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In this numerical study, natural convection of Cu–water nanofluid in a cavity submitted to different heating modes on its vertical walls is analyzed. Maxwell-Garnetts (MG) and Brinkman models have been utilized for calculating the effective thermal conductivity and dynamic viscosity of nanofluid, respectively. Influences of Rayleigh number (Ra = 103−106), nanoparticle volume concentration (f = 0-0.04) and Hartmann number (Ha = 0-90) on the flow and heat transfer characteristics have been examined. The results indicate that the Hartmann number influences the heat transfer at Ra = 106 more than other Raleigh numbers, as the least effect is observed at Ra = 103. Moreover, the results show that the solid volume fraction has a significant influence on heat transfer, depending on the value of Hartmann, heat generation or absorption coefficient and Rayleigh numbers.

In this numerical work, mixed convection and entropy generation of Cu–water nanofluid in a lid-driven square cavity have been investigated numerically using the Lattice Boltzmann Method. Horizontal walls of the cavity are adiabatic and vertical walls have constant temperature but different values. The top wall has been considered as moving from left to right at a constant speed, U0. The effects of different parameters such as nanoparticle volume concentration (0–0.05), Rayleigh number (104–106) and Reynolds numbers (1, 10 and 100) on the entropy generation, flow and temperature fields are studied. The results have shown that addition of nanoparticles to the base fluid affects the entropy generation, flow pattern and thermal behavior especially at higher Rayleigh and low Reynolds numbers. For pure fluid as well as nanofluid, the increase of Reynolds number increases the average Nusselt number and the total entropy generation, linearly. The maximum entropy generation occurs in nanofluid at low Rayleigh number and at high Reynolds number. The minimum entropy generation occurs in pure fluid at low Rayleigh and Reynolds numbers. Also at higher Reynolds number, the effect of Cu nanoparticles on enhancement of heat transfer was decreased because the effect of lid-driven cavity was increased. The present results are validated by favorable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed., {"references":["M. Aghajani Delavar, M. Farhadi, K. Sedighi, \"Effect of the heater\nlocation on heat transfer and entropy generation in the cavity using the\nlattice Boltzmann method,\"Heat Trans. Res, vol. 40, 2009, pp. 505-519.","E. Fattahi, M. Farhadi, K. Sedighi, \"Lattice Boltzmann simulation of\nnatural convection heat transfer in eccentric annulus,\" Int. J. Therm. Sci,\nvol. 49, 2010, pp. 2353-2362","H. Huang, Z. Li, S. Liu, X.Y. Lu, \"Shan-and-Chen-type multiphase\nlattice Boltzmann study of viscous coupling effects for two-phase flow\nin porous media,\" Int. J. Numerical Methods Fluids, vol. 61, 2009, pp.\n341-354","M. Mahmodi, S. M. Hashemi, \"Numerical study of natural convection of\na nanofluid in C-shaped enclosures,\" Int. J. Thermal Sci, vol. 55, 2012,\npp. 76-89","M. Kalteh, H. Hasani, \"Lattice Boltzmann simulation of nanofluid free\nconvection heat transfer in an L-shaped enclosure,\" Super lattices and\nMicrostructures, vol. 66, 2014, pp. 112–128.","H. Reza, M. Mohsen, \"Magnetic field effects on natural convection flow\nof a nanofluid in a horizontal cylindrical annulus using Lattice\nBoltzmann method,\" Int. J. Thermal Sci, vol. 64, 2013, pp. 240-250.","U.S. Choi, \"Enhancing thermal conductivity of fluids with nanoparticles,\ndevelopments and application of non-Newtonian flows, \"ASME, vol. 66,\n1995, pp. 99–105.","K. Khanafer, K. Vafai, M. Lightstone, \"Buoyancy-driven heat transfer\nenhancement in a two dimensional enclosure utilizing nanofluid,\" Int. J.\nHeat Mass Transfer, vol. 46, 2003, pp. 3639–3653.","F.H. Lai, Y.T. Yang, \"Lattice Boltzmann simulation of natural\nconvection heat transfer of Al2O3/water nanofluids in a square enclosure,\n\" Int. J. Therm. Sci, vol. 50, 2011, pp. 1930–1941.\n[10] Z. Alloui, P. Vasseur, M. Reggio, \"Natural convection of nanofluids in a\nshallow cavity heated from below, \" Int. J. Therm. Sci, vol. 50, 2011, pp.\n385–393.\n[11] Y. He, C. Qi, Y. Hu, B. Qin, F. Li, Y. Ding, \"Lattice Boltzmann\nsimulation of alumina–water nanofluid in a square cavity, \" Nanoscale\nRes. Lett, vol. 6, 2011, pp. 1–8.\n[12] C.J. Ho, W.K. Liu, Y.S. Chang, C.C. Lin, \"Natural convection heat\ntransfer of alumina–water nanofluid in vertical square enclosures: an\nexperimental study,\" Int. J. Therm. Sci, vol. 49, 2010, pp. 1345–1353.\n[13] J. Rahmannezhad, A. Ramezani, M. Kalteh, \"Numerical investigation of\nmagnetic field effects on mixed convection flow in a nanofluid-filled liddriven\ncavity,\" Int. J. Eng. Trans. A: Basics, vol. 26, 2013, pp. 1213–\n1224.\n[14] A. Mahmoudi,I. Mejri,M. Ammar Abbassi, A. Omri, \"Numerical Study\nof Natural Convection in an Inclined Triangular Cavity for Different\nThermal Boundary Conditions: Application of the Lattice Boltzmann\nMethod,\" FDMP, vol. 9, 2013, pp. 353-388.\n[15] I. Mejri, A. Mahmoudi,M. Ammar Abbassi, A. Omri, \"Numerical Study\nof Natural Convection in an Inclined Triangular Cavity for Different\nThermal Boundary Conditions: Application of the Lattice Boltzmann\nMethod,\" FDMP, vol. 9, 2013, pp. 353-388.\n[16] G.A. Sheikhzadeh, A. Arefmanesh, M.H. Kheirkhah, R. Abdollahi,\n\"Natural convection of Cu–water nanofluid in a cavity with partially\nactive side walls,\" Eur. J. Mech. B-Fluid, vol. 30, 2011, pp. 166–176.\n[17] E. Abu-Nada, H.F. Oztop,\"Effects of inclination angle on natural\nconvection in enclosures filled with Cu-water nanofluid,\" Int. J. Heat\nFluid Fl, vol. 30, 2009, pp. 669–678.\n[18] S.M. Aminossadati, B. Ghasemi, \"Natural convection cooling of a\nlocalised heat source at the bottom of a nanofluid-filled enclosure,\" Eur.\nJ. Mech. B-Fluid, vol. 28, 2009, pp. 630–640.\n[19] M. Jahanshahi, S.F. Hosseinizadeh, M. Alipanah, A. Dehghani, G.R.\nVakilinejad, \"Numerical simulation of free convection based on\nexperimental measured conductivity in a square cavity using Water/SiO2\nnanofluid,\" Int. Commun. Heat Mass Transfer, vol. 37, 2010, pp. 687–\n694.\n[20] A. Akbarnia, A. Behzadmehr, \"Numerical study of laminar mixed\nconvection of a nanofluid in horizontal curved tubes,\" Appl. Therm. Eng,\nvol. 27, 2007, pp. 1327–1337.\n[21] S. Mirmasoumi, A. Behzadmehr, \"Effect of nanoparticles mean diameter\non mixed convection heat transfer of a nanofluid in a horizontal tube,\"\nInt. J. Heat Fluid Fl, vol. 29, 2008, pp. 557–566.\n[22] T. Basak, S. Roy, P.K. Sharma, I. Pop, \"Analysis of mixed convection\nflows within a square cavity with uniform and non-uniform heating of\nbottom wall,\" Int. J. Therm. Sci, vol. 48, 2009, pp. 891–912. [23] G. Guo, M.A.R. Sharif, \"Mixed convection in rectangular cavities at\nvarious aspect ratios with moving isothermal sidewalls and constant flux\nheat source on the bottom wall,\" Int. J. Therm. Sci, vol. 43, 2004, pp.\n465–475.\n[24] R.K. Tiwari, M.K. Das, \"Heat transfer augmentation in a two-sided liddriven\ndifferentially heated square cavity utilizing nanofluids,\" Int. J.\nHeat Mass Transfer, vol. 50, 2007, pp. 2002–2018.\n[25] M.A. Mansour, R.A. Mohamed, M.M. Abd-Elaziz, S.E. Ahmed, \"\nNumerical simulation of mixed convection flows in a square lid-driven\ncavity partially heated from below using nanofluid,\" Int. Commun. Heat\nMass, vol. 37, 2010, pp. 1504–1512.\n[26] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi, A.A.R. Darzi, \"Lattice\nBoltzmann simulation of nanofluid in lid-driven cavity,\" Int. Commun.\nHeat Mass, vol. 37, 2010, pp. 1528–1534.\n[27] M. Dalavar, M. Farhadi, K. Sedighi, \"Numerical simulation of direct\nmethanol fuel cells using lattice Boltzmann method,\" Int. J. Hydrogen\nEnergy, vol. 35, 2010, pp. 9306-9317.\n[28] A. Mahmoudi, I. Mejri, M. A. Abbassi, A. Omri, \"Lattice Boltzmann\nsimulation of MHD natural convection in a Nanofluids-filled cavity with\nlinear temperature distribution,\" Powder Technology, vol. 256, 2014, pp.\n257-271.\n[29] M. Kalteh, H. Hasani, \"Lattice Boltzmann simulation of nanofluid free\nconvection heat transfer in an L-shaped enclosure,\" Int. J. Superlat.\nMicro, vol. 66, 2014, pp. 112–128.\n[30] Y. Xuan, Q. Li, \"Heat transfer enhancement of nanofluids, Int. J. Heat\nFluid Flow, pp. 58–64, 2000.\n[31] A. Bejan, \"Entropy Generation through Heat and Fluid Flow,\" Wiley,\nNew York, 1982.\n[32] A. Mahmoudi, I. Mejri, M. A. Abbassi, A. 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International audience; The radiative heat transfer problem is investigated numerically for 2D complex geometry biomass pyrolysis reactor composed of two pyrolysis chambers and a heat recuperator. The fumes are a mixture of carbon dioxide and water vapor charged with absorbing and scattering particles and soot. In order to increase gases residence time and heat transfer, the heat recuperator is provided with many inclined, vertical, horizontal, diffuse and grey baffles of finite thickness and has a complex geometry. The Finite Volume Method (FVM) is applied to study radiative heat transfer. The blocked-off region procedure is used to treat the geometrical irregularities. Eight cases are considered in order to demonstrate the effect of adding baffles on the walls of the heat recuperator and on the walls of the pyrolysis rooms then choose the best case giving the maximum heat flux transferred to the biomass in the pyrolysis chambers. Ray effect due to the presence of baffles is studied and demonstrated to have a crucial effect on radiative heat flux on the walls of the pyrolysis rooms. Shadow effect caused by the presence of the baffles is also studied. The non grey radiative heat transfer is studied for the real existent configuration. The Weighted Sum of The Grey Gases (WSGG) Model of Kim and Song is used as non grey model. The effect of soot volumetric fraction on the non grey radiative heat flux is investigated and discussed.

The objective of this work is to use the Fire Dynamics Simulator (FDS) to investigate the behavior of a kerosene small-scale fire. FDS is a Computational Fluid Dynamics (CFD) tool developed specifically for fire applications. Throughout its development, FDS is used for the resolution of practical problems in fire protection engineering. At the same time FDS is used to study fundamental fire dynamics and combustion. Predictions are based on Large Eddy Simulation (LES) with a Smagorinsky turbulence model. LES directly computes the large-scale eddies and the sub-grid scale dissipative processes are modeled. This technique is the default turbulence model which was used in this study. The validation of the numerical prediction is done using a direct comparison of combustion output variables to experimental measurements. Effect of the mesh size on the temperature evolutions is investigated and optimum grid size is suggested. Effect of width openings is investigated. Temperature distribution and species flow are presented for different operating conditions. The effect of the composition of the used fuel on atmospheric pollution is also a focus point within this work. Good predictions are obtained where the size of the computational cells within the fire compartment is less than 1/10th of the characteristic fire diameter., {"references":["G. Yeoh, R. Yuen, and W. Kwok, \"Modelling combustion, radiation and soot processes in compartment fires,\" Build Environ, vol. 38, pp. 593–85, 2003.","H. you, and G. Faeth, \"Turbulent combustion,\" Combust Flame, vol. 38, pp. 261–44, 1982","B. Morton, \"Modeling fires plumes,\" Proc 10th International Symposium on Combustion, pp. 973–982.","V. Novozhilov, \"Computational fluid dynamics modeling of compartment fires,\" Proc. Energy. Combus. Sci, vol. 27, pp. 61–66, 2001.","E. Zukoski, \"Properties of fire plumes,\" San Diego-Academic Press, vol. 50, pp. 4073-4079, 1995.","V. Novozhilov, B. Moghtaderi, and D. Fletcher, \"Computational fluid dynamics modeling of wood combustion,\" Fire. Saf, vol. 27, pp. 69–84, 1996.","W. Sirignano, \"Fuel droplet vaporization and spray combustion theory,\" Proc. Energy Combustion, vol. 9, pp. 291–322, 1983.","I. Kennedy, \"Models of soot formation and oxidation,\" Proc. Energy. Combustion, vol. 23, pp. 95–132, 1997.","V. Novozhilov, \"Validation of fire dynamics simulator (fds) for forced and natural convection flows,\" Proc. Energy. Combustion, Vol. 27, pp. 39–54, 2006.\n[10]\tU. Köylü, G. Fletcher \"Carbon Monoxide and soot emissions from liquid fuel,\" Combustion Flame, vol. 87, pp. 61–76, 1991.\n[11]\tk. McGrattan, \"Fire Dynamic Similator (Version 4) Technical Reference Guide. National Institute of standards and Technology,\" National Institute of standards and Technology, Special Publication 1018, 2006.\n[12]\tJ. Smagorinsky, \"General Circulation Experiments with the Primitive Equations,\" Monthly Weather Review, vol 3, pp. 99–164, 1963.\n[13]\tB. Merci, \"Numerical simulations of full-scale enclosure fires in a small compartment with natural roof ventilation,\" Fire. Safety, vol. 43, pp. 495-511, 2008.\n[14]\tD. Anderson, J. Tannehill, and R. Pletcher, \"Computational Fluid Mechanics and Heat Transfer,\" Hemisphere Publishing Corporation, Philadelphia,1984.\n[15]\tK. McGrattan, H. Baum, and R. Rehm, \"Fire dynamics simulator user's guide,\" National Institute of Standards and Technology, 2001.\n[16]\tH. Baum, K. Mcgrattan, and H. Baum, \"Simulation of Large Industrial Outdoor Fires,\" Proc of the Sixth International Symposium Association for Fire Safety Science, 2000.\n[17]\tW. Mell, K. Mcgrattan, and H. Baum, Proc. Combust, Vol. 26. pp. 1523–30, 1996.\n[18]\tC. Huggett, \"Estimation of the rate of heat release by means of oxygen consumption measurements,\" Fire. Mater, vol. 4, pp. 61–5., 1980.\n[19]\tP. Smardz, and V. Novozhilov, \"Validation of Fire Dynamics Simulator (FDS) for forced and natural convection flows,\" University of Ulster, October 2006."]}

International audience; Une étude numérique des transferts par convection mixte et rayonnement dans un four de combustion des fumées de pyrolyse de la biomasse est présentée. Les équations de mouvement, de la chaleur et de transfert radiatif sont adimensionnalisées puis résolues à l'aide de la méthode des volumes finis et de l'algorithme TDMA. L'adéquation entre les champs de pression et de vitesse est assurée par l'algorithme SIMPLE. Les résultats sont présentés sous forme de lignes de courant, d'isothermes, de profil de vitesse et de densité de flux de chaleur à la paroi du four. Nous analysons l'influence du nombre de Richardson sur les distributions des isothermes et des lignes de courant. L'influence de l'épaisseur optique des fumées sur les écoulements et les transferts à l'intérieur du four est aussi présentée.

The radiative heat transfer problem is investigated numerically for 2D complex geometry biomass pyrolysis reactor composed of two pyrolysis chambers and a heat recuperator. The fumes are a mixture of carbon dioxide and water vapor charged with absorbing and scattering particles and soot. In order to increase gases residence time and heat transfer, the heat recuperator is provided with many inclined, vertical, horizontal, diffuse and grey baffles of finite thickness and has a complex geometry. The Finite Volume Method (FVM) is applied to study radiative heat transfer. The blocked-off region procedure is used to treat the geometrical irregularities. Eight cases are considered in order to demonstrate the effect of adding baffles on the walls of the heat recuperator and on the walls of the pyrolysis rooms then choose the best case giving the maximum heat flux transferred to the biomass in the pyrolysis chambers. Ray effect due to the presence of baffles is studied and demonstrated to have a crucial effect on radiative heat flux on the walls of the pyrolysis rooms. Shadow effect caused by the presence of the baffles is also studied. The non grey radiative heat transfer is studied for the real existent configuration. The Weighted Sum of The Grey Gases (WSGG) Model of Kim and Song is used as non grey model. The effect of soot volumetric fraction on the non grey radiative heat flux is investigated and discussed., {"references":["L. C. Chang, K. T. Yang, and J. R. Lloyd, Radiation-natural convection interactions in two-dimensional complex enclosures, Journal of Heat Transfer, Vol. 105, pp. 89-95, 1983.","M. N. Borjini, H. Farhat and M.-S Radhouani, Analysis of radiative heat transfer in a partitioned idealized furnace, Numerical Heat Transfer, Part A, Vol. 44, pp. 199-218 , 2003.","C. Y. Han and S. W. Baek, The effects of radiation on natural convection in a rectangular enclosure divided by two partitions, Numerical Heat Transfer, Part A: Applications, Vol.37, No.3, pp. 249-270, 2000.","M.A. Abbassi, K. Halouani, X. Chesneau, B. Zeghmati and A. Zoulalian, Modélisation des transferts thermiques couplés à la cinétique réactionnelle dans une chambre de combustion des gaz de pyrolyse de la biomasse, Congrès Français de Thermique, Toulouse, 3-6 juin, pp. 765-770, 2008.","M.A. Abbassi, N. Grioui, K Halouani, A. Zoulalian and B. Zeghmati, Racing modeling of the combustion in a pilot furnace of fumes produced from wood carbonization, ASME ATI, Conference, Milan Italy, 14-17 may, pp. 61-69, 2006.","M.A. Abbassi, N. Grioui, K Halouani, A. Zoulalian and B. Zeghmati, A practical approach for modelling and control of biomass pyrolysis pilot plant with heat recovery from combustion of pyrolysis products, Fuel Processing Technology, Vol. 90, pp. 1278-1285, 2009.","G.B. Raithby and E.H. Chui, A finite volume method for predicting a radiant heat transfer in enclosures with participating media, J. Heat Transfer Vol. 112, pp. 415-423, 1990.","J. Taine and A. Soufiani, From spectroscopic data to approximate models, Adv. Heat transfer Vol.33 pp. 295-414, 1999.","V. Goutiere, F. Liu , A. Charette, An assesement of real-gas modelling in 2D enclosures, J. Quant. Spectroscopic. Radiat. Transfer, Vol. 64, no. 3, pp. 299-326, 2000.\n[10]\tH. C Hottel and A.F Sarofim., Radiative transfer, New York, 1967.\n[11]\tM. F. Modest, The weighted-sum-of-gray-gases model for arbitrary solution methods in radiative transfer. ASME J. of Heat transfer, Vol.113, pp. 650-656, 1991.\n[12]\tA. Soufiani and E. Djavdan, A Comparison between weighted sum of gray gases and statistical narrow-band radiation models for combustion applications, Combustion and Flame, Vol. 97, pp. 240-250, 1994.\n[13]\tM. F. Modest, Radiative Heat Transfer, Mc Graw-Hill, 1993.\n[14]\tM. Young, Yu, S.W. Baek and J. H. Park, An extension of the weighted sum of the gray gases non-gray gas radiation model to a two phase mixture of non-gray gas with particles, Int. J. Heat Mass Transfer, Vol. 43, pp. 1699-1713, 2000. \n[15]\tO.J. Kim and T.H Song, Data base of WSGGM-based spectral model for radiation properties of combustion products, J. Quant. Spectrosc. Radiat. Transfer, Vol. 64, pp. 379–394, 2000. \n[16]\tP. J. Coelho, Numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures, J. Quant. Spectroscopic. Radiat. Transfer, Vol. 74, pp. 307-328, 2002.\n[17]\tM.A. Abbassi, K.Halouani, M.S. Radhouani, and H. Farhat, A parametric study of radiative heat transfer in an industrial combustor of wood carbonization fumes. Numerical Heat Transfer, Part A : Vol. 47, pp. 825-847, 2005.\n[18]\tC.L. Tien, Thermal radiation in packed and fluidized beds, Journal of Heat Transfer, Vol. 110, pp.1230-1242, 1988.\n[19]\tK. Guedri, M.N. Borjini, R. Mechi, and R. Said, Formulation and testing of the FTn finite volume method for radiation in 3-D complex inhomogeneous participating media, J. Quant. Spectrosc. Radiat. Transfer, Vol. 98, pp. 425-445, 2006.\n[20]\tF. Liu and S. N. Tiwari, Investigation of two-dimensional radiating using a narrow band model and Monte Carlo Method, in radiative heat transfer: theory and applications, ASME HTD-Vol. 244, pp. 21-31, 1993.\n[21]\tK. Guedri, M.A. Abbassi, M. N. Borjini and K. Halouani, Application of the finite-volume method to study the effects of baffles on radiative heat transfer in complex enclosures, Numerical Heat Transfer, Part A : Vol. 55, pp. 1-27, 2009.\n[22]\tD.G. Stankevich, Y.G. Shkuratov, K. Muinonen, Shadow-hiding effect in inhomogeneous layered particulate media, J. Quant. Spectrosc. Radiat. Transfer, Vol. 63, pp. 445-458, 1999."]}