Biomedical Engineering Reference
In-Depth Information
On the surface of the skin, convection, radiation, and evaporation are the main modes of heat
transport between the tissue and the surrounding environment. The boundary condition on the sur-
face of the skin is thus expressed as
∂
∂
T
n
(
)
(
)
−
λ
=
hT T
−
+
h
TT
−
+
E
sk
(23.21)
s
c
ambi
ra
ambi
where
T
ambi
is the ambient temperature, λ
s
is the thermal conductivity of skin,
h
c
is the convective
heat transfer coefficient,
h
ra
is the radiative heat transfer coefficient, and
E
sk
is the heat loss due to
evaporation. The heat loss due to evaporation can be written as
EhPP
sk
=
(
−
)
(23.22)
e kin
ambi
where
P
skin
is the vapor pressure at the surface of the skin (kPa) and
P
ambi
is the vapor pressure of air
(kPa). The evaporation coefficient
h
e
is related to the air velocity and can be expressed as
h
=
124
V
W/mkPa
2
(23.23)
e
air
The dimensionless form of the boundary condition equation can be written as
−
∂
∂
T
n
*
=⋅
Bi
(- )
TT
** *
+
E
sk
(23.24)
ambi
*
hD
c
where
Bi
is the Biot number such that
Bi
=
.
λ
s
V
air
< 0.2
m/s
, the heat trans-
fer coefficient on the surface of the hand is 4.2 W/m
2
K. With respect to the radiative heat transfer
coefficient, it is set to be a constant value of 4.8 W/m
2
K as a representative for typical indoor tem-
peratures (ASHRAE 1997).
Equations 23.15, 23.16, and 23.20 have been discretized by using the Galerkin weighted residual
method and a FORTRAN program has been developed to solve these equations. The specific proce-
dures for finite element approximation can be referred to by consulting literature references (Reddy
and Gartling 2001; Hanspal et al. 2006; He and Himeno 2012). The thermal physical properties and
some related parameters are listed in Tables 23.2 and 23.3, respectively.
When the hand is in moving air whose velocity is in the range of 0 <
table 23.3
Parameters used in three-dimensional Finite element element analysis
Parameters
values
notes
E
sk
(W / m
2
)
1030
Evaporative heat
L
c
(m)
4E-3
Capillary length
D
c
(m)
8E-6
Capillary diameter
U
c
(m / s)
2E-3
Capillary flow
µ
(kg / m · s)
1.07E-3
Blood viscosity
Q
m
(W / m
3
)
300
Metabolic heat production rate
T
a
(°C)
37
Arterial blood temperature
T
v
(°C)
35.5
Venous blood temperature
-
a
(KPa)
7.0
Arterial pressure
-
v
(KPa)
1.3
Venous pressure
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