Combined effect of natural convection and non-gray gas radiation with partial heating


The present paper reports numerical results of combined effects of non-gray gas radiation and natural convection between two vertical plates with partial heating at walls. The plates are symmetrical and made of two equal zones alternately isotherm and insulated. The idea is to predict that thermal radiation will attenuate the difference pre-established in the literature, between choosing a partial heating from the top and the bottom of the wall. Computations are carried out to establish flow and temperature fields of the fluid in the enclosure. The effect of enclosure dimensions and boundary conditions are analyzed. Using the computed temperature fields, the mean Nusselt number is calculated. The results show that there is no major influence of two-dimensional radiation to reduce the difference between the reported top and bottom heating for the chosen gas.

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15


  1. 1

    Chu H H S, Churchill S W and Patterson C V S 1976 The effect of heater size, location, aspect ratio and boundary conditions on two-dimensional laminar natural convection rectangular channels. ASME J. Heat Transf. 98(2): 194–201

    Article  Google Scholar 

  2. 2

    Valencia A and Frederick R L 1989 Heat transfer in square cavities with partially active vertical walls. Int. J. Heat Mass Transf. 32(8): 1567–1574

    Article  Google Scholar 

  3. 3

    Shen R, Prasad V and Keyhani M 1989 Effect of aspect ratio and size of heat source on free convection in a discretely heated vertical cavity. ASME, Heat Trans. Division 121: 45–54

    Google Scholar 

  4. 4

    Refai A G and Yovanovich M M 1991 Influence of discrete heat source location on natural convection heat transfer in a vertical square enclosure. ASME J. Electron. Packaging 113(3): 268–274

    Article  Google Scholar 

  5. 5

    Hasnaoui M, Bilgen E and Vasseour P 1992 Natural convection heat transfer in rectangular cavities partially heated from below. J. Thermophys. Heat Transf. 6(2): 255–264

    Article  Google Scholar 

  6. 6

    Nicolas J D and Nansteel M W 1993 Natural convection in a rectangular enclosure with partial heating of the lower surface: experimental results. Int. J. Heat Mass Transf. 36(16): 4067–4071

    Article  Google Scholar 

  7. 7

    Yücel N 1994 Natural convection in rectangular enclosures with partial heating and cooling. Wärme-und Stoffübertragung 29(8): 471–477

    Article  Google Scholar 

  8. 8

    Aydin O and Yang W J 2000 Natural convection in enclosures with localized heating from below and symmetrical cooling from sides. Int. J. Numer. Method. Heat Fluid Flow 10(5): 518–529

    Article  MATH  Google Scholar 

  9. 9

    Berrin Erbay L, Altaç Z and Sülüs B 2004 Entropy generation in a square enclosure with partial heating from a vertical lateral wall. Heat Mass Transf. 40(12): 909–918

    Article  Google Scholar 

  10. 10

    Calcagni B, Marsili F and Paroncini M 2005 Natural convective heat transfer in square enclosures heated from below. Appl. Therm. Eng. 25(16): 2522–2531

    Article  Google Scholar 

  11. 11

    Chen T H and Chen L Y 2007 Study of buoyancy-induced flows subjected to partially heated sources on the left and bottom walls in a square enclosure. Int. J. Therm. Sci. 46(12): 1219–1231

    Article  Google Scholar 

  12. 12

    Ben Cheikh N, Ben Beya B and Lili T 2007 Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below. Int. Commun. Heat Mass Tranf. 34(3): 369–379

    Article  Google Scholar 

  13. 13

    Aghajani Delavar M, Farhadi M and Sedighi K 2011 Effect of discrete heater at the vertical wall of the cavity over the heat transfer and entropy generation using lattice Boltzmann method. Therm. Sci. 15(2): 423–435

    Article  Google Scholar 

  14. 14

    Alam P, Kumar A, Kapoor S and Ansari S R 2012 Numerical investigation of natural convection in a rectangular enclosure due to partial heating and cooling at vertical walls. Commun. Nonlinear Sci. Numer. Simu. 17(6): 2403–2414

    MathSciNet  Article  MATH  Google Scholar 

  15. 15

    Nardini G and Paroncini M 2012 Heat transfer experiment on natural convection in a square cavity with discrete sources. Heat Mass Transf. 48(11): 1855–1865

    Article  Google Scholar 

  16. 16

    Cianfrini C, Corcione M, Habib E and Quintino A 2013 Convective transport in rectangular cavities partially heated at the bottom and cooled at one side. J. Therm. Sci. 22(1): 55–63

    Article  Google Scholar 

  17. 17

    Oueslati F, Ben-Beya B and Lili T 2014 Numerical investigation of thermosolutal natural convection in a rectangular enclosure of an aspect ratio four with heat and solute sources. Heat Mass Transfer 50(5): 721–736

    Article  Google Scholar 

  18. 18

    Mahapatra P S, Manna N K, Ghosh K and Mukhopadhyay A 2015 Heat transfer assessment of an alternately active bi-heater undergoing transient natural convection. Int. J. Heat Mass Transf. 83: 450–464

    Article  Google Scholar 

  19. 19

    Lauriat G 1982 Combined Radiation-Convection in gray fluids enclosed in vertical cavities. J. Heat Transf. 104(4): 609–615

    Article  Google Scholar 

  20. 20

    Fusegi T, Ishii K, Farouk B and Kuwahara K 1991 Natural convection-radiation interactions in a cube with a non-gray gas. Numer. Heat Transf. A-Appl. 19(2): 207–217

    Article  Google Scholar 

  21. 21

    Tan Z and Howell J R 1991 Combined radiation and natural convection in a two-dimensional participating square medium. Int. J. Heat Mass Transf. 34(3): 785–793

    Article  Google Scholar 

  22. 22

    Yücel A, Acharya S and Williams M L 1994 Natural convection of a radiating fluid in a square enclosure with perfectly conducting end walls. Sadhana 19(5): 751–764

    Article  Google Scholar 

  23. 23

    Mesyngier C and Farouk B 1996 Turbulent natural convection-non-gray gas radiation analysis in a square enclosure. Numer. Heat Transf. A-Appl. 29(7): 671–687

    Article  Google Scholar 

  24. 24

    Colomer G, Costa M, Consul R and Oliva A 2004 Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method. Int. J. Heat Mass Transf. 47(2): 257–269

    Article  MATH  Google Scholar 

  25. 25

    Mahapatra S K 2008 Numerical simulation for optimal configuration of heater and cooler locations with natural convection inside a square enclosure and the effect of radiation in the presence of radiatively active medium. Proc. Inst. Mech. Eng. Part C J. Mech. Ing. Sci. 222(8): 1505–1514

    Article  Google Scholar 

  26. 26

    Borjini M N, Ben Aissia H, Halouani K and Zeghmati B 2008 Effect of radiative heat transfer on the three-dimensional buoyancy flow in cubic enclosure heated from the side. Int. J. Heat Fluid Flow 29(1): 107–118

    Article  Google Scholar 

  27. 27

    Mazgar A, Ben Nejma F and Charrada K 2009 Entropy generation through combined non-grey gas radiation and natural convection in vertical pipe. Prog. Comput. Fluid Dyn. 9(8): 495–506

    Article  Google Scholar 

  28. 28

    Mondal B and Mishra S C 2009 Simulation of natural convection in the presence of volumetric radiation using the lattice Boltzmann method. Numer. Heat Transf. A-Appl. 55(1): 18–41

    Article  Google Scholar 

  29. 29

    Mondal B and Li X 2010 Effect of volumetric radiation on natural convection in a square cavity using lattice Boltzmann method with non-uniform lattices. Int. J. Heat Mass Transf. 53: 4935–4948

    Article  MATH  Google Scholar 

  30. 30

    Kumar P and Eswaran V 2010 A numerical simulation of combined radiation and natural convection in a differential heated cubic cavity. J. Heat Transf. 132(2), 1–13.

    Article  Google Scholar 

  31. 31

    Ben Nejma F and Slimi K 2010 Combined natural convection and radiation in humid air bounded by isothermal vertical walls. High Temp. High Press. 39(3): 217–226

    Google Scholar 

  32. 32

    Lari K, Baneshi M, Gandjalikhan Nassab S A, Komiya A and Maruyama S 2011 Combined heat transfer of radiation and natural convection in a square cavity containing participating gases. Int. J. Heat Mass Transf. 54: 5087–5099

    Article  MATH  Google Scholar 

  33. 33

    El Ayachi R, Raji A, Hasnaoui M, Abdelbaki A and Naïmi M 2011 Combined effects of radiation and natural convection in a square cavity submitted to cross gradients of temperature: Case of partial heating and cooling. Comput. Therm. Sci. 3(1): 73–87

    Article  Google Scholar 

  34. 34

    Soufiani A and Taine J 1997 High temperature gas radiative property parameters of statistical narrow-band model for H2O, CO2 and CO, and correlated-k model for H2O and CO2. Int. J. Heat Mass Transf. 40(4): 757–991

    Article  Google Scholar 

  35. 35

    Ben Nejma F, Mazgar A and Charrada K 2008 Entropy generation through combined non-grey gas radiation and forced convection between two parallel plates. Energy 33(7): 1169–1178

    Article  Google Scholar 

  36. 36

    Mazgar A, Ben Nejma F and Charrada K 2013 Second law analysis of coupled mixed convection and non-grey gas radiation within a cylindrical annulus. Int. J. Math. Model. Methods Appl. Sci. 7(3): 265–276

    Google Scholar 

  37. 37

    Ben Nejma F, Mazgar A and Charrada K 2010a Radiative entropy generation in a cylindrical enclosure. In: Eur. Conf. Chem. Eng. ECCE’10, Eur. Conf. Civil Eng., ECCIE’10, Eur. Conf. Mech. Eng., ECME’10, Eur. Conf. Control, ECC’10, 67–70

  38. 38

    Ben Nejma F, Mazgar A and Charrada K 2010b Volumetric and wall non grey gas entropy creation in a cylindrical enclosure. WSEAS Trans. Heat Mass Transf. 5(4): 217–226

    Google Scholar 

  39. 39

    Ben Nejma F, Mazgar A and Charrada K 2011 Application of the statistical narrow-band correlated-k model to entropy generation through non-grey gas radiation inside a spherical enclosure. Int. J. Exergy 8(2): 128–147

    Article  Google Scholar 

  40. 40

    Sakly A, Mazgar A and Ben Nejma F 2015 Thermal radiation contribution on humidification process in a cylindrical annular duct. High Temp.-High Press. 44(3): 163–186

    Google Scholar 

  41. 41

    Taine J and Petit J P 1989 Transferts thermiques: mécanique des fluides anisothermes. Paris: Edition Bordas

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to A Mazgar.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mazgar, A., Ben Nejma, F. Combined effect of natural convection and non-gray gas radiation with partial heating. Sādhanā 41, 805–815 (2016).

Download citation


  • Natural convection
  • partial heating
  • thermal radiation