Abstract
An Analytic solution is presented of the problem of turbulent heat transfer in pipes with internal heat generation and insulated wall by applying a recently-developed eddy conductivity model. The results agree closely with available experimental data for a wide range of Prandtl number (0.02–10.5).
Zusammenfassung
Eine analytische Lösung des Problems der turbulenten Wärmeübertragung in Rohren mit innerer Wärmeerzeugung und isolierender Wandung wird vermittels eines neu entwickelten Modells für das Wirbelleitvermögen angegeben. Die Ergebnisse stimmen mit den zugänglichen experimentellen Werten innerhalb eines ausgedehnten Bereiches der Prandtl-Zahl (0.02–10.5) befriedigend überein.
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Abbreviations
- A+ :
-
damping factor for eddy viscosity
- a:
-
pipe radius
- a+ :
-
dimensionless pipe radius,\(a\sqrt {\tau _w /\rho /v} \)
- B+ :
-
damping factor for eddy conductivity
- Cp :
-
constant pressure specific heat
- k:
-
thermal conductivity
- l:
-
mixing length
- 1+ :
-
dimensionless mixing length,\(l\sqrt {\tau _w /\rho /v} \)
- Nu:
-
Nusselt number
- Pr:
-
Prandtl number
- Pe:
-
Péclet number, Pe=RePr
- p:
-
static pressure
- q:
-
heat flux
- Q:
-
rate of heat generation
- Re:
-
Reynolds number, u(2a)ν
- r:
-
radial coordinate
- St:
-
Stanton number
- T:
-
temperature
- u:
-
axial velocity
- u+ :
-
dimensionless axial velocity,\(u/\sqrt {\tau _w /\rho } \)
- x:
-
axial coordinate
- y:
-
transverse coordinate normal to wall
- y+ :
-
\(y\sqrt {\tau _w /\rho /v} \)
- α:
-
thermal diffusivity
- μ:
-
viscosity
- ɛm, ɛh :
-
eddy viscosity and eddy conductivity, respectively
- ν:
-
kinematic viscosity
- ρ:
-
density
- τ:
-
shearing stress
- B:
-
bulk
- h:
-
heat
- m:
-
momentum
- o:
-
wall
References
Kinney, R.B.; Sparrow, E.M.: Turbulent Pipe Flow of an Internally Heat Generating Fluid, J. of Heat Transfer, Trans. ASME, Series C88 (1966) 314
Chung, B.T.F.; Thomas, L.C.: Turbulent Heat Transfer for Pipe Flow with Prescribed Wall Heat Fluxes and Uniform Heat Sources in the Stream. J. of Heat Transfer, Trans. ASME, Series C96 (1974) 430–431
Muller, G.L.: Experimental Forced Convection Heat Transfer With Adiabatic Walls and Internal Heat Generation in a Liquid Metal. ASME paper 58-HT-17
Poppendiek, H.F.: Forced Convection Heat Transfer in Pipes With Heat Sources Within the Fluid. Chem. Eng. Progress Symposium Series50 (1954) 93
Na, T.Y.; Habib, I.S.: Heat Transfer in Turbulent Pipe Flow Using a New Mixing Length Model. Appl. Sci. Research28 (Nov. 1973) 302–314
Habib, I.S.; Na, T.Y.: Prediction of Heat Transfer in Turbulent Pipe Flowin Pipes With Constant Wall Temperature. J. of Heat Transfer, Trans. ASME, Series C96 (May 1974) 253–254
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Na, T.Y., Chiou, J.P. Turbulent heat transfer for pipe flow with uniform heat generation. Wärme- und Stoffübertragung 12, 55–58 (1979). https://doi.org/10.1007/BF01672441
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DOI: https://doi.org/10.1007/BF01672441