## THERMAL SCIENCE

International Scientific Journal

### NUSSELT NUMBER EVALUATION FOR COMBINED RADIATIVE AND CONVECTIVE HEAT TRANSFER IN FLOW OF GASEOUS PRODUCTS FROM COMBUSTION

**ABSTRACT**

Combined convection and radiation in simultaneously developing laminar flow and heat transfer is numerically considered with a discrete-direction method. Coupled heat transfer in absorbing emitting but not scattering gases is presented in some cases of practical situations such as combustion of natural gas, propane and heavy fuel. Numerical calculations are performed to evaluate the thermal radiation effects on heat transfer through combustion products flowing inside circular ducts. The radiative properties of the flowing gases are modeled by using the absorption distribution function (ADF) model. The fluid is a mixture of carbon dioxide, water vapor, and nitrogen. The flow and energy balance equations are solved simultaneously with temperature dependent fluid properties. The bulk mean temperature variations and Nusselt numbers are shown for a uniform inlet temperature. Total, radiative and convective mean Nusselt numbers and their axial evolution for different gas mixtures produced by combustion with oxygen are explored.

**KEYWORDS**

PAPER SUBMITTED: 2011-05-31

PAPER REVISED: 2012-04-12

PAPER ACCEPTED: 2012-04-13

**THERMAL SCIENCE** YEAR

**2013**, VOLUME

**17**, ISSUE

**4**, PAGES [1093 - 1106]

- Crnomarkovic Nenad D., Sijercic Miroslav A., Belosevic Srđan V., Tucakovic Dragan R., Zivanovic Titoslav V. Influence of application of Hottel's zonal model and six-flux model of thermal radiation on numerical simulations results of pulverized coal fired furnace. Thermal Science, (2011) OnLine-First Issue 00, pp. 126-126. doi:10.2298/TSCI110627126C.
- Baburić, M, Raulot, A, and Duić, N. Implementation of discrete transfer radiation method into swift computational fluid dynamics code. Thermal Science. 8 (2004), 1, pp.19-28.
- Hui, L, Shuai, D, Ben-Wen, L, Hai-Geng, C. Parametric investigations of premixed methane-air combustion in two-section porous media by numerical simulation. Fuel, 89 (2010), pp.1736-1742
- Saario, A, Rebola, A, Coelho, P.J., Costa, M, Oksanen, A. Heavy fuel oil combustion in a cylindrical laboratory furnace: measurements and modelling. Fuel, 84(2005), pp.359-369
- Dombrovsky, LA, Sazhin, S S, Sazhina, E M, Feng, G, Heikal, M R, Bardsley, M E A, Mikhalovsky, S V. Heating and evaporation of semi-transparent diesel fuel droplets in the presence of thermal radiation. Fuel, 80(2001), pp.1535-1544
- Risto V. Filkoski, Ilija J. Petrovski, and Karas, P. Optimisation of pulverized coal combustion by means of CFD/CTA modeling. Thermal Science, 10 (2006), No. 3, pp. 161-179
- Caliot, C, Abanades,S, Soufiani, A, Flamant, G. Effects of non-gray thermal radiation on the heating of a methane laminar flow at high temperature. Fuel, 8(2009), pp.617-624
- Cumber, P S, Fairweather, M, Ledin, HS. Application of wide band radiation models to non-homogeneous combustion system. International Journal of Heat and Mass Transfer,41(1998), pp.1573-1584
- Cumber, P S, Fairweather, M. Evaluation of flame emission models combined with the discrete transfer method for combustion system simulation. International Journal of Heat and Mass Transfer, 48(2005), pp.5222-5239
- Pessoa-Filho, J B,. Thermal radiation in combustion systems. Journal of the Brazilian Society of Mechanics Sciences,21(1999, pp. 537-547
- S. Dembele, J, Wen, X. Investigation of a spectral formulation for radiative heat transfer in one-dimensional fires and combustion system. International Journal of Heat and Mass Transfer, 43(2000), pp.4019-4030
- Kontogeeorgos, D A, Keramida, E P, Founti, M A. Assessment of simplified thermal radiation models for engineering calculations in natural gas-fired furnace, International Journal of Heat and Mass Transfer, 50(2007), pp. 5260-5268
- Sediki, E, Soufiani, A, Sifaoui, MS. Spectrally Correlated Radiation and Laminar Forced Convection in the Entrance Region of Circular Duct. International Journal of Heat and Mass Transfer, 45(2002), pp.5069-5081
- Pierrot L. Développement, Etude Critique et Validation de Modèles de Propriétés Radiatives Infrarouges de CO2 et H2O à Haute Température. Application au Calcul des Transferts dans des Chambres Aéronautiques et à la Télédètection. Ph.D.thesis, Ecole Centrale Paris, France,1997
- Pierrot, L, Soufiani, A, Taine J. Accuracy of Narrow Band and Global Models for Radiative Transfer in H2O, CO2 and H2O-CO2 Mixtures at High Temperature. Journal of Quantitative Spectroscopy and Radiative Transfer, 62(1999), pp.523-548
- Pierrot, L, Rivière, Ph, Soufiani, A. A Fictitious-Gas-Based Absorption Distribution Function Global Model for Radiative Transfer in Hot Gases, Journal of Quantitative Spectroscopy and Radiative Transfer, 62(1999), pp.609-624
- Taine, J, Soufiani, A. Gas IR Radiatives Properties: From Spectroscopic Data to Approximate Models, In J. Houseman (Ed.), J.P. Hartnett and T.F. Irvine, Academic Press, 33: 295-414,New York, (1999)
- Sediki, E, Soufiani, A, Sifaoui, MS. Combined Gas Radiation and Laminar Mixed Convection in Vertical Circular Tubes. International Journal of Heat and Fluid Flow, 24(2003), pp.736-746
- Zhang, L, Soufiani, A, Taine J. Spectral correlated and non correlated radiative transfer in a finite axisymmetric system containing an absorbing and emitting real gas particle mixture. International Journal of Heat Mass Transfer, 31(1988), pp.2261-2272
- Soufiani, A., Taine, J. Spectrally correlated Radiative Transfer in Real 3D Axisymmetrical Systems, The sixth International Symposium on Transport Phenomena in Thermal Engineering, Begell House Inc .Publisher,(1994), pp.185-190
- Rivière, Ph., Langlois,S., Soufiani, A. An Approximate Data Base of H2O Infrared Lines for High Temperature Applications at Low Resolution Statistical Narrow Band Models Parameters, Journal of Quantitative Spectroscopy and Radiative Transfer, 53(1995), pp. 221-234
- Scutaru, D., Rosenman, L., Taine, J. Approximate Band Intensities of CO2 Hot Bands at 2.7, 4.3 and 12μm for High Temperature and Medium Resolution Applications, Journal of Quantitative Spectroscopy and Radiative Transfer, 53(1994), pp.765-781
- Touloukian, Y.S., Liley, P.E., Saxena, S. C. Thermophysical Properties of Matter, 3, IFI/Plenum, New York/Washington, USA, 1970
- Patankar, S.V., Spalding, D.B. International Journal of Heat Mass Transfer Transfer, 15(1972), pp.1787-1806
- Bankston, C. A., McEligot, D. M. Turbulant and Laminar Heat Transfer to Gases with Varying Properties in the Entry Region of Circular Ducts, International Journal of Heat and Mass Transfer, 13(1970), pp. 319-343
- Worsoe-Schmidt, P M, Leppert, G. Heat Transfer and Local Friction for Laminar Flow of Gas in a Circular Tube at High Heating Rate. International Journal of Heat and Mass Transfer, 8(1965), pp.1281-1301
- Baek, S.W. Yu, J.M. Kim, T. K. Thermally developing Poiseuille flow affected by radiation. Numerical Heat Transfer, Part A 35 (1999) pp. 681-694