Wärme - und Stoffübertragung

, Volume 24, Issue 2, pp 125–132 | Cite as

Heat transfer in buoyancy-driven channel flows with the simultaneous presence of laminar, transitional and turbulent flow regimes

  • W. M. Yan
  • T. F. Lin
Article

Abstract

The characteristics of transitional natural convection from laminar to turbulent flows in vertical open channel are numerically investigated. Results are especially presented for air under different conditions. Particular attention is paid to the effects of the channel length, channel width and heating conditions on the transitional natural convection heat transfer and flows.

Keywords

Heat Transfer Convection Apply Physic Convection Heat Flow Regime 

Nomenclature

Bb

transitional criterion of beginning of transition, Eq. (1)

Be

transitional criterion of end transitional point, Eq. (2)

b

channel width

cp

specific heat

c1,c2,cμ

constants appearing inkε turbulence model

Dh

hydraulic diameter,D h =2b

f1,f2,fμ

functions appearing inkε turbulence model

Gr

Grasfhof number,g β(T h T0)b3/v2

Grx

Grashof number based on the channel heightx, g β(T h T0)x3/v2

\(\overline {Gr} \)

average Grashof number, defined in Eq. (18)

\(\overline {Gr} _x \)

average Grashof number, based on the channel leightx, g β[(T h +T c )/2−T0]x3/v2

g

gravitational acceleration

h

heat transfer coefficient,q″ w /(T w −T0)

k

turbulent kinetic energy

l

channel length

M

dimensionless volume flow rate,Re/(2\(\overline {Gr} \))

Nu

local Nusselt number based on hydraulic diameter,Nu=h D h /λ

Nux

local Nusselt number based on local channel lengthx, Nu x =hx/λ

p

pressure of the air in the channel

pm

motion pressure (or dynamic pressure),p−p0

qw

heat flux at the channel wall

Re

Reynolds number based on hydraulic diameter,u0(2b)/v

Rt

turbulence Reynolds number,k2/(ν ε)

rT

ratio of wall temperature differences, (T c −T0)/(T h −T0)

T

temperature

Tc

temperature on the cold wall

Th

temperature on the hot wall

T0

inlet temperature

Tw

wall temperature

u

axial velocity

u0

inlet axial velocity

\(\overline {u' T'} \)

longitudinal turbulent heat flux

v

transvere velocity

\(\overline {\upsilon ' T'} \)

transverse turbulent heart flux

x

coordinate in the flow direction

y

coordinate in the transverse direction

yw

distance from the channel walls, Eq. (10)

Greek symbols

α

thermal diffusivity

β

thermal expansion coefficient, 1/T0

γ

turbulent intermittency

ε

rate of dissipation of turbulent kinetic energy

λ

molecular thermal conductivity

ν

molecular kinematic viscosity

νt

turbulent eddy viscosity

ϱ

density

σ

Prandtl number

σk

turbulent Prandtl number fork

σT

turbulent Prandtl number forT

σε

turbulent Prandtl number forε

Subscripts

c

condition on the cold wall

h

condition on the hot wall

o

at ambient condition

Superscript

-

average

Wärmeübergang in Kanalströmen aufgrund von Auftrieb mit gleichzeitigem Vorkommen von laminarer, Übergangs-und turbulenter Strömung

Zusammenfassung

Die Eigenschaften von freier Konvektion im Übergangsbereich von laminarer und turbulenter Strömung in einem senkrechten offenen Kanal wird numerisch untersucht. Die Ergebnisse werden insbesondere für Luft unter verschiedenen Bedingungen vorgestellt. Besonders beachtet wurde der Einfluß der Kanallänge, der Kanalbreite und der Heizbedingungen auf den Wärmeübergang und die Strömung im Übergangsbereich bei freier Konvektion.

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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • W. M. Yan
    • 1
  • T. F. Lin
    • 1
  1. 1.Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchuTaiwan, Republic of China

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