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

Turbulente Wärmeübertragung längs einer beheizten Wand eines Umkehrkrümmers mit rechteckigem Querschnitt

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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.

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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Abbreviations

c :

clearance of duct

c p :

specific heat at constant pressure

De :

Dean number, [ū·(2c)/ν] √/c/R

d e :

hydraulic diameter of duct

f e :

centrifugal force per unit volume,ρ(ū2/R)

h m :

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

h x :

local heat-transfer rate atx, q/Δt

¯Nu :

mean Nusselt number,h m 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)

(Nu x ) de :

local Nusselt number based ond e ,h x δ d e /λ

Nu ∞ :

Nusselt number of hydrodynamically and thermally fully developed flow

Pr :

Prandtl number, μδ c p/λ

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

Re d :

Reynolds number based ond e ,ūδ d e /ν

Re x :

local Reynolds number, ūδ x/ν

R o :

radius of curvature of convex wall

St :

Stanton number, ax/ρūc p

T :

local temperature on convex wall atx

t in :

uniform inlet temperature

T w :

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

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]Pr 0.47

ϕ in :

Re 1.2 De −0.2 Pr 0.47

ϕ out :

Re 1.45 De −0.45 Pr 0.47

d e :

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

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hokkaido University, 060, Sapporo, Japan

    N. Seki (Prof.), S. Fukusako (Ass. Prof.) & M. Yoneta (Graduate Student)

Authors
  1. N. Seki
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  2. S. Fukusako
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  3. M. Yoneta
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Seki, N., Fukusako, S. & Yoneta, M. Turbulent heat-transfer characteristics along the heated convex wall of a rectangular cross-sectional return bend. Warme- und Stoffubertragung 17, 85–92 (1983). https://doi.org/10.1007/BF01007223

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  • DOI: https://doi.org/10.1007/BF01007223

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