## THERMAL SCIENCE

International Scientific Journal

### COMBINED NATURAL-CONVECTION AND RADIATION IN PRESENCE OF INTERNAL HEAT GENERATION SOURCE IN ABSORBING-EMITTING-SCATTERING MEDIUM

**ABSTRACT**

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.

**KEYWORDS**

PAPER SUBMITTED: 2022-06-06

PAPER REVISED: 2022-09-01

PAPER ACCEPTED: 2022-09-08

PUBLISHED ONLINE: 2022-11-12

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 2**, PAGES [1673 - 1685]

- Mckenzie, D. P., et al., Convection in the Earth's Mantle: Toward a Numerical Simulation, Journal Fluid Mech., 62 (1974), 3, pp. 465-538
- Travis, B., et al., The 3-D Convection Planforms with Internal Heat Generation, Geophys, Res. Lett., 17 (1990), 3, pp. 243-246
- 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
- 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
- Lauriat, G., Combined Radiation-Convection in Gray Fluids Enclosed in Vertical Cavities, Journal Heat Transfer, 104 (1982), 4, pp. 609-615
- Yucel, A., et al., Natural-Convection and Radiation in a Square Enclosure, Numer. Heat Tr. A-Appl., 15 (1989), 2, pp. 261-278
- 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
- Fusegi, T., Farouk, B., Laminar and Turbulent Natural-convection-Radiation Interactions in a Square Enclosure Filled with a Non-gray Gas, Numer. Heat Tr. A-Appl., 15 (1989), 3, pp. 303-322
- Tan, Z., Howell, J. R., Combined Radiation and Convection in a 2-D Participating Square Medium, Int. J. Heat Mass Transfer, 34 (1991), 3, pp. 785-793
- Colomer, G., et al., The 3-D 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
- Ibrahim, A., Coupling of Natural-convection and Radiation in Absorbing-Emitting Gas Mixtures (in French), Ph. D. thesis, University of Poitiers, Poitiers, France, 2010
- 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 (2015), ID586913
- Moufekkir, F., et al., Numerical Prediction of Heat Transfer by Natural-convection and Radiation in an Enclosure Filled with an Isotropic Scattering Medium, Journal Quant. Spectrosc. Radiat. Transf., 113 (2012), 13, pp. 1689-1704
- 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
- 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 (2014), Jan., pp. 403690-1-10
- 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 (2020), 19, pp. 195501-1-16
- 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
- Kumar, P., Eswaran, V., A Numerical Simulation of Combined Radiation and Natural-Convection in a Differential Heated Cubic Cavity, Journal Heat Transfer, 132 (2010), Oct., pp. 1-13
- Chaabane, R., et al., Numerical Study of Transient Convection with Volumetric Radiation Using an Hybrid Lattice Boltzmann BGK-Control Volume Finite Element Method, Journal Heat Transfer, 139 (2017), 9, pp. 1-7
- 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
- Akiyama, M., Chong, Q. P., Numerical Analysis of Natural-Convection with Surface Radiation in a Square Enclosure, Numer. Heat Tr. A-Appl., 32 (1997), 4, pp. 419-433
- 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
- Wang, H., et al., Numerical Study of Natural-convection-Surface Radiation Coupling in Air-Filled Square Cavities, C.R. Mec., 334 (2006), 1, pp. 48-57
- Hamimid, S., et al., Numerical Simulation of Combined Natural-convection Surface Radiation for Large Temperature Gradients, Journal Thermophys. Heat Transfer, 29 (2015), 3, pp. 1509-1517
- Bouafia, M., et al., Non-Boussinesq Convection in a Square Cavity with Surface Thermal Radiation, Int. J. Therm. Sci., 96 (2015), Oct., pp. 236-247
- Ashraf, M., et al., Computational Analysis of the Effect of NanoParticle Material Motion on Mixed Convection Flow in the Presence of Heat Generation and Absorption, CMC-Comput. Mater. Con., 65 (2020), 2, pp. 1809-1823
- Waqas, M., et al., Interaction of Heat Generation in Non-linear Mixed/Forced Convective Flow of Williamson Fluid-Flow Subject to Generalized Fourier's and Fick's Concept, Journal Mater. Res. Technol., 9 (2020), 5, pp. 11080-11086
- 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
- Hamimid, S., et al., Numerical Analysis of Combined Natural-convection-Internal Generation Source-Surface Radiation, Thermal Science, 20 (2016), 6, pp. 1879-1889
- 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
- Modest, M. F., Radiative Heat Transfer, 2nd ed., Academic Press, San Diego, Cal., USA, 2003
- Fiveland, W. A., Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures, Journal Heat Transfer, 106 (1984), 4, pp. 699-706
- Crosbie, A. L., Schrenker, R. G., Exact Expression for Radiative Transfer in a 3-D Rectangular Geometry, Journal Quant. Spectrosc. Radiat. Transf., 28 (1982), 6, pp. 507-526
- El Kasmi, A., Application of the Discrete Ordinate Method to Radiative Transfer in Complex 2-D Geometries, Radiation-Convection Coupling (in French), M. Sc. thesis, University of Quebec, Canada, 1999
- Shim, Y. M., et al., Transient Confined Natural-convection with Internal Heat Generation, Int. J. Heat Fluid-Flow, 18 (1997), 3, pp. 328-333
- Oztop, H. F., et al., Natural-Convection in Wavy Enclosures with Volumetric Heat Sources, Int. J. Therm. Sci., 50 (2011), 4, pp. 502-514