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Temperature and velocity field characteristics of turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

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Abstract

Turbulent natural convection in an asymmetrically heated vertical parallel-plate channel has been studied experimentally and numerically using LDA and CFD. Simultaneous velocity and temperature measurements across the channel at different elevations have been carried out. Three different Ra(b/h) values of 1.91  ×  107, 2.74  ×  107 and 3.19  ×  107 are considered with the channel aspect ratio of b/h = 1/20. Experimental and numerical data are presented in the form of streamwise direction heated wall surface temperature, mean velocity, mean temperature, Reynolds shear stress and turbulent kinetic energy profiles along the channel for one case. These profiles exhibit the flow field development along the channel emphatically. The numerical technique used predicts temperature field fairly well, considerably over-estimating velocity field in the core region.

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Abbreviations

A:

Surface area of the heated wall, [m2]

b:

Channel width

b/H:

Channel aspect ratio

CFD:

Computational fluid dynamics

\({\hbox{C}_{\mu},\, \hbox{C}_{\varepsilon 1},\, \hbox{C}_{\varepsilon 2}}\) :

LRN k−ɛ model constants

cp :

Specific heat

DA:

Davidson turbulence model or results obtained using it

Exp:

Experimental value

fμ,  f1,  f2 :

LRN k−ɛ model functions

g:

Gravitational acceleration

G:

Production of k due to buoyancy

Gr:

Grashof number, \({{\hbox{Gr}} = {\hbox{g}}\beta {\hbox{q}}_{{\rm {c}}} {\hbox{b}}^{{\rm {4}}} /\upsilon ^{2}}\)

h:

Overall convective heat transfer coefficient, \({\hbox{h} = \hbox{q}_{\rm c} /(\hbox{T}_{{\rm w,ave}} -\bar{\hbox{T}}_{{\rm b,ave}})}\)

H:

Channel height

k:

Turbulent kinetic energy

LB:

Lam and Bremhorst turbulence model or results obtained using it

LDA:

Laser-Doppler anemometry

LRN:

Low Reynolds number

m:

Mass flow rate

Nu:

Average Nusselt number, Nu =  hb/λ

p:

Static pressure

ph :

Hydrostatic pressure

pm :

Motion pressure

P:

Production of k due to shearing

Pr:

Prandtl number

qc :

Heat convected from unit area of the heated wall, \(\hbox{q}_{\rm c} = \hbox{c}_{\rm p}\hbox{m}(\bar{\hbox{T}}_{{\rm b,1}} -\bar{\hbox{T}}_{{\rm b,0}})/\hbox{A}\)

Ra:

Rayleigh number, Ra =  Gr Pr

Ret :

Turbulent Reynolds number, Re t = k2 /υ ɛ

Rey :

Turbulent Reynolds number, \({\hbox{Re} _{\rm y} = \hbox{y}\sqrt{\hbox{k}}/\upsilon }\)

t:

Time

T:

Temperature

\({\bar{\hbox{T}}_{{\rm b,ave}} }\) :

Average bulk temperature \({\bar{\hbox{T}}_{{\rm b,ave}} = (\bar{\hbox{T}}_{{\rm b,1}} + \bar{\hbox{T}}_{{\rm b,2}})/2}\)

TH:

To and Humphrey turbulence model, or results obtained using it

u, v:

x, y components of velocity

x, y:

Cartesian coordinates

y+ :

Dimensionless transverse coordinate, \({\hbox{y}^{+} = \hbox{y}/ \nu (\nu \partial \hbox{u}/ \partial \hbox{y})^{-1/2}}\)

X:

Dimensionless channel height, x/H

β:

Thermal expansion coefficient

ɛ:

Dissipation of turbulent kinetic energy

κ:

Von Karman coefficient

λ:

Thermal conductivity

μ:

Dynamic viscosity

μt :

Dynamic turbulent viscosity

ν:

Kinematic viscosity

νt :

Kinematic turbulent viscosity

ρ:

Density

σt :

Turbulent Prandtl number

σk :

Prandtl number of k

σɛ :

Prandtl number of ɛ

ave:

Averaged quantity

b:

Bulk quantity

c:

Convective, channel or case

exp:

Experimental value

m:

Maximum value

num:

Numerical value

w:

Quantity at the wall

0:

Quantity at the inlet

1:

Quantity at the outlet

∞:

Reference quantity, ambient quantity

ɛ:

Quantity referring to the dissipation of turbulent kinetic energy

k:

Quantity referring to turbulent kinetic energy

t:

Quantity referring to turbulence

′:

Fluctuating quantity

−:

Time averaged quantity

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Mechanical Engineering Department, Istanbul Technical University, Gümüşsuyu, 34437, Istanbul, Turkey

    Turgut Yilmaz

  2. Department of Mechanical Engineering, University of Strathclyde, 75 Montrose Street, Glasgow, G1 1XJ, UK

    Alastair Gilchrist

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  1. Turgut Yilmaz
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  2. Alastair Gilchrist
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Correspondence to Turgut Yilmaz.

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Yilmaz, T., Gilchrist, A. Temperature and velocity field characteristics of turbulent natural convection in a vertical parallel-plate channel with asymmetric heating. Heat Mass Transfer 43, 707–719 (2007). https://doi.org/10.1007/s00231-007-0234-y

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