Conjugate Mixed Convection in a Horizontal Cylindrical Duct under the Solid Shell Internal Heat Generation

Document Type : Research Paper

Authors

1 Laboratoire LEAP, Departement de Génie Mécanique, Université Frères Mentouri-Constantine 1, ‎Route de Ain El. Bey, Constantine, 25000, Algérie‎

2 CNRS, IUSTI UMR 7343, Aix-MARSEILLE Universit2, 5 rue Enrico Fermi, Marseille Cedex 13, 13453, France

Abstract

This paper deals with three-dimensional, mixed convection in a cylindrical duct horizontally. This latter is partially subjected to a uniform volumetric heat generation at the solid-liquid interface. The working fluid (water) with a parabolic velocity profile and a constant temperature T0 enters the tube. The study was carried out for different Richardson numbers values Ri=0.1-8 at Reynolds number Re=600. Results were conducted so that to show the influence of Richardson number Ri on the dynamic and thermal fields and local Nusselt number Nu(q,z) and peripherally averaged axial Nusselt number Nu(z). Also, analyses of the results showed that the hydrodynamic effects are manifested by the existence of secondary flow, inducing temperature gradient at a cross-section between the top and bottom of the duct. The reversed flow is observed for a low Reynolds number Re=10. A significant increase in heat exchange is observed in mixed convection compared to pure forced convection flow. Correlations for the variation of average Nusselt number Nu (Ri,z) at the entrance region with Ri and z=z¢/Di and local Nusselt Nu(Ri) number in the hydrodynamics establishment zone are proposed and compared with the present numerical results.

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Main Subjects

‎[1] Abid, C., Papini, F., Ropke, A., Veyret, D., Etude de la Convection Mixte dans un Conduit Cylindrique. Approches Analytique/Numérique et ‎Détermination Expérimentales de la Température de Paroi par Thermographie Infrarouge, International Journal of Heat and Mass Transfer, 37, 1994, 91-101.‎
‎[2] Choi, D.K., Choi, D.H., Developing Mixed Convection Flow in a Horizontal Tube under Circumferentially Non-Uniform Heating, International Journal of Heat and Mass Transfer, 37, 1994, 1899-1913.‎
‎[3] Hwang, G.J., Lai, H.C., Laminar Convective Heat Transfer in a Horizontal Isothermal Tube for High Rayleigh Numbers, International Journal of Heat and Mass Transfer, 37, 1994, 1631-1640.‎
‎[4] Ouzzane, M., Galanis, N., Effets de la Conduction Pariétale et de la Répartition du Flux Thermique sur la Convection Mixte près de l’Entrée d’une Conduite Inclinée, International Journal of Thermal Sciences, 38, 1999, 622-633.‎
‎[5] Habib, M.A., Negm, A.A.A., Laminar Mixed Convection in Horizontal Concentric Annuli with Non-Uniform Circumferential Heating, Heat and Mass Transfer, 37, 2001, 427-435.‎
‎[6] Orfi, J., Galanis, N., Developing Laminar Mixed Convection with Heat and Mass Transfer in Horizontal and Vertical Tubes, International Journal of Thermal Sciences, 41, 2002, 319-331.‎
‎[7] Orfi, J., Galanis, N., Mixed Convection with Heat and Mass Transfer in Horizontal Tubes, International Communications in Heat and Mass Transfer, 32, 2005, 511-519.‎
‎[8] Mohammed, H.A., Salman, Y.K., Combined Convection Heat Transfer for Thermally Developing Aiding Flow in an Inclined Circular Cylinder with Constant Heat Flux, Applied Thermal Engineering, 27, 2007, 1236-1247. ‎
‎[9] Mohammed, H.A., Salman, Y.K., Free and Forced Convection Heat Transfer in the Thermal Entry Region for Laminar Flow Inside a Circular Cylinder Horizontally Oriented, Energy Conversion and Management, 48, 2007, 2185-2195.‎
‎[10] Mohammed, H.A., Salman, Y.K., Combined Natural and Forced Convection Heat Transfer for Assisting Thermally Developing Flow in ‎a Uniformly Heated Vertical Circular Cylinder, International Communications in Heat and Mass Transfer, 34, 2007, 474-491.‎
‎[11] Mohammed, H.A., Salman, Y.K., Experimental Investigation of Mixed Convection Heat Transfer for Thermally Developing Flow in a Horizontal Circular Cylinder, Applied Thermal Engineering, 27, 2007, 1522-1533.‎
‎[12] Mohammed , H.A., Salman, Y.K., The Effects of Different Entrance Sections Lengths and Heating on Free and Forced Convective Heat ‎Transfer Inside a Horizontal Circular Tube, International Communications in Heat and Mass Transfer, 34, 2007, 769-784.‎
‎[13] Mohammed, H.A., The Effect of Different Inlet Geometries on Laminar Flow Combined Heat Transfer Inside a Horizontal Circular Pipe, ‎Applied Thermal Engineering, 29, 2009, 581-590.‎
‎[14] Shiniyan, B., Hosseini, R., Naderan, H., The Effect of Geometric Parameters on Mixed Convection in an Inclined Eccentric Annulus, International Journal of Thermal Sciences, 68, 2013, 136-147.‎
‎[15] Testi, D., Novel, A., Correlation for Azimuthal and Longitudinal Distributions of Heat Transfer Coefficients in Developing Horizontal Pipe Flow under Transitional Mixed Convection, International Journal of Heat and Mass Transfer, 60, 2013, 221-229.‎
‎[16] Chae, M-S., Chung, B-J., Laminar Mixed-Convection Experiments in Horizontal Pipes and Derivation of a Semi-Empirical Buoyancy Coefficient, International Journal of Thermal Sciences, 84, 2014, 335-346.‎
‎[17] Schriener, T.M., El-Genk, M.S., Convection Heat Transfer of NaK-78 Liquid Metal in a Circular Tube and a Tri-lobe Channel, International Journal of Heat and Mass Transfer, 86, 2015, 234-243.‎
‎[18] Colombo, L.P.M., Lucchini, A., Muzzio, A., Fully Developed Laminar Mixed Convection in Uniformly Heated Horizontal Annular Ducts, International Journal of Thermal Sciences, 94, 2015, 204-220. ‎
‎[19] Ganesan, R., Narayanaswamy, R., Perumal, K., Mixed Convection and Radiation Heat Transfer in a Horizontal Duct with Variable Wall Temperature, Heat Transfer Engineering, 36, 2015, 335-345.‎
‎[20] Sheikholeslami, M., Seyyed, A.F., Ahmad, S., Houman, B., Performance of Solar Collector with Turbulator Involving Nanomaterial Turbulent Regime, Renewable Energy, 163, 2021, 1222-1237.‎
‎[21] Sheikholeslami, M., Seyyed, A.F., Nanoparticle Transportation Inside a Tube with Quad-Channel Tapes Involving Solar ‎Radiation, Powder Technology, 378, 2021, 145-159.‎
‎[22] Sheikholeslami, M., Jafaryar, M., Zafar, S., Alsabery, A.I., Babazadeh, H., Shafee, A., Modification for Helical Turbulator to Augment Heat Transfer Behavior of Nanomaterial via Numerical Approach, Applied Thermal Engineering, 182, 2021, 115935.‎
‎[23] Abid, C., Martin, R., Papini, F., Thermal Instabilities in a Horizontal Cylindrical Duct: A Physical Approach, International Journal of Heat and Mass Transfer, 45, 2002, 2153-2157.‎
‎[24] Bejan, A., Convection Heat Transfer, 3rd edition, John Wiley and Sons, New-York, 2004‎.
‎[25] Bergman, L., Lavine, S., Incropera, F., Dewitt, D., Fundamentals of Heat and Mass Transfer, 7th edition, John Wiley & Sons, USA, 2011.‎
‎[26] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC, 1980.‎
‎[27] Barozzi, G.S., Zanchini, E., Mariotti, M., Experimental Investigation of Combined Forced and Free Convection in ‎Horizontal and Inclined Tubes, Meccanica, 20, 1985, 18–27.‎
‎[28] Akbari, M., Behzadmehr, A., Shahraki, F., Fully Developed Mixed Convection in Horizontal and Inclined Tubes with Uniform Heat Flux Using Nanofluid, International Journal of Heat and Fluid Flow, 29, 2008, 545–556.