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Wärme - und Stoffübertragung

, Volume 17, Issue 2, pp 85–92 | Cite as

Turbulent heat-transfer characteristics along the heated convex wall of a rectangular cross-sectional return bend

  • N. Seki
  • S. Fukusako
  • M. Yoneta
Article

Abstract

The turbulent heat-transfer characteristics along the heated convex wall of a return bend which has rectangular cross section with large ratio have been examined for various clearances of the duct in detail.

The experiments are performed under condition that the convex wall is heated at uniform heat flux while the concave wall is insulated. Water as a working fluid is utilized. Using four kinds of clearances of 15, 40, 60 and 80 mm, the Reynolds number in the turbulent range is varied from 8×103 to 8×104 with Prandtl number ranging from 6.5 to 8.5.

In consequence, it is found that both the local and the mean heat-transfer rates are always smaller than those for straight parallel plates or for the straight duct. It is also found that the local heat-transfer characteristics in the outlet region of the return bend are more sensitively influenced by the variation of duct clearance than those in the inlet region.

Keywords

Heat Flux Reynolds Number Prandtl Number Working Fluid Uniform Heat Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

c

clearance of duct

cp

specific heat at constant pressure

De

Dean number, [ū·(2c)/ν] √/c/R

de

hydraulic diameter of duct

fe

centrifugal force per unit volume,ρ2/R)

hm

mean heat-transfer rate, defined in Eq. (3)

hx

local heat-transfer rate atx, q/Δt

¯Nu

mean Nusselt number,hm δ (2c)/λ

(¯Nu)in

mean Nusselt number over inlet region, defined in Eq. (5)

(¯Nu)out

mean Nusselt number over outlet region, defined in Eq. (6)

(Nux)de

local Nusselt number based ond e ,h x δd e /λ

Nu

Nusselt number of hydrodynamically and thermally fully developed flow

Pr

Prandtl number, μδ cp

q

uniform heat flux from convex wall

R

radius of curvature of center line of passage in return bend, R o + c/2

Re

Reynolds number, ūδ (2c)/ν

Red

Reynolds number based ond e ,ūδd e /ν

Rex

local Reynolds number, ūδ x/ν

Ro

radius of curvature of convex wall

St

Stanton number, ax/ρūc p

T

local temperature on convex wall atx

tin

uniform inlet temperature

Tw

general wall temperature

Δt

temperature difference,T-T in

¯u

fluid mean velocity

W

width of duct

x

streamwise coordinate along convex wall with origin at beginning of heating

γ

coordinate perpendicular tox

z

nondimensional distance to determine mean Nusselt number

Greek symbols

Θ

angle of advance of convex wall taken from inlet

λ

thermal conductivity of fluid

μ

coefficient of viscosity of fluid

ν

kinematic viscosity of fluid

ρ

density of fluid

φ

implicit function to determineh m

ϕ

(1/2)Re(Re/De)0.2[1 + (Re/De)1/4]Pr0.47

ϕin

Re 1.2 De −0.2 Pr 0.47

ϕout

Re 1.45 De −0.45 Pr 0.47

Subscripts

de

condition based on hydraulic diameter

in

inlet of return bend (Θ = 0 ∼ π/2)

out

outlet of return bend (Θ=π/2∼ π)

condition of hydrodynamically and thermally fully developed straight flow

Turbulente Wärmeübertragung längs einer beheizten Wand eines Umkehrkrümmers mit rechteckigem Querschnitt

Zusammenfassung

Es wird der turbulente Wärmeübergang längs der beheizten konvexen Wand eines Umkehrkrümmers mit rechteckigem Querschnitt und großem Verhältnis Breite zu Höhe bei verschiedenen Höhen untersucht. Die konvexe Wand war mit konstanter Wärmestromdichte beheizt, die konkave war isoliert. Arbeitsfluid ist Wasser. Für die vier Kanalhöhen 15, 40, 60 und 80 mm liegen die Reynolds-Zahlen zwischen 8 δ 103 und 8 δ 104, die Prandtl-Zahlen reichen von 6,5 bis 8,5. Die gemessene lokale und mittlere Wärmeübertragung ist immer kleiner als jene zwischen parallelen Platten oder im geraden Kanal. Die lokale Wärmeübertragung im Austrittsbereich des Umkehrkrümmers ist empfindlicher gegen Änderungen der Kanalhöhe als jene des Einlaßbereichs.

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References

  1. 1.
    Itaya, M.: Hydrodynamics. Print of JSME St (1959) 146–148Google Scholar
  2. 2.
    Murakami, M.: Hydraulic Resistance of Pipes and Ducts. Print of JSME St (1976) 76–78Google Scholar
  3. 3.
    Seki, N.; Fukusako, S.; Yoneta, M.; Tago, M.: Heat Transfer from the Heated Concave Wall of a Return Bend with Rectangular Cross Section. Preprint of National Heat Transfer Symposium of Japan 1982Google Scholar
  4. 4.
    So, R. M. C.; Mellor, G. L.: Experiment on Turbulent Boundary Layers on Concave Wall. Aero. Quart. 26 (1975) 35–40Google Scholar
  5. 5.
    Ellis, L. B.; Joubert, P. N.: Turbulent Shear Flow in a curved Duct. Journal of Fluid Mechanics 62 (1974) 65–84Google Scholar
  6. 6.
    Kreith, F.: The Influence of Curvature on Heat Transfer to Incompressible Fluids. Trans. ASME 77 (1955) 1247–1256Google Scholar
  7. 7.
    Thomann, H.: Effect of Streamwise Wall Curvature on Heat Transfer in a Turbulent Boundary Layer. J. Fluid Mech. 33 (1968) 283–292Google Scholar
  8. 8.
    Mayle, R. E.; Blair, M. F.; Kopper, F. C.: Turbulent Boundary Layer Heat Transfer on Curved Surfaces. Trans. ASME J. Heat Transfer 101 (1979) 521–525Google Scholar
  9. 9.
    Katto, Y.: Den-netsu-gairon. Yokendo 15th (1976) 100–146Google Scholar
  10. 10.
    Depew, C. A.: Heat Transfer to Air in a Circular Tube Having Uniform Heat Flux. Trans. ASME 84 (1962) 186–187Google Scholar
  11. 11.
    Mills, A. F.: Experimental Investigation of Turbulent Heat Transfer in the Entrance Region of Circular Conduit. J. Mech. Engng. Sci. 4 (1962) 63–77Google Scholar
  12. 12.
    Sparrow, E. N.; Hallman, T. M.; Siegel, R.: Turbulent Heat Transfer in the Thermal Entrance Region of a Pipe with Uniform Heat Flux. Applied Scientific Research 7 (1962) 37–52Google Scholar
  13. 13.
    Hatten, A. P.; Quarmby, A.: The Effect of Axially Varying and Unsymmetrical Boundary Conditions on Heat Transfer with Turbulent Flow between Parallel Plates. Int. J. Heat Mass Transfer 6 (1963) 903–914Google Scholar
  14. 14.
    Reynolds, W. C.; Kays, W. M.; Kline, S. J.: Heat Transfer in a Turbulent Incompressible Boundary Layer. NASA Memo. 12-1-58w(1958)Google Scholar
  15. 15.
    Mori, Y.; Nakayama, W.: Study on Forced Convective Heat Transfer in Curved Pipes. Int. J. Heat Mass Transfer 10 (1967) 681–695Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • N. Seki
    • 1
  • S. Fukusako
    • 1
  • M. Yoneta
    • 1
  1. 1.Department of Mechanical EngineeringHokkaido UniversitySapporoJapan

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