Interaction of laminar natural convection and radiation in an inclined square cavity containing participating gases

Document Type: Research Paper

Authors

Mechanical Engineering Department, School of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

Two-dimensional numerical study of flow and temperature fields for laminar natural convection and radiation in the inclined cavity is performed in the present work. The walls of the square cavity are assumed kept at constant temperatures. An absorbing, emitting, and scattering gray medium is enclosed by the opaque and diffusely emitting walls. The set of governing equations, including conservation of mass, momentum, and energy for fluid flow, is solved numerically by the CFD method, while radiation computation is based on the numerical solution of the radiative transfer equation. The finite volume method has been adopted to solve the governing equations, and the discrete ordinates method (DOM) is used to model the radiative transfer in the absorbing-emitting medium. The effects of Rayleigh number from 103 to 106 and inclination angle in a broad range from 0 to 90o on temperature and velocity distributions and Nusselt numbers are investigated. It was found that the total heat transfer in the cavity is increased under thermal radiation, and variation of inclination angle causes a sweep behavior in the flow pattern inside the cavity.

Keywords


[1] Vahl Davis, G. "Natural convection of air in a square cavity: a comparison exercise", International Journal Numerical Methods Fluids, 3, pp. 227–248 (1983).
[2] Ostrach, S. "Completely confined natural convection", Developments in Mechanics, 10th Midwestern Mechanics Conference, 4, Johnson, Chicago Illinois, pp. 53-81 (1967).
[3] Ostrach, S. "Natural convection in enclosures", in Advances in Heat Transfer (edited by J. P. Hartnett and T. F. Irvine. Jr), 8, Academic Press, New York, pp. 161-227 (1972).
[4] Catton, I. "Natural convection in enclosures", In Heat Transfer, 6, National Research Council of Canada (1978).
[5] Markatos, N.C. and Pericleous, K.A. "Laminar and turbulent natural convection in an enclosed cavity", International Journal of Heat Mass Transfer, 27, pp.755–772 (1984).      
[6] Fusegi, T., Hyun, J.M., Kuwaharas, K. and Farouk, K. "A numerical study of three dimensional natural convection in a differentially heated cubical enclosure", International Journal of Heat Mass Transfer, 34, pp. 1543–1557 (1991).
[7] Chang, L.C., Yang, K.T. and Lloyd, J.R. "Radiation natural convection interaction in two-dimensional complex enclosures", ASME Journal Hear Transfer, 105, pp. 89-95 (1983).
[8] Webb, B.W. and Viskanta, R. "Radiation-induced buoyancy-driven flow in rectangular enclosures: experiment and analysis", ASME Journal Heat Transfer, 109, pp. 427-433 (1987).
[9] Yang, K.T. "Numerical modeling of natural convection radiation interactions in enclosures", In Heat Transfer 8th International Heat Transfer Conference, 1, Hemisphere, Washington, DC, pp. 131-140 (1986).
[10] Yucel, A., Acharya, S. and Williams, M.L. "Natural convection and radiation in a square enclosure", Numerical Heat Transfer A, 15, pp. 261-277 (1989).
[11] Lauriat, G. "Combined radiation–convection in gray fluids enclosed in vertical cavities", Journal Heat Transfer, 104, pp. 609–615 (1982).
[12] Lauriat, G. "Numerical study of the interaction of natural convection with radiation in nongray gases in a narrow vertical cavity", International Journal Heat Mass Transfer, pp. 153-158 (1982).
[13] Tan, Z., Howell, J.R. "Combined radiation and natural convection in a two dimensional participating square medium", International Journal Heat Mass Transfer, 34 (3), pp. 785–793 (1991).
[14] Moufekkir, F., Moussaoui, M.A., Mezrhab, A., Naji, H. and Lemonnier, D. "Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium", Journal of Quantitative Spectroscopy & Radiative Transfer, 113, pp. 1689-1704 (2012).
[15] Lari, K., Baneshi, M., Gandjalikhan Nassab, S.A, Komiya, A. and Maruyama, S. "Combined heat transfer of radiation and natural convection in a square cavity containing participating gases", International Journal of Heat and Mass Transfer, 54, pp. 5087-5099 (2011).
[16] Colomer, G., Costa, M., Consul, R. and Oliva, A. "Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinate method", International Journal of Heat and Mass Transfer, 47, pp. 257-269 (2004).
[17] Capdevila, R., Lehmkuhl, O., Colomer, G. and Perez-Segarra, C.D. "Study of turbulent natural convection in a tall differentially heated cavity filled with either non-participating, participating grey or participating semigrey media", J. Phys: Conf. Ser. 395 012155 (2012).
[18] Capdevila, R., Lehmkuhl, O., Trias, F.X., Perez-Segarra, C.D. and Colomer, G. "Turbulent natural convection in a differentially heated cavity of aspect ratio 5 filled with non-participating and participating grey media", J. Phys: Conf. Ser. 318 042048 (2011).
[19] Capdevila, R., Perez-Segarra, C.D. Lehmkuhl, O. and Colomer, G. "Numerical simulation of turbulent natural convection and gas radiation in differentially heated cavities using FVM, DOM and LES", 6th International Symposium on Radiative Transfer, Antalya, Turkey (2010).
[20] Ibrahim, A., Saury, D. and Lemonnier, D. "Coupling of turbulent natural convection with radiation in an air-filled differentially-heated cavity at Ra =1.5×109", Computers and Fluids, 88, pp. 115–125 (2013).
[21] Baytas, A.C. "Entropy generation for natural convection in an inclined porous cavity", International Journal Heat Mass Transfer, 43, pp. 2089–2099 (2000).
[22] Oztop, H.F. "Natural convection in partially cooled and inclined porous rectangular enclosures", International Journal of Thermal Science, 46, pp. 149–156 (2007).
[23] Varol, Y., Oztop, H.F., Koca, A. and Özgen, F. "Natural convection and fluid flow in inclined enclosure with corner heater", Applied Thermal Engineering, 29, pp. 340–350 (2009).
[24] Bouali, H., Mezrhab, A., Amaoui, H. and Bouzidi, M. "Radiation-natural convection heat transfer in an inclined rectangular enclosure", International Journal of Thermal Science, 45, pp. 553-566 (2006).
[25] Ahmed, S.E, Oztop H.F. and Al-Salem, K. "Natural convection coupled with radiation heat transfer in an inclined porous cavity with corner heater", Computers and Fluids, 102, pp. 74-84 (2014).
[26] Mezrhab, A., Bouali, H. and Abid, C. "Radiation-natural convection interactionsin an enclosures with a heat-generating conducting body", Congress Francis de Thermique SFT, pp. 25-28 (2004).
[27] Mezrhab, A., Bouali, H. and Abid, C. "Modeling of combined radiative and convective heat transfer in an enclosure with a heat-generating conducting body", International Journal Computer Methods, 2(3), pp. 431-450 (2005).
[28] Moein Addini, M., Gandjalikhan Nasab A. "Combined mixed convection and radiation simulation of inclined lid driven cavity", Energy Equipment and Systems, 6(3), pp.261-277(2018).
[30] Patankar S.V. "Numerical Heat Transfer and Fluid Flow", Hemisphere Publishing, Washington, DC (1980).[29] Rabhi, M., Bouali, H. and Mezrhab, A. "Radiation-natural convection heat transfer in inclined rectangular enclosures with multiple partitions", Journal of Energy Conversion and Management, 49, pp. 1228-1236 (2008).
[31] Modest, M. F., 2003, Radiative Heat Transfer, Academic, San Diego, CA, Chap. 16.
[32] Patankar, S.V. "Numerical Heat Transfer and Fluid Flow", Taylor & Francis, Philadelphia, PA, Chap. 7 (1981).
[33] Byun, K.H. and Hyuk, Im. M. "Radiation-laminar free convection in a square duct with specular reflection by absorbing-emitting medium", KSME International Journal, 16(10) pp. 1346-1354 (2002).
[34] Mahapatra, S.K., Dandapat, B.K. and Sarkar, A. "Analysis of Combined Conduction and Radiation Heat Transfer in Presence of Participating Medium by the Development of Hybrid Method", Journal of Quantitative Spectroscopy & Radiative Transfer, 102, pp. 277–292 (2006).