Plant leaves possess small channels that connect the interior moist region of the leaf to the environment. The channels, called stomata, pose the primary resistance to moisture transport through the entire plant, and the diameter of an individual stoma is sensitive to the level of CO 2 in the atmosphere. Consider a leaf of corn (maize) whose top surface is exposed to solar irradiation of G s = 600 W / m 2 and an effective skytemperature of T s k y = 0 ∘ C . The bottom side of the leaf is irradiated from the ground which is at a temperature of T g = 20 ∘ C . Both the top and bottom of the leaf are subjected to convective conditions characterized by h = 35 W/m 2 ⋅ K , T ∞ = 25 ∘ C , and also experience evaporation through the stomata. Assuming the evaporative flux of water vapor is 50 x 10 − 6 k g / m 2 ⋅ s under rural atmospheric C O 2 concentrations and is reduced to 50 x 10 − 6 k g / m 2 ⋅ s when ambient C O 2 concentrations are doubled near an urban area, calculate the leaf temperature in the rural and urban locations. The heat of vaporization of water is h f g = 2400 kJ/Kg and assume α = ε =0 .97 for radiation exchange with the sky and the ground, and α s = 0.76 for solar irradiation.
Plant leaves possess small channels that connect the interior moist region of the leaf to the environment. The channels, called stomata, pose the primary resistance to moisture transport through the entire plant, and the diameter of an individual stoma is sensitive to the level of CO 2 in the atmosphere. Consider a leaf of corn (maize) whose top surface is exposed to solar irradiation of G s = 600 W / m 2 and an effective skytemperature of T s k y = 0 ∘ C . The bottom side of the leaf is irradiated from the ground which is at a temperature of T g = 20 ∘ C . Both the top and bottom of the leaf are subjected to convective conditions characterized by h = 35 W/m 2 ⋅ K , T ∞ = 25 ∘ C , and also experience evaporation through the stomata. Assuming the evaporative flux of water vapor is 50 x 10 − 6 k g / m 2 ⋅ s under rural atmospheric C O 2 concentrations and is reduced to 50 x 10 − 6 k g / m 2 ⋅ s when ambient C O 2 concentrations are doubled near an urban area, calculate the leaf temperature in the rural and urban locations. The heat of vaporization of water is h f g = 2400 kJ/Kg and assume α = ε =0 .97 for radiation exchange with the sky and the ground, and α s = 0.76 for solar irradiation.
Solution Summary: The author compares the leaf temperature in the rural and urban area.
Plant leaves possess small channels that connect the interior moist region of the leaf to the environment. The channels, called stomata, pose the primary resistance to moisture transport through the entire plant, and the diameter of an individual stoma is sensitive to the level of
CO
2
in the atmosphere. Consider a leaf of corn (maize) whose top surface is exposed to solar irradiation of
G
s
=
600
W
/
m
2
and an effective skytemperature of
T
s
k
y
=
0
∘
C
. The bottom side of the leaf is irradiated from the ground which is at a temperature of
T
g
=
20
∘
C
. Both the top and bottom of the leaf are subjected to convective conditions characterized by
h
=
35
W/m
2
⋅
K
,
T
∞
=
25
∘
C
, and also experience evaporation through the stomata. Assuming the evaporative flux of water vapor is
50
x 10
−
6
k
g
/
m
2
⋅
s
under rural atmospheric
C
O
2
concentrations and is reduced to
50
x 10
−
6
k
g
/
m
2
⋅
s
when ambient
C
O
2
concentrations are doubled near an urban area, calculate the leaf temperature in the rural and urban locations. The heat of vaporization of water is
h
f
g
=
2400
kJ/Kg
and assume
α
=
ε
=0
.97
for radiation exchange with the sky and the ground, and
α
s
=
0.76
for solar irradiation.
[1] Determine the view factor F12 between the rectangular surfaces:
1 m
1 m
t.
3 m
1 m
1 m
3 m
1 m
1
1
1 m
-4 m
-4 m
3 m
(a)
(b)
(c)
a.) F12 for rectangle (a)
А. 0.09
B. 0.07
С. 0.08
D. 0.06
b.) F12 for rectangle (a)
A. 0.07
В. 0.09
C. 0.08
D. 0.05
c.) F12 for rectangle (b)
A. 0.08
В. 0.07
C. 0.09
D. 0.06
Give step-by-step calculation and explanation
Consider a person sitting nude on a beach in Florida. On a sunny day, visible radiation energy from the
sun is absorbed by the person at a rate of 30 kcal/h or 34.9 W. The air temperature is a warm 30 °C and
the individual’s skin temperature is 32 °C. The effective body surface exposed to the sun is 0.9 m².
(Assume this same area for sun absorption, radiative transfer, and convective loss. Is this a good
assumption?)
a. Find the net energy gain or loss from thermal radiation each hour. (Assume thermal radiative
gain and loss according to the equation 6.51 in Herman and an emissivity of 1.)
-(4).
Equalion
(6.51)
- (40Tin)Eskin Aşkin (Tskin – Troom)
dt
= (4 x 5.67 x 10¬8 w/m²–K*
x (307 K)')€skin Askin (Tskin – Troom).
(6.52)
b. If there is a 4 m/s breeze, find the energy lost by convection each hour. (Use Eq. 6.61 with eq.
6.63.)
1
Equation
he(Tskin – Tair),
(6.61)
A
dt
he
10.45 – w + 10w0.5
(6.63)
-
c. If the individual’s metabolic rate is…
Two parallel rectangular surfaces 1m x 2m are opposite to each other at adistance of 4 m. The surfaces are black and at 100 °C and 200 °C, respectively.Calculate the heat exchange by radiation between the two surfaces.
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Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning