tion and radiation within an enclosure. Results of numerical and experimental
investigations are combined to obtain a methodology for the two-dimensional ther-
mal analysis of utilidors.
BACKGROUND
The governing equations for incompressible Newtonian fluid flow in an enclo-
sure are the Navier-Stokes (momentum) equations, the energy equation, and the
continuity equation. The steady state, laminar flow momentum equations are
2u
2u
u 1 p
u
+v
+
- υ 2 +
=0
(1)
u
y ρ x
x2
x
y
2v
2v
v
1 p
v
v y + u x - gβ (T - Tref ) + ρ y - υ 2 +
=0
(2)
y2
x
for a two-dimensional flow field, where y is the vertical direction and x is the hori-
zontal direction. The continuity equation is
u
v
+
=0
(3)
x
y
and the energy equation (neglecting viscous dissipation) is
2T
2T
T
T
+u
- k 2 +
-Q = 0.
(4)
Cv v
x
y2
y
x
The energy equation reduces to
2T
2T
-k 2 +
-Q = 0
(5)
y2
x
for solid regions with homogeneous, isotropic materials, and constant thermal con-
ductivity (k). These equations are coupled and result in four equations and four
unknowns: pressure, temperature, and the x and y components of velocity (p, T, u,
and v). For complex geometries, these equations cannot be simplified and solved
directly.
Heat transfer correlations for convective heat flow in enclosures are generally
expressed in terms of the Nusselt number (Nu) and the Rayleigh number (Ra). These
dimensionless parameters are defined as
hcL
Nu =
(6)
k
gβρ2 ∆TL3
Gr =
(7)
2
υ
Pr =
(8)
α
gβρ2 ∆TL3 υ
Ra = PrGr =
(9)
α
2
3
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