Skip to main content
SpringerLink
Log in

CVFEM modeling of fluid flow induced by convective heat transfer from a hot pipe buried in soil

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

In this investigation, fluid flow numerical evaluation induced by convective heat transfer due to a buried hot pipe in the soil is performed. The numerical method implemented is the control volume-based finite element method (CVFEM). The physical domain consists of a circular pipe enclosed in a square cylinder. The temperature of the enclosure upper wall was kept uniform cold while remaining walls were insulated. The research was conducted by fixed non-dimensional parameters, that is, porosity (ε), location of pipe (K), Prandtl number (Pr), permeability (K (X, Y)), Darcy number (Da), and the Rayleigh number (Ra). The simulation of porous medium was performed by the application of Brinkman-extended Darcy model. Results are illustrated through isotherm and streamlines. The results depicted that the effect of Darcy on the average Nusselt number (Nuave), at larger Ra, is more noticeable. Additionally, Da reduction causes suppression in the fluid flow and, in addition, less heat transfer among the hot pipe and enclosure. The non-homogeneity reduces the Nu over the hot pipe. Moreover, the value of pipe location, as well as its radius, significantly affects the pipe heat transferring.

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

Similar content being viewed by others

References

  1. Mehryan SAM, Ghalambaz M, Izadi M. 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. 2019;135:1047–67.

    Article  CAS  Google Scholar 

  2. Abedini A, Armaghani T, Chamkha AJ. MHD free convection heat transfer of a water–Fe 3 O 4 nanofluid in a baffled C-shaped enclosure. J Therm Anal Calorim. 2019;135:685–95.

    Article  CAS  Google Scholar 

  3. Pordanjani AH, Aghakhani S, Karimipour A, Afrand M, Goodarzi M. Investigation of free convection heat transfer and entropy generation of nanofluid flow inside a cavity affected by magnetic field and thermal radiation. J Therm Anal Calorim. 2019;137:997–1019.

    Article  Google Scholar 

  4. Yu Q, Lu Y, Zhang C, Wu Y, Sunden B. Experimental and numerical study of natural convection in bottom-heated cylindrical cavity filled with molten salt nanofluids. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-09112-9.

    Article  Google Scholar 

  5. Esfe MH, Saedodin S, Malekshah EH, Babaie A, Rostamian H. Mixed convection inside lid-driven cavities filled with nanofluids. J Therm Anal Calorim. 2019;135:813–59.

    Article  Google Scholar 

  6. Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2019;137:267–87.

    Article  CAS  Google Scholar 

  7. Ingham DB, Pop I. Transport phenomena in porous media. Amsterdam: Elsevier; 1998.

    Google Scholar 

  8. Vafai K. Handbook of Porous Media. Boca Raton: CRC Press; 2000. https://doi.org/10.1201/b18614.

    Book  Google Scholar 

  9. Baytaş AC, Pop I. Natural convection in a trapezoidal enclosure filled with a porous medium. Int J Eng Sci. 2001;39:125–34. https://doi.org/10.1016/S0020-7225(00)00033-1.

    Article  Google Scholar 

  10. Nield DA, Bejan A. Convection in porous media, vol. 3. Switzerland: Springer; 2006.

    Google Scholar 

  11. Nithiarasu P, Seetharamu KN, Sundararajan T. Natural convective heat transfer in a fluid saturated variable porosity medium. Int J Heat Mass Transf. 1997;40:3955–67. https://doi.org/10.1016/S0017-9310(97)00008-2.

    Article  CAS  Google Scholar 

  12. Sheikholeslami M, Jafaryar M, Shafee A, Babazadeh H. Acceleration of discharge process of clean energy storage unit with insertion of porous foam considering nanoparticle enhanced paraffin. J Clean Prod. 2020;261:121206.

    Article  CAS  Google Scholar 

  13. Pakdee W, Rattanadecho P. Unsteady effects on natural convective heat transfer through porous media in cavity due to top surface partial convection. Appl Therm Eng. 2006;26:2316–26. https://doi.org/10.1016/j.applthermaleng.2006.03.004.

    Article  Google Scholar 

  14. Sheikholeslami M. 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. 2019;344:319–33. https://doi.org/10.1016/j.cma.2018.09.044.

    Article  Google Scholar 

  15. Kaviany M. Non-Darcian effects on natural convection in porous media confined between horizontal cylinders. Int J Heat Mass Transf. 1986;29:1513–9.

    Article  CAS  Google Scholar 

  16. Merkin JH. Free convection boundary layers on axi-symmetric and two-dimensional bodies of arbitrary shape in a saturated porous medium. Int J Heat Mass Transf. 1979;22:1461–2. https://doi.org/10.1016/0017-9310(79)90210-2.

    Article  Google Scholar 

  17. Cheng P. Natural convection in a porous medium: external flows. Nat Convect Fundam Appl. 1985;17:475–513.

    Google Scholar 

  18. Mehta KN, Nandakumar K. Natural convection with combined heat and mass transfer buoyancy effects in non-homogeneous porous medium. Int J Heat Mass Transf. 1987;30:2651–6.

    Article  Google Scholar 

  19. Sheikholeslami M. Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method. Comput Methods Appl Mech Eng. 2019;344:306–18.

    Article  Google Scholar 

  20. Saidi C, Legay-Desesquelles F, Prunet-Foch B. Laminar flow past a sinusoidal cavity. Int J Heat Mass Transf. 1987;30:649–61. https://doi.org/10.1016/0017-9310(87)90195-5.

    Article  CAS  Google Scholar 

  21. Yao LS. Natural convection along a vertical wavy surface. J Heat Trans. 1983;105:465. https://doi.org/10.1115/1.3245608.

    Article  Google Scholar 

  22. Das PK, Mahmud S. Numerical investigation of natural convection inside a wavy enclosure. Int J Therm Sci. 2003;42:397–406.

    Article  Google Scholar 

  23. Chen XB, Yu P, Winoto SH, Low HT. Free convection in a porous wavy cavity based on the Darcy–Brinkman–Forchheimer extended model. Numer Heat Transf Part A Appl. 2007;52:377–97.

    Article  Google Scholar 

  24. Babazadeh H, Shah Z, Ullah I, Kumam P, Shafee A. Analysis of hybrid nanofluid behavior within a porous cavity including Lorentz forces and radiation impacts. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09416-1.

    Article  Google Scholar 

  25. Sheikholeslami M, Sheremet MA, Shafee A, Li Z. CVFEM approach for EHD flow of nanofluid through porous medium within a wavy chamber under the impacts of radiation and moving walls. J Therm Anal Calorim. 2019;138:573–81.

    Article  CAS  Google Scholar 

  26. Babazadeh H, Ambreen T, Shehzad SA, Shafee A. Ferrofluid non-Darcy heat transfer involving second law analysis: an application of CVFEM. J Therm Anal Calorim. 2020. https://doi.org/10.1007/s10973-020-09264-z.

    Article  Google Scholar 

  27. Alrobaian AA, Alsagri AS, Ali JA, Hamad SM, Shafee A, Nguyen TK, et al. Investigation of convective nanomaterial flow and exergy drop considering CVFEM within a porous tank. J Therm Anal Calorim. 2020;139:2337–50.

    Article  CAS  Google Scholar 

  28. Brinkman HC. On the permeability of media consisting of closely packed porous particles. Flow Turbul Combust. 1949;1:81.

    Article  Google Scholar 

  29. Lauriat G, Prasad V. Natural convection in a vertical porous cavity: a numerical study for Brinkman-extended Darcy formulation. J Heat Transfer. 1987;109:688–96.

    Article  CAS  Google Scholar 

  30. Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf. 2003;46:3639–53.

    Article  CAS  Google Scholar 

  31. Sheikholeslami M, Zeeshan A. Analysis of flow and heat transfer in water based nanofluid due to magnetic field in a porous enclosure with constant heat flux using CVFEM. Comput Methods Appl Mech Eng. 2017;320:68–81.

    Article  Google Scholar 

  32. Goering DJ. Passively cooled railway embankments for use in permafrost areas. J Cold Reg Eng. 2003;17:119–33. https://doi.org/10.1061/(ASCE)0887-381X(2003)17:3(119).

    Article  Google Scholar 

  33. Goering DJ, Kumar P. Permeability effects on winter-time natural convection in gravel embankments. Adv Cold-reg Therm Eng Sci. 1999; 455–64.

  34. Konrad J, Ladet R, Langlois P, Larochelle S, Smith M. Study of the drain blockage mechanisms in a rockfill dam in northern Quebec. Trans Int Congr Large Dams. 2006;22:361.

    Google Scholar 

  35. Lebeau M, Konrad J-M. Natural convection of compressible and incompressible gases in undeformable porous media under cold climate conditions. Comput Geotech. 2009;36:435–45.

    Article  Google Scholar 

  36. de Vahl Davis G. Natural convection of air in a square cavity: a bench mark numerical solution. Int J Numer Methods Fluids. 1983;3:249–64.

    Article  Google Scholar 

  37. Kim BS, Lee DS, Ha MY, Yoon HS. A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations. Int J Heat Mass Transf. 2008;51:1888–906.

    Article  CAS  Google Scholar 

Download references

Funding

The study was not funded.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Seyyed Mostafa Seyyedi

  2. Department of Civil Engineering, Babol Noshirvani University of Technology, Babol, Iran

    Moein Ghadakpour

  3. Department of Civil and Environmental Engineering, University of Pittsburgh, 3700 O’Hara Street, 729 Benedum Hall, Pittsburgh, PA, 15261, USA

    Mahmoud Bayat

  4. Department of Chemical Engineering, University of Tehran, Tehran, Iran

    Mohsen Pilehvar

  5. Department of Civil Engineering, Rouzbahan Institute of Higher Education, Sari, Iran

    Saman Soleimani Kutanaei

  6. Department of Civil Engineering, University of Mazandaran, Babolsar, Iran

    Mohammad Abdollahtabar

  7. Department of Civil Engineering, Tabari University of Babol, Babol, Iran

    Meisam Mahmudi Kardarkolai

Authors
  1. Seyyed Mostafa Seyyedi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Moein Ghadakpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mahmoud Bayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohsen Pilehvar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Saman Soleimani Kutanaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Mohammad Abdollahtabar
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Meisam Mahmudi Kardarkolai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moein Ghadakpour.

Ethics declarations

Conflict of interest

It is declared by the authors that there is no conflict of interest.

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

Seyyedi, S.M., Ghadakpour, M., Bayat, M. et al. CVFEM modeling of fluid flow induced by convective heat transfer from a hot pipe buried in soil. J Therm Anal Calorim 146, 367–379 (2021). https://doi.org/10.1007/s10973-020-09906-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-09906-2

Keywords

Search

Navigation