Unformatted text preview: Chapter 3 Steady Heat Conduction
3167 Two persons are wearing different clothes made of different materials with different surface areas.
The fractions of heat lost from each person’s body by respiration are to be determined.
Assumptions 1 Heat transfer is steady. 2 Heat transfer is onedimensional. 3 Thermal conductivities are
constant. 4 Heat transfer by radiation is accounted for in the heat transfer coefficient. 5 The human body is
assumed to be cylindrical in shape for heat transfer purposes.
Properties The thermal conductivities of the leather and synthetic fabric are given to be k = 0.159 W/m⋅°C
and k = 0.13 W/m⋅°C, respectively.
Analysis The surface area of each body is first determined from A1 = πDL / 2 = π(0.25 m)(1.7 m)/2 = 0.6675 m 2
A2 = 2 A1 = 2 × 0.6675 = 1.335 m 2
The sensible heat lost from the first person’s body is Rleather 0.001 m
L
=
= 0.00942 °C/W
kA (0.159 W/m.°C)(0.6675 m 2 )
1
1
=
=
= 0.09988 °C/W
hA (15 W/m 2 .°C)(0.6675 m 2 ) Rleather =
Rconv Rconv T1 T∞2 R total = Rleather + Rconv = 0.00942 + 0.09988 = 0.10930 °C/W The total sensible heat transfer is the sum of heat transferred through the clothes and the skin T −T
(32 − 30)°C
&
Qclothes = 1 ∞ 2 =
= 18.3 W
R total
0.10930°C/W
T −T
(32 − 30)°C
&
Qskin = 1 ∞ 2 =
= 20.0 W
Rconv
0.09988°C/W
&
&
&
Qsensible = Qclothes + Qskin = 18.3 + 20 = 38.3 W
Then the fraction of heat lost by respiration becomes
f=
& &
&
&
Q respiration Q total − Qsensible 60 − 38.3
=
=
= 0.362
&
&
60
Q total
Q total Repeating similar calculations for the second person’s body
L
0.001 m
=
= 0.00576 °C/W
kA (0.13 W/m.°C)(1.335 m 2 )
1
1
=
=
= 0.04994 °C/W
2
hA (15 W/m .°C)(1.335 m 2 ) Rsynthetic =
Rconv R total = Rleather + Rconv = 0.00576 + 0.04994 = 0.05570 °C/W
T − T∞ 2
(32 − 30)°C
&
=
= 35.9 W
Qsensible = 1
0.05570°C/W
R total
f=
& &
&
&
Q respiration Q total − Qsensible 60 − 35.9
=
=
= 0.402
&
&
60
Q total
Q total 3121 T1 Rsynthetic Rconv
T∞2 ...
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, Grammatical person, Thermal conductivity, Rleather, Qsensible

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