For turbulent flows in ducts, streamwise heat conduction effects within the flow can be important for low Prandtl number fluids (liquid metals). The paper presents a numerical investigation of the influence of axial heat conduction within the flow on the heat transfer for hydrodynamically fully developed flow. The calculations have been carried out for a semi-infinite heated section as well as for a heated section of finite length. Additionally, by considering different models for calculating the turbulent heat flux, the normally used assumption that the eddy diffusivity in axial and normal direction are the same was investigated.
Issue Section:
Forced Convection
1.
Batchelor
, G. K.
, 1949
, “Diffusion in a Field of Homogeneous Turbulence
,” Austral. J. Sci. Res.
, A2
, pp. 437
–450
.2.
Chieng
, C. C.
, and Launder
, B. E.
, 1980
, “On the Calculation of Turbulent Heat Transfer Downstream From an Abrupt Pipe Expansion
,” Numer. Heat Transfer
, 3
, pp. 189
–207
.3.
Faggiani
, S.
, and Gori
, F.
, 1980
, “Influence of Streamwise Molecular Heat Conduction on the Heat Transfer for Liquid Metals in Turbulent Flow Between Parallel Plates
,” ASME J. Heat Transfer
, 102
, pp. 292
–296
.4.
Gatski
, T. B.
, and Speziale
, C. G.
, 1993
, “On Explicit Algebraic Stress Models for Complex Turbulent Flows
,” J. Fluid Mech.
, 254
, pp. 59
–78
.5.
Gibson
, M. M.
, and Launder
, B. E.
, 1976
, “On the Calculation of Horizontal Turbulent Free Shear Flows Under Gravitational Influence
,” ASME J. Heat Transfer
, 98
, pp. 81
–97
.6.
Graetz
, L.
, 1883
, “Uber die Wa¨rmeleitungsfa¨higkeit von Flu¨ssigkeiten,”
Ann. Phys. Chem.
, 1
(18
), pp. 79
–94
.7.
Graetz
, L.
, 1885
, “U¨ber die Wa¨rmeleitfa¨higkeit von Flu¨ssigkeiten
,” Ann. Phys. Chem
, 2
(25
), pp. 337
–357
.8.
Hennecke
, D. K.
, 1968
, “Heat Transfer by Hagen-Poiseuille Flow in the Thermal Development Region With Axial Conduction
,” Waerme-und Stoffuebertrag.
, 1
, pp. 177
–184
.9.
Kader
, B. A.
, 1981
, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers
,” Int. J. Heat Mass Transf.
, 24
(9
), pp. 1541
–1544
.10.
Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, Mc Graw-Hill, New York.
11.
Kim, J., and Moin, P., 1989, “Transport of Passive Scalars in Turbulent Channel Flow,” in Turbulent Shear Flows, 6, Springer-Verlag, Berlin, pp. 85–96.
12.
Lee
, S. L.
, 1982
, “Forced Convection Heat Transfer in Low Prandtl Number Turbulent Flows: Influence of Axial Conduction
,” Can. J. Chem. Eng.
, 60
, pp. 482
–486
.13.
Nguyen
, T. V.
, 1992
, “Laminar Heat Transfer for Thermally Developing Flow in Ducts
,” Int. J. Heat Mass Transf.
, 35
(7
), pp. 1733
–1741
.14.
Nusselt
, W.
, 1910
, “Die Abha¨ngigkeit der Wa¨rmeu¨bergangszahl von der Rohrla¨nge
,” VDI Zeitschrift
, 54
, pp. 1154
–1158
.15.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in Fortran77, 1, 2nd ed., Cambridge University Press.
16.
Reed, C. B., 1987, “Convective Heat Transfer in Liquid Metals,” in S. Kakac, R. K. Shah, and W. Aung, eds., Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, Chap 8.
17.
Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, New York, Chap. V and VI.
18.
So
, R. M. C.
, and Sommer
, T. P.
, 1996
, “An Explicit Algebraic Heat-Flux Model for the Temperature Field
,” Int. J. Heat Mass Transf.
, 39
(3
), pp. 455
–465
.19.
Sommer, T. P., 1994, “Near-Wall Modeling of Turbulent Heat Transport in Non-Buoyant and Buoyant Flows,” Ph.D. thesis, Arizona State University, Tempe, AZ.
20.
Weigand
, B.
, 1996
, “An Exact Analytical Solution for the Extended Turbulent Graetz Problem With Dirichlet Wall Boundary Conditions for Pipe and Channel Flows
,” Int. J. Heat Mass Transf.
, 39
(8
), pp. 1625
–1637
.21.
Weigand, B., 1997, Ausgewa¨hlte analytische Lo¨sungsmethoden fu¨r komplexe, knovektive Wa¨rmeu¨bertragungsprobleme, Dr. Ha¨nsel-Hohenhausen Verlag der Deutschen Hochschulschriften, ISBN3-8267-2624-3.
22.
Weigand
, B.
, Ferguson
, J. R.
, and Crawford
, M. E.
, 1997
, “An Extended Kays and Crawford Turbulent Prandtl Number Model
,” Int. J. Heat Mass Transf.
, 40
(17
), pp. 4191
–4196
.23.
Weigand
, B.
, Kanzamar
, M.
, and Beer
, H.
, 2000
, “The Extended Graetz Problem With Piecewise Constant Wall Heat Flux for Pipe and Channel Flows
,” Int. J. Heat Mass Transf.
.24.
Younis, B. A., Speziale, C. G., and Clark, T. T., 1996, “A Non-Linear Algebraic Model for the Turbulent Scalar Flux,” International Conference on Turbulent Heat Transfer, March 1996.
Copyright © 2002
by ASME
You do not currently have access to this content.