A flat-plate solar collector is used w heat atmospheric air flowing through a rectangular channel. The bottom surface of the channel is well insulated, while the top surface is subjected to a uniform heat flux q o " , which is due to the net effect of solar radiation absorption and heat exchange between the absorber and cover plates. (a) Beginning with an appropriate differential control volume, obtain an equation that could be used to determine the mean air temperature T m ( x ) as a function of distance along the channel. Solve this equation lo obtain an expression for the mean temperature of the air leaving the collector. (b) With air inlet conditions of m ˙ = 0.1 kg/s and T m , i = 40 ° C , what is the air outlet temperature if L = 3 m , w = 1 m , and q o ' ' = 700 W / m 2 ? The specific heat of air is c p = 1008 J/kg ⋅ K .
A flat-plate solar collector is used w heat atmospheric air flowing through a rectangular channel. The bottom surface of the channel is well insulated, while the top surface is subjected to a uniform heat flux q o " , which is due to the net effect of solar radiation absorption and heat exchange between the absorber and cover plates. (a) Beginning with an appropriate differential control volume, obtain an equation that could be used to determine the mean air temperature T m ( x ) as a function of distance along the channel. Solve this equation lo obtain an expression for the mean temperature of the air leaving the collector. (b) With air inlet conditions of m ˙ = 0.1 kg/s and T m , i = 40 ° C , what is the air outlet temperature if L = 3 m , w = 1 m , and q o ' ' = 700 W / m 2 ? The specific heat of air is c p = 1008 J/kg ⋅ K .
Solution Summary: The author explains the expression for the differential equation of the control volume for air.
A flat-plate solar collector is used w heat atmospheric air flowing through a rectangular channel. The bottom surface of the channel is well insulated, while the top surface is subjected to a uniform heat flux
q
o
"
, which is due to the net effect of solar radiation absorption and heat exchange between the absorber and cover plates.
(a) Beginning with an appropriate differential control volume, obtain an equation that could be used to determine the mean air temperature
T
m
(
x
)
as a function of distance along the channel. Solve this equation lo obtain an expression for the mean temperature of the air leaving the collector. (b) With air inlet conditions of
m
˙
=
0.1
kg/s
and
T
m
,
i
=
40
°
C
, what is the air outlet temperature if
L
=
3
m
,
w
=
1
m
,
and
q
o
'
'
=
700
W
/
m
2
? The specific heat of air is
c
p
=
1008
J/kg
⋅
K
.
The TPD method measures temperature elevations in a tissue region during a heating pulse
and its later temperature decay after the pulse. It is then using the Pennes bioheat equation to perform a
curve fitting to determine the local blood perfusion rate. If the TPD probe is placed in the vicinity of very
large blood vessel, will the TPD technique provide an accurate measurement of the local blood perfusion
in the vicinity of this large blood vessel? Explain briefly. (Hint: Is the Pennes bioheat equation accurate
surrounding a large blood vessel?)
A plate-shaped glass wall with a thickness of 3 cm and a heat transfer coefficient of 2W / m.K has 30C air on the inside and 10C ambient air on the outside. The internal and external convulsion coefficients are 30 W / m ^ 2.K and Since it is 15W / m ^ 2.K,a.) The amount of heat in the unit area of the wall,b.) Calculate the inner and outer surface temperatures of the wall.
Mass flow rate of hot fluid is 0.007 kg/s. Convection heat transfer coefficient of hot fluid stream is 1000
W/m?.°C. Thermophysical properties are given as follows.
Hot fluid; c, = 5000 J/kg.°C
Water; dynamic viscosity, µ = 0.001 Pa.s; Prandti number, Pr = 6.14; thermal conductivity, k = 0.607 W/m.°C;
density, p = 1000 kg/m³; specific heat c, = 4200 J/kg.°C.
Neglecting conduction resistance of the pipe, calculate heat exchanger effectiveness (ɛ), heat transfer rate (Q
in J/s), outlet temperatures of the hot fluid (Thout) and water (Tw.out) for varying mass flow rate values of water
provided below.
Mass flow rate of water, m (kg/s)
0.0025
0.01
0.025
0.05
0.075
0.1
Plot heat exchanger effectiveness (ɛ), heat transfer rate (Q in J/s), outlet temperatures of the hot fluid (Thout)
and water (Tw.out) as a function of water mass flow rate (m .).
Comment on the results.
Hot
fluid in (65 °C)
Water
Water
in (25 °C)
out
d = 0.5 cm
Hot fluid out
L= 5 m
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