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TECHNICAL PAPERS: Forced Convection

A Numerical Investigation of the Heat Transfer in a Parallel Plate Channel With Piecewise Constant Wall Temperature Boundary Conditions

[+] Author and Article Information
B. Weigand

Universität Stuttgart, Institut für Thermodynamik der Luft- und Raumfahrt, Pfaffenwaldring 31, 70569 Stuttgart, Germany

T. Schwartzkopff

Universität Stuttgart, Institut für Aerodynamik und Gasdynamik, Pfaffenwaldring 21, 70569 Stuttgart, Germany

T. P. Sommer

ALSTOM Power Generation Ltd, 5401 Baden, Switzerland

J. Heat Transfer 124(4), 626-634 (Jul 16, 2002) (9 pages) doi:10.1115/1.1482085 History: Received July 10, 2001; Revised March 14, 2002; Online July 16, 2002
Copyright © 2002 by ASME
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References

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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.
Gatski,  T. B., and Speziale,  C. G., 1993, “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” J. Fluid Mech., 254, pp. 59–78.
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Graetz,  L., 1883, “Uber die Wärmeleitungsfähigkeit von Flüssigkeiten,” Ann. Phys. Chem., 1(18), pp. 79–94.
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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.
Kader,  B. A., 1981, “Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transf., 24(9), pp. 1541–1544.
Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, Mc Graw-Hill, New York.
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.
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.
Nguyen,  T. V., 1992, “Laminar Heat Transfer for Thermally Developing Flow in Ducts,” Int. J. Heat Mass Transf., 35(7), pp. 1733–1741.
Nusselt,  W., 1910, “Die Abhängigkeit der Wärmeübergangszahl von der Rohrlänge,” VDI Zeitschrift, 54, pp. 1154–1158.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in Fortran77, 1 , 2nd ed., Cambridge University Press.
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.
Shah, R. K., and London, A. L., 1978, Laminar Flow Forced Convection in Ducts, Academic Press, New York, Chap. V and VI.
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.
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Figures

Grahic Jump Location
Geometry and coordinate system
Grahic Jump Location
Comparison of the numerically obtained fluid temperature at ỹ=0 with the analytical solution for a laminar flow. Grid: 257×65 points. Heating: half infinite.
Grahic Jump Location
Comparison of the numerically obtained fluid temperature Θ+(y+) with the formula given by Kader 9 for ReD=13000,Pr=0.025 and Reτ=206.8. Resolution of the grid used in the computation 2049×257.
Grahic Jump Location
Comparison of numerically calculated and analytical Nusselt number for turbulent flow. Constant Prandtl number Pr=0.72. Grid 513×65. Heating: half infinite.
Grahic Jump Location
Comparison of numerically calculated and analytical Nusselt number for turbulent flow. Constant Reynolds number ReD=5000. Grid 513×65. Heating: half infinite.
Grahic Jump Location
Comparison of a numerical calculated local Nusselt number for laminar flow on different grids with an analytical solution at x/(hPeh)>0 (top) and x/(hPeh)<0 (bottom) for PeD=4. Heating: half infinite.
Grahic Jump Location
Example of a grid used for the computation for a half infinite heated zone. Temperature jump at x̃=0.0. Resolution: 257×65 points.
Grahic Jump Location
Influence of the length of the heated zone on the Nusselt Number. PeD=400,Pr=0.01, grid 1025×129. Top: Δxheat/DPeD=0.00625, bottom: Δxheat/DPeD=0.0625.
Grahic Jump Location
Dimensionless temperature gradient at the wall for Δxheat/DPeD=0.00625,PeD=400,Pr=0.01 and a grid 1025×129.
Grahic Jump Location
Dimensionless wall temperature Θw and bulk temperature Θm for Δxheat/DPeD=0.00625,PeD=400,Pr=0.01 and a grid 1025×129.
Grahic Jump Location
Influence of the Pe number on the Nu number for a heated duct with a finite heated zone. ReD=40000, grid 1025×129 (Δxheat/DPeD)=0.025. Top: PeD=40, bottom: PeD=4000.
Grahic Jump Location
Region where the flow is hyperbolic as a function of PeD for the EAHF model. ReD=40000,jmax=513.

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