Natural Convection and Radiation in Enclosures with Semi-transparent Medium: Conjugate CFD Analysis

Document Type : Regular Article


1 Federal University of Viçosa, Department of Engineering, Viçosa, Minas Gerais, 36570-900, Brazil

2 Federal University of São Carlos, Department of Chemistry, São Carlos, São Paulo, 13565-905, Brazil



Radiation heat transfer is often ignored in several studies as it has few significant effects in some cases. However, when using a participating fluid, where the molecules interact with the radiative spectrum, these effects cannot be disregarded. A numerical study of the heat transfer by natural convection and radiation in two square enclosures (with and without protrusions) using a transparent (non-participating) and semi-transparent (participating) fluid medium was carried out in this study. The governing equations were discretized using the finite volume technique and solved using a CFD code ANSYS CFX. The heat transfer by radiation was modeled using the differential approach. The model proposed in this study was validated with the data available in the literature with errors of less than 3%. The results showed that the addition of the participant fluid (CO2) promotes a better condition for heat transfer. It was proven that the use of the participating medium caused an increase in the Nusselt number, indicating an increase in heat transfer by convection. The presence of protrusions reduces the thermal stratification zone for the pure convection case (CP) and provides a better temperature distribution for the cases conjugated with air (CRAIR) and CO2 (CRCO2) when compared to the cases without protrusions. It is observed that for all cases, the geometry with protrusion presented the highest values for the Nusselt number, indicating that the insertion of the protrusion increases the heat transfer in the enclosure by up to 11%. The airflow values for the conjugated cases are more than 300% higher than those presented for the pure convection case for any Rayleigh number value. The heat flow increased by up to 4 times when the radiation effect was considered. The average Nusselt number increased with the increase in the Rayleigh number and with the coupling of radiation in the energy equation. This indicates that the effect of radiation cannot be disregarded in the study of heat transfer in enclosures.


Abu-nada, E. and H. F. Oztop (2009). Effects of inclination angle on natural convection in enclosures filled with Cu–water nanofluid. International Journal of Heat and Fluid Flow 30 (4), 669-678.##
Ahmed, S. E., H. F. Oztop and K. Al-Salem (2014). Natural convection coupled with radiation heat transfer in an inclined porous cavity with corner heater.  Computers & Fluids 102 (Oct.), 74-84.##
Ampofo, F. and T. G. Karayiannis (2003). Experimental benchmark data for turbulent natural convection in an air filled square cavity. International Journal of Heat and Mass Transfer 46 (19), 3551-3572.##
Araujo, M. E. A., E. G. Barbosa, M. A. Martins and P. C. Corrêa (2022). Conjugated analysis of heat transfer by natural convection and radiation in a fin array using a semitransparent fluid medium. Heat and Mass Transfer 58 (Jan.), 1119–1132.##
Baïri, A. (2008). Nusselt–Rayleigh correlations for design of industrial elements: Experimental and numerical investigation of natural convection in tilted square air filled enclosures. Energy Conversion and Management 49 (4), 771-782.##
Bajorek, S. M. and J. R. Lloyd (1982). Experimental Investigation of Natural Convection in Partitioned Enclosures. Journal of Heat Transfer 104 (3), 527-532.##
Bilgen, E. and H. Oztop (2005). Natural convection heat transfer in partially open inclined square cavities. International Journal of Heat and Mass Transfer 48 (8), 1470-1479.##
Cui, Y., Y. Wang, Q. Huang and S. Wei (2016). Effect of radiation and convection heat transfer on cooling performance of radiative panel. Renewable Energy 99 (Dec.), 10-17.##
Dehbi, A., S. Kelm, J. Kalilainen and H. Mueller (2019). The influence of thermal radiation on the free convection inside enclosures. Nuclear Engineering and Design 341 (Jan.), 176-185.##
Eby, S. D., J. Y. Trepanier and X. D. Zhang (1998). Modelling radiative transfer in SF6 circuit-breaker arcs with the P-1 approximation. Journal of Physics 31 (13), 1578–1588.##
Gireesha, B. J., G. Sowmya, M. I. Khan and H. F. Öztop (2020). Flow of hybrid nanofluid across a permeable longitudinal moving fin along with thermal radiation and natural convection. Computer Methods and Programs in Biomedicine 185 (Mar.), 105166.##
Goebel, F. and C. Mundt (2011, April). Implementation of the P1 radiation model in the CFD solver NSMB and investigation of radiative heat transfer in the SSME main combustion chamber. 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, San Francisco, USA.##
Goodarzi, M., M. R. Safaei, H. F. Oztop, A. Karimipour, E. Sadeghinezhad, M. Dahari, S. N. Kazi and N. Jomhari (2014). Numerical Study of Entropy Generation due to Coupled Laminar and Turbulent Mixed Convection and Thermal Radiation in an Enclosure Filled with a Semitransparent Medium. The Scientific World Journal 2014 (Mar.), 761745, 1-8.##
Ibrahim, A., D. Saury and D. Lemonnier (2013). Coupling of turbulent natural convection with radiation in an air-filled differentially-heated cavity at Ra = 1.5 × 109. Computers & Fluids 88 (Dec.), 115-125.##
Karimipour, A. (2017). A novel case study for thermal radiation through a nanofluid as a semitransparent medium via discrete ordinates method to consider the absorption and scattering of nanoparticles along the radiation beams coupled with natural convection. International Communications in Heat and Mass Transfer 87 (Oct.), 256-269.##
Li, X. and J. Tu (2019). Evaluation of the eddy viscosity turbulence models for the simulation of convection–radiation coupled heat transfer in indoor environment. Energy and Buildings 184 (Feb.), 8-18.##
Meftah, S., A. Ibrahim, D. Lemonnier and A. Benbrik (2009). Coupled radiation and double diffusive convection in nongray Air-CO2 and air-h2o mixtures in cooperating situations. Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology 56 (1), 1-19.##
Meng, X., Y. Wang, T. Liu, X. Xing, Y. Cao and J. Zhao (2016). Influence of radiation on predictive accuracy in numerical simulations of the thermal environment in industrial buildings with buoyancy-driven natural ventilation. Applied Thermal Engineering 96 (Mar.), 473-480.##
Mikhailenko, S. A., I. V. Miroshnichenko and M. A. Sheremet (2021). Thermal radiation and natural convection in a large-scale enclosure heated from below: Building application. Building Simulation 14 (Jul.), 681-691.##
Miroshnichenko, I. V., M. A. Sheremet and A. A. Mohamad (2016). Numerical simulation of a conjugate turbulent natural convection combined with surface thermal radiation in an enclosure with a heat source. International Journal of Thermal Sciences 109 (Nov.), 172-181.##
Modest, M. F. (2013). Radiative heat transfer. Academic Press: San Diego, California, USA, 2013, 896p.##
Moufekkir, F., M. A. Moussaoui, A. Mezrhab, D. Lemonnier and H. Haji (2012a). MRT-lattice Boltzmann computations of natural convection and volumetric radiation in a tilted square enclosure. International Journal of Thermal Sciences 54 (Apr.), 125-141.##
Moufekkir, F., M. A. Moussaoui, A. Mezrhab, H. Naji and D. Lemonnier (2012b). Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium. Journal of Quantitative Spectroscopy and Radiative Transfer 113 (13), 1689-1704.##
Nia, M. F., S. A. G. Nassab and A. B. Ansari (2018). Transient combined natural convection and radiation in a double space cavity with conducting walls. International Journal of Thermal Sciences 128 (Jun.), 94-104.##
Oguntala, G., G. Sobamowo and R. Abd-Alhameed (2019). Numerical analysis of transient response of convective-radiative cooling fin with convective tip under magnetic field for reliable thermal management of electronic systems. Thermal Science and Engineering Progress 9 (Mar.), 289-298.##
Patil, S., A. K. Sharma and K. Velusamy (2016). Conjugate laminar natural convection and surface radiation in enclosures: Effects of protrusion shape and position. International Communications in Heat and Mass Transfer 76 (Aug.), 139-146.##
Pishkar, I., B. Ghasemi, A. Raisi and S. M. Aminossadati (2022). Simulation of variable magnetic field effect on natural convection heat transfer of fe3o4/graphite slurry based on experimental properties of slurries. Journal of Applied Fluid Mechanics 15 (1), 1-14.##
Rahimi, M. and A. Sabernaeemi (2011). Experimental study of radiation and free convection in an enclosure with under-floor heating system. Energy Conversion and Management 52 (7), 2752-2757. ##
Rashidi, I., O. Mahian, G. Lorenzini, C. Biserni and S. Wongwises (2014). Natural convection of Al2O3/water nanofluid in a square cavity: Effects of heterogeneous heating. International Journal of Heat and Mass Transfer 74 (Jul.), 391-402.##
Saedodin, S. and M. S. M. Barforoush (2014). Comprehensive analytical study for convective–radiative continuously moving plates with multiple non-linearities. Energy Conversion and Management 81 (May), 160-168.##
Saha, S. and Y. T. Gu (2015). Natural convection in a triangular enclosure heated from below and non-uniformly cooled from top. International Journal of Heat and Mass Transfer 80 (Jan.), 529-538.##
Saravanan, S. and N. Raja (2020). Combined radiation-convection in an air filled enclosure with in-line heaters. International Communications in Heat and Mass Transfer 110 (Jan.), 104399.##
Serrano-Arellano, J. and M. Gijón-Rivera (2014). Conjugate heat and mass transfer by natural convection in a square cavity filled with a mixture of Air–CO2. International Journal of Heat and Mass Transfer 70 (Mar.), 103-113.##
Sharma, A. K., K. Velusamy, C. Balaji and S. P. Venkateshan (2007). Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures. International Journal of Heat and Mass Transfer 50 (3-4), 625-639.##
Siegel, R., J. R. Howell and M. P. Mengüç (2010). Thermal Radiation Heat Transfer. Boca Raton, FL, USA: CRC Press.##
Tsuji, N., M. Nakano, E. Takada, K. Tokuhara, K. Ohashi, F. Okamoto, Y. Tazawa, Y. Inaba and Y. Tachibana (2014). Study of the applicability of CFD calculation for HTTR reactor. Nuclear Engineering and Design 271 (May), 564-568.##
Valh Davis, G. (1983). Natural convection of air in a square cavity: a bench mark numerical solution. International Journal for Numerical Methods in Fluids 3 (3), 249-264.##
Vivek, V., A. K. Sharma and C. Balaji (2012). Interaction effects between laminar natural convection and surface radiation in tilted square and shallow enclosures. International Journal of Thermal Sciences 60 (Oct.), 70-84.##
Wang, Y., X. Meng, X. Yang and J. Liu (2014). Influence of convection and radiation on the thermal environment in an industrial building with buoyancy-driven natural ventilation. Energy and Buildings 75 (Jun.), 394-401.##