International Scientific Journal

Thermal Science - Online First

online first only

Combined natural convection and radiation in presence of internal heat generation source in absorbing-emitting-scattering medium

Numerical investigation of combined laminar natural convection and volumetric radiation with internal heat generation is presented in this paper and computations are performed for a grey gas-filled square cavity whose horizontal walls are adiabatic and vertical walls are differentially heated. The convection is treated under Boussinesq approximation by an approach based on finite-volumes and the volumetric radiation by the discrete ordinates method. Flow and heat transfer characteristics through isotherms, streamlines and average Nusselt numbers have been presented for an external Rayleigh number 106, internal Rayleigh number 0 to 4x1012, optical thickness 0 to 10 and Albedo 0 to 1. Representative results illustrating the effects of the optical thickness and the internal heat generation on the flow and the temperature distribution within the cavity are presented. The results reveal that the fluid flow and heat transfer are influenced significantly by the volumetric radiation and the internal heat generation. By comparing the solutions in pure convection, the results in combined convection-volumetric radiation show that when the medium is participating, the effect of internal source presence is very important.
PAPER REVISED: 2022-09-01
PAPER ACCEPTED: 2022-09-08
  1. Mckenzie, D. P., et al., Convection in the Earth's Mantle: Toward a Numerical Simulation, J. Fluid Mech., 62 (1974), 3, pp. 465-538
  2. Travis, B., et al., Three-Dimensional Convection Planforms with Internal Heat Generation, Geophys. Res. Lett., 17(1990), pp. 243-246
  3. Sharma, A. K., et al., Conjugate Transient Natural Convection in a Cylindrical Enclosure with Internal Volumetric Heat Generation, Ann. Nucl. Energy, 35(2008), 8, pp. 1502-1514
  4. Lee, S. D., et al., Natural Convection Thermo Fluid Dynamics In a Volumetrically Heated Rectangular Pool, Nucl. Eng. Des., 237(2007), 5, pp. 473-483
  5. G. Lauriat, Combined Radiation-Convection in Gray Fluids Enclosed in Vertical Cavities, J. Heat Transfer, 104(1982), 4, pp. 609-615
  6. YĆ¼cel, A., et al., Natural Convection and Radiation in a Square Enclosure, Numer. Heat Tr. A-Appl., 15 (1989), 2, pp. 261-278
  7. Draoui, A., et al., Numerical Analysis of Heat Transfer by Natural Convection and Radiation in Participating Fluids Enclosed in Square Cavities, Numer. Heat Tr. A-Appl., 20 (1991), 2, pp. 253-261
  8. Fusegi, T., Farouk, B., Laminar and Turbulent Natural Convection-Radiation Interactions in a Square Enclosure Filled with a Nongray Gas, Numer. Heat Tr. A-Appl., 15(1989), 3, pp. 303-322
  9. Tan, Z., Howell, J. R., Combined Radiation and Convection in a Two-Dimensional Participating Square Medium, Int. J. Heat Mass Transfer, 34(1991), 3, pp. 785-793
  10. G Colomer, G., et al., Three-Dimensional Numerical Simulation of Convection and Radiation in a Differentially Heated Cavity Using the Discrete Ordinates Method, Int. J. Heat Mass Transfer, 47 (2004), 2, pp. 257-269
  11. Ibrahim, A., Coupling of Natural Convection and Radiation in Absorbing-Emitting Gas Mixtures (in French language), Ph. D. thesis, University of Poitiers, France, 2010
  12. Laouar-Meftah, S., et al., Comparative Study of Radiative Effects on Double Diffusive Convection in Non gray Air-CO2 Mixtures in Cooperating and Opposing Flow, Math. Probl. Eng., (2015), pp. 1-17
  13. Moufekkir, F., et. al., Numerical Prediction of Heat Transfer by Natural Convection and Radiation in an Enclosure Filled with an Isotropic Scattering Medium, J. Quant. Spectrosc. Radiat. Transf., 113 (2012), 13, pp. 1689-1704
  14. Lari, K., et al., Combined Heat Transfer of Radiation and Natural Convection in a Square Cavity Containing Participating Gases, Int. J. Heat Mass Transfer, 54(2011), 23-24, pp. 5087-5099
  15. Liu, X., et al., Combined Natural Convection and Radiation Heat Transfer of Various Absorbing-Emitting-Scattering Media in a Square Cavity, Adv. Mech. Eng., 6(2015), pp. 403690-1-10
  16. Mezrhab, A., et al., Numerical Study of Double-Diffusion Convection Coupled to Radiation in a Square Cavity Filled with a Participating Grey Gas, J. Phys. D: Appl. Phys., 41(20), 19, pp. 195501-1-16
  17. Byun, K.-H., HyukIm, M., Radiation Laminar Free Convection in a Square Duct with Specular by Absorbing-Emitting Medium, KSMEI Int. J., 16(2002), 10, pp. 1346-1354
  18. Kumar, P., Eswaran, V., A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity, J. Heat Transfer, 132(2010), pp. -1-13
  19. Chaabane, R., et. al., Numerical Study of Transient Convection with Volumetric Radiation Using an Hybrid Lattice Boltzmann BGK-Control Volume Finite Element Method, J. Heat Transfer, 139(2017), 9, pp.1-7
  20. Balaji, C. Venkateshan, S. P., Interaction of Surface Radiation with Free Convection in a Square Cavity, Int. J. Heat Fluid Flow, 14(1993), 3, pp. 260-267
  21. Akiyama, M., Chong, Q. P., Numerical Analysis Of Natural Convection with Surface Radiation in a Square Enclosure, Numer. Heat Tr. A-Appl., 32(1997), pp. 419-433
  22. Lauriat, G., Desrayaud, G., Effect of Surface Radiation on Conjugate Natural Convection in Partially Open Enclosures, Int. J. Therm. Sci., 45 (2006), 4, pp. 335-346
  23. Wang, H.,, Numerical Study of Natural Convection-Surface Radiation Coupling in Air-Filled Square Cavities, C.R. Mec., 334 (2006), 1, pp. 48-57
  24. Hamimid, S., et al., Numerical Simulation of Combined Natural Convection Surface Radiation for Large Temperature Gradients, J. Thermophys. Heat Transfer, 29 (2015), 3, pp.1509-1517
  25. Bouafia, M., et al., Non-Boussinesq Convection in a Square Cavity with Surface Thermal Radiation, Int. J. Therm. Sci., 96 (2015), pp.236-247
  26. Ashraf, M., et al., Computational Analysis of the Effect of Nano Particle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption, CMC-Comput. Mater. Con., 65 (2020), 2, pp. 1809-1823
  27. Waqas, M., et al., Interaction of Heat Generation in Nonlinear Mixed/Forced Convective Flow of Williamson Fluid Flow Subject to Generalized Fourier's and Fick's Concept, J. Mater. Res. Technol., 9 (2020), 5, pp. 11080-11086
  28. Elbashbeshy, E. M. A., et al., Effect of Thermal Radiation on Free Convection Flow and Heat Transfer over a Truncated Cone in the Presence of Pressure Work and Heat Generation/Absorption, Thermal Science, 20 (2016), 2, pp. 555-565
  29. Hamimid, S., et al., Numerical Analysis of Combined Natural Convection-Internal Generation Source-Surface Radiation, Thermal Science, 20 (2016), 6, pp. 1879-1889.
  30. Rachedi, N., et al., Effect of Radiation on the Flow Structure and Heat Transfer in a 2-D Gray Medium, Thermal Science, 23(2019), 6A, pp. 3603-3614
  31. Modest, M. F., Radiative Heat Transfer, 2nd ed., Academic Press, Sandi ego, USA, 2003
  32. Fiveland, W. A., Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures, J. Heat Transfer, 106(1984), 4, pp. 699-706
  33. Crosbie, A. L., Schrenker, R. G., Exact Expression for Radiative Transfer in a Three-Dimensional Rectangular Geometry, J. Quant. Spectrosc. Radiat. Transf., 28 (1982), 6, pp. 507-526
  34. El Kasmi, A., Application Of The Discrete Ordinate Method to Radiative Transfer in Complex Two-Dimensional Geometries, Radiation-Convection Coupling (in French language), Master's thesis, University of Quebec, Canada, 1999
  35. Shim, Y.M., et al., Transient Confined Natural Convection with Internal Heat Generation, Int. J. Heat Fluid Flow, 18(1997), pp. 328-333
  36. Oztop, H. F., et al., Natural Convection in Wavy Enclosures with Volumetric Heat Sources, Int. J. Therm. Sci., 50(2011), pp. 502-514