An Exact Analytical Solution for Convective Heat Transfer in Elliptical Pipes

[1] R. Shah, Laminar flow friction and forced convection heat transfer in ducts of arbitrary geometry, International Journal of Heat and Mass Transfer, 18(7) (1975) 849- 862.

[2] R.K. Shah, A.L. London, Laminar flow forced convection in ducts: a source book for compact heat exchanger analytical data, Academic press, 1978.

[3] P. Wibulswas, Laminar-flow heat-transfer in non-circular ducts, University of London, 1966.

[4] R. Lyczkowski, C. Solbrig, D. Gidaspow, Forced convection heat transfer in rectangular ducts—general case of wall resistances and peripheral conduction for ventilation cooling of nuclear waste repositories, Nuclear Engineering and Design, 67(3) (1982) 357-378.

[5] H. Zhang, M. Ebadian, A. Campo, An analytical/ numerical solution of convective heat transfer in the thermal entrance region of irregular ducts, International communications in heat and mass transfer, 18(2) (1991) 273-291.

[6] A. Barletta, E. Rossi di Schio, E. Zanchini, Combined forced and free flow in a vertical rectangular duct with prescribed wall heat flux, International journal of heat and fluid flow, 24(6) (2003) 874-887.

[7] C. Nonino, S. Del Giudice, S. Savino, Temperature dependent viscosity effects on laminar forced convection in the entrance region of straight ducts, International journal of heat and mass transfer, 49(23) (2006) 4469- 4481.

[8] T.J. Rennie, G.V. Raghavan, Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger, Applied Thermal Engineering, 27(5) (2007) 862-868.

[9] H. Iacovides, G. Kelemenis, M. Raisee, Flow and heat transfer in straight cooling passages with inclined ribs on opposite walls: an experimental and computational study, Experimental Thermal and Fluid Science, 27(3) (2003) 283-294.

[10] A. Jaurker, J. Saini, B. Gandhi, Heat transfer and friction characteristics of rectangular solar air heater duct using rib-grooved artificial roughness, Solar Energy, 80(8) (2006) 895-907.

[11] S.W. Chang, T.L. Yang, R.F. Huang, K.C. Sung, Influence of channel-height on heat transfer in rectangular channels with skewed ribs at different bleed conditions, International Journal of Heat and Mass Transfer, 50(23) (2007) 4581-4599.

[12] S.K. Saha, Thermal and friction characteristics of laminar flow through rectangular and square ducts with transverse ribs and wire coil inserts, Experimental Thermal and Fluid Science, 34(1) (2010) 63-72.

[13] S. Ray, D. Misra, Laminar fully developed flow through square and equilateral triangular ducts with rounded corners subjected to H1 and H2 boundary conditions, International Journal of Thermal Sciences, 49(9) (2010) 1763-1775.

[14] L.-z. Zhang, Z.-y. Chen, Convective heat transfer in cross-corrugated triangular ducts under uniform heat flux boundary conditions, International Journal of Heat and Mass Transfer, 54(1) (2011) 597-605.

[15] M.M. Shahmardan, M. Norouzi, M.H. Kayhani, A.A. Delouei, An exact analytical solution for convective heat transfer in rectangular ducts, Journal of Zhejiang University SCIENCE A, 13(10) (2012) 768-781.

[16] M. Shahmardan, M. Sedaghat, M. Norouzi, An analytical solution for fully developed forced convection in triangular ducts, Heat Transfer—Asian Research, 44(6) (2015) 489-498.

[17] M. Sayed-Ahmed, K.M. Kishk, Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct, International Communications in Heat and Mass Transfer, 35(8) (2008) 1007-1016.

[18] M. Norouzi, M. Kayhani, M. Nobari, Mixed and forced convection of viscoelastic materials in straight duct with rectangular cross section, World Applied Sciences Journal, 7(3) (2009) 285-296.

[19] H. Claiborne, HEAT TRANSFER IN NONCIRCULAR DUCTS PART I, Oak Ridge National Lab., 1951.

[20] L. Tao, On some laminar forced-convection problems, Journal of Heat Transfer, 83(4) (1961) 466-472.

[21] C.-Y. Cheng, The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section, International communications in heat and mass transfer, 33(8) (2006) 1021-1028.

[22] V. Sakalis, P. Hatzikonstantinou, N. Kafousias, Thermally developing flow in elliptic ducts with axially variable wall temperature distribution, International journal of heat and mass transfer, 45(1) (2002) 25-35.

[23] K. Velusamy, V.K. Garg, G. Vaidyanathan, Fully developed flow and heat transfer in semi-elliptical ducts, International journal of heat and fluid flow, 16(2) (1995) 145-152.

[24] K. Velusamy, V.K. Garg, Laminar mixed convection in vertical elliptic ducts, International journal of heat and mass transfer, 39(4) (1996) 745-752.

[25] V. Javeri, Analysis of laminar thermal entrance region of elliptical and rectangular channels with Kantorowich method, Heat and Mass Transfer, 9(2) (1976) 85-98.

[26] R. Abdel-Wahed, A. Attia, M. Hifni, Experiments on laminar flow and heat transfer in an elliptical duct, International journal of heat and mass transfer, 27(12) (1984) 2397-2413.

[27] http://en.wikipedia.org/wiki/Ellipse.

[28] W. Kays, M. Crawford, B. Weigand, Convective Heat and Mass Transfer-Four edition, in, Mc Graw-Hill Publishing Co. Ltd, 2005.

[29] T. Papanastasiou, G. Georgiou, A.N. Alexandrou, Viscous fluid flow, CRC Press, 1999.