A way to explain the thermal boundary effects on laminar convection through a square duct

Abstract

A way using the reformulation of the energy conservation equation in terms of heat flux to explain the thermal boundary effects on laminar convective heat transfer through a square duct is presented. For a laminar convection through a square duct, it explains that on the wall surface, the velocity is zero, but convection occurs for uniform wall heat flux (UWHF) boundary in the developing region due to the velocity gradient term; for uniform wall temperature (UWT) boundary, only diffusion process occurs on the wall surface because both velocity and velocity gradient do not contribute to convection; for UWHF, the largest term of the gradient of velocity components (the main flow velocity) on the wall surface takes a role in the convection of the heat flux normal to the wall surface, and this role exists in the fully developed region. Therefore, a stronger convection process occurs for UWHF than for UWT on the wall surface. The thermal boundary effects on the laminar convection inside the flow are also detailed.

Keywords

convective transport / heat transfer / mass transfer / laminar flow / thermal boundary effects

References

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 50876040)

Notation

a	thermal diffusivity/(m2·s-1)
C	combined with other symbol means cross-averaged value of this symbol
cp	specific heat capacity/(kJ·kg-1·K-1)
dh	hydraulic diameter/m
ei,j	second order tensor or velocity gradient/s-1
f	friction factor
h	heat transfer coefficient/(W·m-2·K-1)
BoldItalic,BoldItalic,BoldItalic	unit vector respecting to x, y, z direction
n	normal direction/m
Nu	Nusselt number
W	combination terms in heat flux convection equation/(W·m-2·s-1)
x, y, z	coordinator axes/m
l	thermal conductivity/(W·m-1·K-1)
m	viscosity/(kg·m-1·s-1)
r	density/(kg·m-3)
Ñ	operator/m-1
p	static pressure/(N·m-2)
q	components of heat flux vector/(W·m-2)
BoldItalic	vector heat flux/(W·m-2)
S	combined with other symbol means span-averaged value of this symbol
SW	span averaged value of W /(W·m-2·s-1)
t	time/s
T	temperature/K
Subscript
u, v, w	components of velocity vector/(m·s-1)
BoldItalic	velocity vector/(m·s-1)
bulk	cross averaged value
c-x, c-y, c-z	terms in heat flux equation related to velocity
e-x, e-y, e-z	terms in heat flux equation related to velocity gradient
local	local value
s	span averaged value
x, y, z	along x, y, z direction, respectively
w	wall

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