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A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct

Eine numerische Studie zum laminaren Wärmeübergang am Boden von Vertiefungen im Bereich abgelöster Kanalströmung

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Abstract

For the two cavity models whose upward and downward wall heights are different from each other, laminar heat transfer is studied numerically in a finite difference method. The effects of cavity configuration, free-stream velocity and buoyancy force on flow and temperature fields as well as heat transfer at the bottom surface are discussed.

The flow pattern of DOF (Downward-Facing cavity)-model is more intricated than that of UPF (Upward-Facing cavity)-model, depending on the aspect ratio of cavity or main flow velocity. The mean Nusselt numberNu m at the bottom surface of both cavity models tends generally to increase with increasing ReHorGr w/Re 2H . However, in the flow region ofRe H & 500 for DOF-cavity, theNu m for 0.4 ≦ D2/D1 ≦ 0.6 is somewhat lower than that obtained from the other cavities and does not always increase with increasingRe H.

Zusammenfassung

Für die beiden Modelle mit stromauf oder stromab höheren Wänden wird der laminare Wärmeübergang numerisch berechnet. Die Wirkungen der Geometrie, der Freistromgeschwindigkeit und der Auftriebskraft auf Geschwindigkeits- und Temperaturfelder sowie auf den Wärmeübergang werden diskutiert.

In einer Vertiefung mit stromauf höherer Wand (DOF) ist die Strömung verwickelter als in einer mit stromab höherer Wand (UPF), abhängig vom Höhenverhältnis und der Mittelgeschwindigkeit. Die mittlere Nusselt-Zahl am Boden beider VertiefungenNu m steigt im allgemeinen an mit steigendemRe H oderGr w/Re 2H . Allerdings ist fürRe ≧ 500 bei der DOF-Vertiefung im Bereich 0,4 ≦D 2/D1 ≦ 0,6 der WertNu m etwas kleiner ist als bei der anderen Vertiefung und steigt auch nicht immer mit steigendemRe H.

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Abbreviations

Gr w :

Grashof number, Eq. (3)

h x′:

local heat transfer coefficient,q w(θx′ - θ0)

H :

duct height in upstream of cavity

k :

thermal conductivity

Nu x′:

local Nusselt number, Eq. (14)

Nu m :

mean Nusselt number, Eq. (15)

P :

dimensionless pressure,p/(ϱ0 U 20 )

Pr :

Prandtl number, Eq. (3)

q w :

heat flux at heated bottom surface

Re H :

Reynolds number, Eq. (3)

T :

dimensionless temperature, Eq. (10)

u, v :

velocity components inx- andy-directions

U 0 :

maximum velocity ofU (Y) at inflow section

U, V :

dimensionless velocity components inX- andY-directions, u/U0 and v/U0

W :

bottom width of cavity

x, y :

distances along and normal to duct wall

x′ :

distance in x-direction measured from upstream downcorner of cavity

X, Y :

dimensionless coordinates,x/W andy /W

α :

thermal diffusivity

β :

thermal expansion coefficient

C:

dimensionless vorticity

θ :

temperature

θ 0 :

temperature at flow section

v :

kinematic viscosity

ϱ 0 :

density at temperature θ0

ϕ :

functions ofψ, ζ orT

ψ :

dimensionless stream-function

ω(ϕ) :

over-relaxation parameter

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Authors and Affiliations

  1. Department of Mechanical Engineering, Asahikawa Technical College, 070, Asahikawa, Japan

    H. Yamamoto (Associate Professor)

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

    N. Seki (Professor) & S. Fukusako (Associate Professor)

Authors
  1. H. Yamamoto
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  2. N. Seki
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  3. S. Fukusako
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Yamamoto, H., Seki, N. & Fukusako, S. A numerical study of laminar heat transfer at bottom surface of a cavity submerged in separated flow region of duct. Wärme- und Stoffübertragung 16, 219–227 (1982). https://doi.org/10.1007/BF01375646

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  • DOI: https://doi.org/10.1007/BF01375646

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