MHD natural convection from two heating modes in fined triangular enclosures filled with porous media using nanofluids

  • Sameh E. Ahmed
  • M. A. Mansour
  • A. M. RashadEmail author
  • T. Salah


In this paper, numerical investigations for magnetohydrodynamic natural convection from two heating systems inside fined triangular enclosures filled with an isotropic porous medium using the nanofluids are performed. The two heating modes are represented by two cases, namely, case 1 a triangular enclosure with a heated part at the left wall and including a cold fin at the bottom wall and case 2 in which a cold part at the left wall and a heated fin located at the bottom wall. The copper is considered as nanoparticles and the Darcy model is applied to the porous medium. The triangular physical model is transformed to a rectangular computational model using suitable grid transformations and then the finite-volume method is applied to solve the resulting system. The key parameters in this study are the height, width and locations of the fin, different lengths and locations of the active part, nanoparticles volume fraction, heat generation/absorption parameter, and the Hartmann number. The results revealed that the increase in height of the fins decays the nanofluid flow in case 1, but in case 2, it accelerates the fluid motion. In addition, the increase in width and height of the fin enhances the rate of the heat transfer regardless the heating mode.


MHD Active part Heated/cold fin Nanofluids Heating mode 

List of symbols


Heat source/sink length (m)


Dimensionless heat source/sink length


External magnetic field (Tesla)


Specific heat at constant pressure (kg m2 K s−2)


Heat source/sink position (m)


Dimensionless heat source/sink position


Darcy number


Location of the fin


Dimensionless location of the fin


Gravitational acceleration (m s−2)


Height of fin


Dimensionless height of fin


Length of the bottom and height wall of triangle (m)


Hartmann number


Thermal conductivity (W mK−1)


Permeability of the porous medium (m2)


Local Nusselt number


Average Nusselt number


Pressure (N/m2)


Prandtl number \(\Pr = \nu_{\text{f}} /\alpha_{\text{f}}\)


Dimensionless heat generation/absorption parameter


Dimensional heat generation/absorption parameter


Rayleigh number \({\text{Ra}} = g\,\beta \,\Delta T\,H^{3} /\nu_{\text{f}} \alpha_{\text{f}}\)


Temperature (K)


Dimensional temperature


Dimensionless velocity component along x-direction


Dimensionless velocity component along y-direction

x, y

Cartesian coordinates (m)


Width of fin


Dimensionless fin width

X, Y

Dimensionless Cartesian coordinates

Greek symbols


Thermal diffusivity (m2 s−1)


Thermal expansion coefficient (K−1)


Nanoparticles volume fraction


Dynamic viscosity (Pa s)


Dimensionless vorticity




Dimensionless temperature


Density (kg m−3)


Heat capacity ratio


Electrical conductivity of fluid (S m−1)


Electrical conductivity of nanofluid (S m−1)


Dimensionless time parameter


Stream function (m2 s−1)


Dimensionless stream function














The authors would like to extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through General Research Project under Grant Number (R.G.P1./91/40).


  1. 1.
    Choi S. Enhancing thermal conductivity of fluids with nanoparticles. FED. 1995; 99:103–231.Google Scholar
  2. 2.
    Rashidi I, Mahian O, Lorenzini G, Biserni C, Wongwises S. Natural convection of Al2O3/water nanofluid in a square cavity: effects of heterogeneous heating. Int J Heat Mass Transf. 2014;74:391–402.CrossRefGoogle Scholar
  3. 3.
    Estellé P, Mahian O, Maré T, Öztop HF. Natural convection of CNT water based nanofluids in a differentially heated square cavity. J Therm Anal Calorim. 2017;128:1765–70.CrossRefGoogle Scholar
  4. 4.
    Heris SZ, Pour MB, Mahian O, Wongwises S. A comparative experimental study on the natural convection heat transfer of different metal oxide nanopowders suspended in turbine oil inside an inclined cavity. Int J Heat Mass Transf. 2014;73:231–8.CrossRefGoogle Scholar
  5. 5.
    Putra N, Roetzel W, Das SK. Natural convection of nanofluids. Heat Mass Transfer. 2003;39:775–84.CrossRefGoogle Scholar
  6. 6.
    Sheremet MA, Pop I. Free convection in a triangular cavity filled with a porous medium saturated by a nanofluid: Buongiorno’s mathematical model. Int J Numer Methods Heat Fluid Flow. 2015;25:1138–61.CrossRefGoogle Scholar
  7. 7.
    Ho CJ, Liu WK, Chang YS, Lin CC. Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study. Int J Thermal Sci. 2010;49:1345–53.CrossRefGoogle Scholar
  8. 8.
    Öztop HF, Abu-Nada E. Numerical study of natural convection in partially heated rectangular enclosure filled with nanofluids. Int J Heat Fluid. 2008;29:1326–36.CrossRefGoogle Scholar
  9. 9.
    Siddiqa RSR, Mansour MA, Rashad AM, Salah T. Heat source/sink effects on natural convection of a hybrid nanofluid-filled porous cavity. J Thermophys Heat Transf. 2017;3:847–57.Google Scholar
  10. 10.
    Miroshnichenko IV, Sheremet MA, Öztop HF, Abu-Hamdeh N. Natural convection of Al2O3/H2O nanofluid in an open inclined cavity with a heat-generating element. Int J Heat Mass Transf. 2018;126:184–91.CrossRefGoogle Scholar
  11. 11.
    Sheremet MA, Öztop HF, Gvozdyakov DV, Ali ME. Impacts of heat-conducting solid wall and heat-generating element on free convection of Al2O3/H2O nanofluid in a cavity with open border. Energies. 2018;11(12):3434.CrossRefGoogle Scholar
  12. 12.
    Bondarenko DS, Sheremet MA, Oztop HF, Ali ME. Natural convection of Al2O3/H2O nanofluid in a cavity with a heat-generating element heatline visualization. Int J Heat Mass Transf. 2019;130:564–74.CrossRefGoogle Scholar
  13. 13.
    Selimefendigil F, Öztop HF. Conjugate mixed convection of nanofluid in a cubic enclosure separated with a conductive plate and having an inner rotating cylinder. Int J Heat Mass Transf. 2019;139:1000–17.CrossRefGoogle Scholar
  14. 14.
    Ghasemi B, Aminossadati SM, Raisi A. Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int J Therm Sci. 2011;50:1748–56.CrossRefGoogle Scholar
  15. 15.
    Yu PX, Qiu JX, Qin Q, Tian ZF. Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field. Int J Heat Mass Transf. 2013;67:1131–44.CrossRefGoogle Scholar
  16. 16.
    Bondareva NS, Sheremet MA, Pop I. Magnetic field effect on the unsteady natural convection in a right-angle trapezoidal cavity filled with a nanofluid. Int J Numer Methods Heat Fluid Flow. 2015;25:1924–46.CrossRefGoogle Scholar
  17. 17.
    Teamah MA, EI-Maghlany WM. Augmentation of natural convection heat transfer in square cavity by utilizing nanofluids in the presence of magnetic field and uniform heat generation/absorption. Int J Therm Sci. 2012;58:130–42.CrossRefGoogle Scholar
  18. 18.
    Nemati H, Farhadi M, Sedighi K, Ashorynejad HR, Fattahi E. Magnetic field effects on natural convection of nanofluid in a rectangular cavity using the Lattice Boltzmann model. Sci Iranica Trans B Mech Eng. 2012;19:303–10.Google Scholar
  19. 19.
    Hamida MBB, Charrada K. Natural convection heat transfer in an enclosure filled with an ethylene glycol-copper nanofluid under magnetic fields. Numer Heat Transf Part A. 2015;67:902–20.CrossRefGoogle Scholar
  20. 20.
    Mansour MA, Ahmed SE, Rashad AM. MHD natural convection in a square enclosure using nanofluid with the influence of thermal boundary conditions. J Appl Fluid Mech. 2016;9(5):2515–25.Google Scholar
  21. 21.
    Rashad AM, Ismael MA, Chamkha AJ, Mansour MA. MHD mixed convection of localized heat source/sink in a nanofluid-filled lid-driven square cavity with partial slip. J Taiwan Inst Chem Eng. 2016;68:173–86.CrossRefGoogle Scholar
  22. 22.
    Rashad AM, Gorla RSR, Mansour MA, Ahmed SE. Magnetohydrodynamic effect on natural convection in a cavity filled with porous medium saturated with nanofluid. J Porous Media. 2017;20(4):363–79.CrossRefGoogle Scholar
  23. 23.
    Rashad AM, Sivasankaran S, Mansour MA, Bhuvaneswari M. Magneto-convection of nanofluids in a lid-driven trapezoidal cavity with internal heat generation and discrete heating. Numer Heat Transf Part A Appl. 2017;71(12):1223–34.CrossRefGoogle Scholar
  24. 24.
    Selimefendigil F, Öztop HF. Corrugated conductive partition effects on MHD free convection of CNT-water nanofluid in a cavity. Int J Heat Mass Transf. 2019;129:265–77.CrossRefGoogle Scholar
  25. 25.
    Selimefendigil F, Chamkha AJ. Magnetohydrodynamics mixed convection in a lid-driven cavity having a corrugated bottom wall and filled with a non-Newtonian power-law fluid under the influence of an inclined magnetic field. J Thermal Sci Eng Appl. 2016;8(2):021023.CrossRefGoogle Scholar
  26. 26.
    Selimefendigil F, Öztop HF. 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. 2018;136:264–78.CrossRefGoogle Scholar
  27. 27.
    Chamkha AJ, Selimefendigil F, Ismael MA. Mixed convection in a partially layered porous cavity with an inner rotating cylinder. J Numer Heat Transf Part A Appl Int J Comput Methodol. 2016;69:659–75.CrossRefGoogle Scholar
  28. 28.
    Selimefendigil F, Öztop HF. MHD pulsating forced convection of nanofluid over parallel plates with blocks in a channel. Int J Mech Sci. 2019;157–158:726–40.CrossRefGoogle Scholar
  29. 29.
    Selimefendigil F, Öztop HF. Mixed convection of nanofluid filled cavity with oscillating lid under the influence of an inclined magnetic field. J Taiwan Inst Chem Eng. 2016;63:202–15.CrossRefGoogle Scholar
  30. 30.
    Selimefendigil F, Öztop HF. Fluid-solid interaction of elastic-step type corrugation effects on the mixed convection of nanofluid in a vented cavity with magnetic field. Int J Mech Sci. 2019;152:185–97.CrossRefGoogle Scholar
  31. 31.
    Dogonchi AS, Sheremet MA, Pop I, Ganji DD. MHD natural convection of Cu/H2O nanofluid in a horizontal semi-cylinder with a local triangular heater. Int J Numer Methods Heat Fluid Flow. 2018;28:2979–96.CrossRefGoogle Scholar
  32. 32.
    Ahmed SE, Elshehabey HM. Buoyancy-driven flow of nanofluids in an inclined enclosure containing an adiabatic obstacle with heat generation/absorption: effects of periodic thermal conditions. Int J Heat Mass Transf. 2018;124:58–73.CrossRefGoogle Scholar
  33. 33.
    Ahmed SE, Raizah ZAS. Natural convection flow of nanofluids in a composite system with variable-porosity media. J Thermophys Heat Transf. 2018;32(2):495–502.CrossRefGoogle Scholar
  34. 34.
    Hussain S, Ahmed SE, Saleem F. Impact of periodic magnetic field on entropy generation and mixed convection. J Thermophys Heat Transf. 2018;32(4):999–1012.CrossRefGoogle Scholar
  35. 35.
    Ahmed SE, Hussein AK, Mansour MA, Raizah ZA, Zhang X. MHD mixed convection in trapezoidal enclosures filled with micropolar nanofluids. Nanosci Technol Int J. 2018;9(4):343–72.CrossRefGoogle Scholar
  36. 36.
    Hatami M. Numerical study of nanofluids natural convection in a rectangular cavity including heated fins. J Mol Liq. 2017;233:1–8.CrossRefGoogle Scholar
  37. 37.
    Mansour MA, Mohamed RA, Abd-Elaziz MM, Ahmed SE. Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid. Int Commun Heat Mass Transf. 2010;37(10):1504–12.CrossRefGoogle Scholar
  38. 38.
    Rashad AM, Chamkha AJ, Ismael MA, Salah T. Magnetohydrodynamics natural convection in a triangular cavity filled with a Cu-Al2O3/water hybrid nanofluid with localized heating from below and internal heat generation. J Heat Transf. 2018;140(7):072502.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Khalid UniversityAbhaSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceSouth Valley UniversityQenaEgypt
  3. 3.Department of Mathematics, Faculty of ScienceAssuit UniversityAssuitEgypt
  4. 4.Department of Mathematics, Faculty of ScienceAswan UniversityAswanEgypt
  5. 5.Basic and Applied Sciences Department, College of Engineering and TechnologyArab Academy for Science & Technology and Maritime Transport (AASTMT), Aswan BranchAswanEgypt

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