Numerical Investigation of Developing Mixed Convection in Isothermal Circular and Annular Sector Ducts

Authors: Ayad A. Abdalla, Elhadi I. Elhadi, Hisham A. Elfergani

Abstract:

Developing mixed convection in circular and annular sector ducts is investigated numerically for steady laminar flow of an incompressible Newtonian fluid with Pr = 0.7 and a wide range of Grashof number (0 £ Gr £ 10⁷). Investigation is limited to the case of heating in circular and annular sector ducts with apex angle of 2ϕ = π/4 for the thermal boundary condition of uniform wall temperature axially and peripherally. A numerical, finite control volume approach based on the SIMPLER algorithm is employed to solve the 3D governing equations. Numerical analysis is conducted using marching technique in the axial direction with axial conduction, axial mass diffusion, and viscous dissipation within the fluid are assumed negligible. The results include developing secondary flow patterns, developing temperature and axial velocity fields, local Nusselt number, local friction factor, and local apparent friction factor. Comparisons are made with the literature and satisfactory agreement is obtained. It is found that free convection enhances the local heat transfer in some cases by up to 2.5 times from predictions which account for forced convection only and the enhancement increases as Grashof number increases. Duct geometry and Grashof number strongly influence the heat transfer and pressure drop characteristics.

Keywords: Mixed convection, annular and circular sector ducts, heat transfer enhancement, pressure drop.

References:

[1] I.M. Rustum and H.M. Soliman, “Numerical analysis of laminar forced convection in the entrance region of tubes with longitudinal internal fins,” Journal of Heat Transfer, vol. 110, no. 2, pp. 310–313, 1988.
[2] I.M. Rustum and H.M. Soliman, “Numerical analysis of laminar mixed convection in horizontal internally finned tubes,” International Journal of Heat and Mass Transfer, vol. 33, no. 7, pp. 1485–1496, 1990.
[3] C.A. Hieber and S.K. Sreenivasan, “Mixed convection in an isothermally heated horizontal pipe,” International Journal of Heat and Mass Transfer, vol. 17, no. 11, pp. 1337–1348, 1974.
[4] J.-W. Ou and K.C. Cheng, “Natural convection effects on Graetz problem in horizontal isothermal tubes,” International Journal of Heat and Mass Transfer, vol. 20, no. 9, pp. 953–960, 1977.
[5] C.A. Hieber, “Mixed convection in an isothermal horizontal tube: some recent theories,” International Journal of Heat and Mass Transfer, vol. 24, no. 2, pp. 315–322, 1981.
[6] M. Hishida, Y. Nagano, and M.S. Montesclaros, “Combined forced and free convection in the entrance region of an isothermally heated horizontal pipe,” Journal of Heat Transfer, vol. 104, no. 1, pp. 153-159, 1982.
[7] M. Wang, T. Tsuji, and Y. Nagano, “Mixed convection with flow reversal in the thermal entrance region of horizontal and vertical pipes,” International Journal of Heat and Mass Transfer, vol. 37, no. 15, pp. 2305–2319, 1994.
[8] B. Shome and M.K. Jensen, “Mixed convection laminar flow and heat transfer of liquids in isothermal horizontal circular ducts,” International Journal of Heat and Mass Transfer, vol. 38, no. 11, pp. 1945–1956, 1995.
[9] A.R. Brown and M.A. Thomas, “Combined free and forced convection heat transfer for laminar flow in horizontal tubes,” Journal of Mechanical Engineering Science, vol. 7, no. 4, pp. 440–448, 1965.
[10] C.A. Depew and S.E. August, “Heat transfer due to combined free and forced convection in a horizontal and isothermal tube,” Journal of Heat Transfer, vol. 93, no. 4, pp. 380-384, 1971.
[11] W.W. Yousef and J.D. Tarasuk, “An Interferometric Study of Combined Free and Forced Convection in a Horizontal Isothermal Tube,” Journal of Heat Transfer, vol. 103, no. 2, pp. 249–256, 1981.
[12] W.W. Yousef and J.D. Tarasuk, “Free Convection Effects on Laminar Forced Convective Heat Transfer in a Horizontal Isothermal Tube,” Journal of Heat Transfer, vol. 104, no. 1, pp. 145–152, 1982.
[13] J.P. Coutier and R. Greif, “An investigation of laminar mixed convection inside a horizontal tube with isothermal wall conditions,” International journal of heat and mass transfer, vol. 28, no. 7, pp. 1293–1305, 1985.
[14] C. Prakash and Y.-D. Liu, “Analysis of laminar flow and heat transfer in the entrance region of an internally finned circular duct.,” Journal of Heat Transfer, vol. 107, no. 1, pp. 84-91, 1985.
[15] S.W. Hong, and A.E. Bergels, “Laminar flow heat transfer in the entrance region of semi-circular tubes with uniform heat flux,” International Journal of Heat and Mass Transfer, vol. 19, no. 1, pp. 123-124, 1976.
[16] Q.M. Lei and A.C. Trupp, “Further analyses of laminar flow heat transfer in circular sector ducts,” Journal of Heat Transfer, vol. 111, no. 4, pp. 1088-1090, 1989.
[17] Q.M. Lei and A.C. Trupp, “Maximum velocity location and pressure drop of fully developed laminar flow in circular sector ducts,” Journal of Heat Transfer, vol. 111, no. 4, pp. 1085-1087, 1989.
[18] Q.M. Lei and A.C. Trupp, “Predictions of laminar mixed convection in a horizontal semicircular duct,” in Proceedings of the 6th International Symposium on Heat and Mass Transfer, 1990, pp. 10–12.
[19] Q.M. Lei and A.C. Trupp, “Experimental study of laminar mixed convection in the entrance region of a horizontal semicircular duct,” International journal of heat and mass transfer, vol. 34, no. 9, pp. 2361–2372, 1991.
[20] K.C. Karki, P.S. Sathyamurthy, and S. V Patankar, “Laminar mixed convection in a horizontal semicircular duct with axially nonuniform thermal boundary condition on the flat wall,” Numerical Heat Transfer, vol. 25, no. 2, pp. 171–189, 1994.
[21] A.A. Busedra and H.M. Soliman, “Analysis of laminar mixed convection in inclined semicircular ducts under buoyancy-assisted and-opposed conditions,” Numerical Heat Transfer: Part A: Applications, vol. 36, no. 5, pp. 527–544, 1999.
[22] A.A. Busedra and H.M. Soliman, “Experimental investigation of laminar mixed convection in an inclined semicircular duct under buoyancy assisted and opposed conditions,” International Journal of Heat and Mass Transfer, vol. 43, no. 7, pp. 1103–1111, 2000.
[23] Y. El. Hasadi, I. Rustum, and A. Abdalla, “Laminar Mixed Convection in the Entrance Region of Semicircular Duct with Constant Heat Flux,” In: 9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 2006, pp. 1-13.
[24] C. Chinporncharoenpong, “Combined convection in horizontal circular sector ducts of various cross-sectional orientations,” 1993.
[25] C. Chinporncharoenpong, A.C. Trupp, and H.M. Soliman, “Laminar Mixed Convection in Horizontal Circular Sector Ducts,” in International Heat Transfer Conference,1994, pp. 447-452.
[26] R.K. Shah and A.L. London, Laminar flow forced convection in ducts, Advances in heat transfer, supplement 1. Academic Press, New York, 1978.
[27] H.S. Heaton, W.C. Reynolds, and W.M. Kays, “Heat transfer in annular passages. Simultaneous development of velocity and temperature fields in laminar flow,” International Journal of Heat and Mass Transfer, vol. 7, no. 7, pp. 763–781, 1964.
[28] H.M. Soliman, “Laminar heat transfer in annular sector ducts,” Journal of Heat Transfer, vol. 109, no. 1, pp. 247–249, 1987.
[29] T.M. Ben-Ali, H.M. Soliman, and E.K. Zariffeh, “Further results for laminar heat transfer in annular sector and circular sector ducts,” Journal of Heat Transfer, vol. 111, no. 4, pp. 1090-1093, 1989.
[30] C.Y. Han and S.W. Baek, “Natural convection phenomena affected by radiation in concentric and eccentric horizontal cylindrical annuli,” Numerical Heat Transfer: Part A: Applications, vol. 36, no. 5, pp. 473–488, 1999.
[31] N. Islam, U.N. Gaitonde, and G.K. Sharma, “Mixed convection heat transfer in the entrance region of horizontal annuli,” International journal of heat and mass transfer. vol. 44, no. 11, pp. 2107–2120, 2001.
[32] D. Poulikakos and M. Kazmierczak, “Forced convection in a duct partially filled with a porous material,” Journal of Heat Transfer, vol. 109, no. 3, pp. 653–662, 1987.
[33] M. Parang and M. Keyhani, “Boundary effects in laminar mixed convection flow through an annular porous medium,” Journal of Heat Transfer, vol. 109, no. 4, pp. 1039-1041,1987.
[34] A. Haji-Sheikh, “Fully developed heat transfer to fluid flow in rectangular passages filled with porous materials.,” Journal of Heat Transfer, vol. 128, no. 6, pp. 550–556, 2006.
[35] K. Hooman and A.A. Merrikh, “Analytical solution of forced convection in a duct of rectangular cross section saturated by a porous medium.,” Journal of Heat Transfer, vol. 128, no. 6, pp. 596-600, 2006.
[36] C.Y. Wang, “Analytical Solution for Forced Convection in a Semi-Circular Channel Filled with a Porous Medium,” Transport in Porous Media, vol. 73, no. 3, pp. 369–378, 2008.
[37] C.Y. Wang, “Analytical Solution for Forced Convection in a Sector Duct Filled With a Porous Medium,” Journal of Heat Transfer, vol. 132, no. 8, 2010.
[38] V.K. Verma and S. Datta, “Flow in an annular channel filled with a porous medium of variable permeability,” Journal of Porous Media, vol. 15, no. 10, pp. 891–899, 2012.
[39] M. Iqbal and H. Afaq, “Fluid flow and heat transfer through an annular sector duct filled with porous media,” Journal of Porous Media, vol. 18, no. 7, pp. 679-687, 2015.
[40] M. Nasiri, S.G. Etemad, and R. Bagheri, “Experimental heat transfer of nanofluid through an annular duct,” International Communications in Heat and Mass Transfer, vol. 38, no. 7, pp. 958–963, 2011.
[41] M.H. Shedid, “Computational heat transfer for nanofluids through an annular tube,” in Proc, the International Conference on Heat Transfer and Fluid Flow. Prague, Czech Republic, 2014, pp.206:1-10.
[42] A. Beheshti, M.K. Moraveji, and M. Hejazian, “Comparative numerical study of nanofluid heat transfer through an annular channel,” Numerical Heat Transfer, Part A: Applications, vol. 67, no. 1, pp. 100–117, 2015.
[43] F. Ahmed, M. Iqbal, and P. Ioan, “Numerical simulation of forced convective power law nanofluid through circular annulus sector,” Journal of Thermal Analysis and Calorimetry, vol. 135, no. 2, pp. 861–871, 2019.
[44] F. Ahmed and M. Iqbal, “Heat Transfer Analysis of MHD Power Law Nano Fluid Flow through Annular Sector Duct,” Journal of Thermal Science, vol. 29, no. 1, pp. 169–181, 2020.
[45] S. V Patankar and D.B. Spalding, “A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows,” in Numerical prediction of flow, heat transfer, turbulence and combustion. Elsevier, 1983, pp. 54–73
[46] W. M. Kays, Convective Heat and Mass Transfer. New York: McGraw-Hill, 1966, pp. 62.
[47] S. Patankar, Numerical heat transfer and fluid flow. Taylor & Francis, 2018.