scholar 

  48. P. Sudarsana Reddy, P. Sreedevi, Buongiorno’s model nanofluid natural convection inside a square cavity with thermal radiation. Chin. J. Phys. (2020). https://doi.org/10.1016/j.cjph.2020.08.016

    Article  Google Scholar 

  49. A. Mahmoudi, I. Mejri, M.A. Abbassi, A. Omri, Analysis of MHD natural convection in a nanofluid-filled open cavity with non-uniform boundary condition in the presence of uniform heat generation/absorption. Powder Technol. 269, 275–289 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rajeev Gandhi Memorial College of Engineering and Technology, Nandyal, AP, India

    P. Sudarsana Reddy & P. Sreedevi

Authors
  1. P. Sudarsana Reddy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Sreedevi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Sudarsana Reddy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sudarsana Reddy, P., Sreedevi, P. Effect of zero mass flux condition on heat and mass transfer analysis of nanofluid flow inside a cavity with magnetic field. Eur. Phys. J. Plus 136, 102 (2021). https://doi.org/10.1140/epjp/s13360-021-01095-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01095-7

Search

Navigation