ASHRAE Journal - November 2019 - 58

TECHNICAL FEATURE

is equal to 58.1 W/m2 [18.42 Btu/h·ft2], a clothing insulation of 0.6 clo (1 clo = 0.155 m2K/W [0.88 ft2·h·°F/Btu])
and a mean radiant temperature of 25°C (77°F).

K2
v
T = Cµ Cd
ε
I m = Cd

K 3/ 2
ε

Boundary Conditions

The model constants are:
Cµ = 0.5478; Cd = 0.1643; s K = 1.0; se = 1.314;
C1e =1.44; C2e = 1.92; C3e =1.0
The buoyancy production Pb is < 0 for stably stratified
layers, so that K is reduced and turbulence is damped.
The radiative heat transfer is modeled using the
IMMERSOL model using the following governing
equations:
CdT0
− div ( kdT0 ) = q
dt
div ( γ dJ 0 ) = ( a + s ) ( J − J 0 )
J 0 = σT04
γ=

4

1
3 a + s + 
L0 


where
a, m-1(ft-1) = absorptivity of the fluid medium per
unit length
3
C, W/m ·K(Btu/h·ft3·°F) = specific heat capacity of the
solid
2
2
J0,W/m (Btu/h·ft ) = radiosity
J, W/m2(Btu/h·ft2) = face surface average of s T4
k, W/m·K (Btu/h·ft·°F) = face surface's thermal
conductivity
L0,m (ft) = distance between adjacent walls
q ,W/m3 (Btu/h·ft3) = heat source per unit volume
s, m-1(ft-1) = scattering coefficient of that medium
per unit length
T0, K (°R) = temperature of the solid phase,
s = Stefan-Boltzmann constant, 5.6704 × 10-8
W/m2·K4 (1.714 × 10-9 Btu/h·ft2·°R4)
e = dissipation rate, m2/s3 (ft2/s3)
In the IMMERSOL model, both the absorption a and
scattering s coefficients are set to zero. A person is modeled inside the room to study comfort indices based on
the metabolic rate of sedentary work (about 1 met, which
58

ASHRAE JOURNAL

ashrae.org

N O V E M B E R 2 0 19

Regarding the boundary conditions of wall surfaces,
the classical no-slip boundary conditions are applied to
the ceiling and the walls. For the radiant ceiling arrangement, the room is cooled using a radiant ceiling panel
covering the entire ceiling area, 3.93 × 3.86 m (12.9 ×
12.7 ft). The panel temperature is kept constant at 18°C
(64.4°F) to avoid indoor condensation. For the radiant walls arrangement, the room is cooled using two
opposed radiant panels covering the entire area of the
opposed 3.86 m × 2.25 m (12.7 ft × 7.38 ft) vertical walls.
The total area of the wall panels in this case is larger
than the ceiling panel area in the previous case. This is
due to the less encountered viewing factor caused by
the limited exposure of load sources to the wall panels
in comparison to their exposure to the ceiling panel.
The temperature of both panels is kept constant at 18°C
(64.4°F). Finally, for the convection arrangement, the
room is cooled using a conventional convection HVAC
system, configured to achieve a unidirectional, laminar,
and low-velocity airflow.
The system shown in Figure 3 supplies air to the room
at 14°C (57.2°F) via a 0.8 m × 0.8 m (2.62 × 2.62 ft) perforated ceiling diffuser. The supply air temperature is
chosen to achieve a temperature difference capable of
accomplishing low velocity and comfortable conditions
as per the ASHRAE requirements (ASHRAE 1999). The
diffuser is located at the center of the ceiling, delivering 115.2 m3/h (67.8 cfm) of air at a velocity of 0.1 m/s
(19.7 fpm). The effective diffuser area ratio, defined as
the actual air passage area divided by the entire diffuser surface area, is 0.5. Return air is extracted from
the room via two 0.8 × 0.4 m (2.62 × 1.31 ft) low-level
return- side wall grills located at the bottom center
of the opposing 3.86 × 2.25 m (12.7 × 7.38 ft) vertical
walls. The effective area ratio of the return grills is
0.5. Concerning the turbulence quantities, they are
imposed assuming a fully developed flow upstream.
In the same way as the inlet boundary conditions,
the outlet boundary conditions are imposed at a fully
developed flow section. The outlet velocity is computed
from the mass and balance equation and the gradients
are assumed normal to flow direction. Other variables



ASHRAE Journal - November 2019

Table of Contents for the Digital Edition of ASHRAE Journal - November 2019

Contents
ASHRAE Journal - November 2019 - Intro
ASHRAE Journal - November 2019 - Cover1
ASHRAE Journal - November 2019 - Cover2
ASHRAE Journal - November 2019 - 1
ASHRAE Journal - November 2019 - Contents
ASHRAE Journal - November 2019 - 3
ASHRAE Journal - November 2019 - 4
ASHRAE Journal - November 2019 - 5
ASHRAE Journal - November 2019 - 6
ASHRAE Journal - November 2019 - 7
ASHRAE Journal - November 2019 - 8
ASHRAE Journal - November 2019 - 9
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ASHRAE Journal - November 2019 - 11
ASHRAE Journal - November 2019 - 12
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ASHRAE Journal - November 2019 - 14
ASHRAE Journal - November 2019 - 15
ASHRAE Journal - November 2019 - 16
ASHRAE Journal - November 2019 - 17
ASHRAE Journal - November 2019 - 18
ASHRAE Journal - November 2019 - 19
ASHRAE Journal - November 2019 - 20
ASHRAE Journal - November 2019 - 21
ASHRAE Journal - November 2019 - 22
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