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Heat and Mass Transfer

, 43:907 | Cite as

Conjugate heat transfer in square enclosures

  • Fu-Yun Zhao
  • Di Liu
  • Guang-Fa TangEmail author
Original

Abstract

Building elements represented by square vertical enclosures encircled with finite walls or with centered solid body, could maintain the equivalent fluid volumes through the volume ratio scale. Present work aims to investigate the fluid flow and heat transfer in these two building elements. Complete two-dimensional numerical simulation of the conjugate heat conduction and natural convection occurring in both enclosures is carried out. An analytical expression for the minimum size of the inserted body at which the body begins to suppress the natural convection flow is proposed and validated by the numerical results. The fluid flow and heat transfer characteristics are analyzed through the streamlines, heatlines, and total heat transfer rates across both enclosures. Results reveal that heat transfer rates across both enclosures are complex functions of the volume ratio scale, Rayleigh number, and the relative thermal conductivity.

Keywords

Heat Transfer Nusselt Number Natural Convection Rayleigh Number Heat Transfer Rate 
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.

List of Symbols

CP

isobaric specific heat (J/K kg)

g

gravitational acceleration (m/s2)

H

heat function

k

thermal conductivity (W/m K)

K

thermal conductivity ratio

Kr

thermal conductivity ratio of solid to fluid

L

length of square enclosure (m)

n

normal direction

Nu

local Nusselt number

p

pressure (N/m2)

P

dimensionless pressure

Pr

Prandtl number, ν/α

Q

total heat transfer rate (W/m2)

Ra

Rayleigh number, gβ(t ht c)L 3/να

S

distance (m)

t

temperature (K)

T

dimensionless temperature

u

velocity component in x directions (m/s)

v

velocity component in y directions (m/s)

U

dimensionless velocity component in X

V

dimensionless velocity component in Y

W

length of inner cavity or body (m)

x, y

Cartesian coordinates (m)

X, Y

dimensionless Cartesian coordinates

Greek Symbols

α

thermal diffusivity (m2/s)

β

volume expansion coefficient (1/K)

θ

volume ratio scale (°)

ξ

void fraction of enclosure A

η

solid-to-fluid volume ratio of enclosure B

ν

kinematics viscosity (m2/s)

ρ

density (kg/m3)

Ψ

stream function

Subscripts

a

average value

A

enclosure encircled with finite walls

B

enclosure inserted with solid body

c

cold wall

f

value of the fluid domain

h

hot wall

max

maximum

min

minimum

s

value of the solid domain

Superscripts

*

dimensionless

Notes

Acknowledgements

The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (No. 50578059). The authors are also grateful to the anonymous referees who provided detailed and constructive comments.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.College of Civil EngineeringHunan UniversityChangshaPeople’s Republic of China

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