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HEAT TRANSFER PROCESSES
• Conductive heat transfer
• Convective heat transfer
• Radiation heat transfer
Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultravioletvisiblelightinfraredmicrowaves x-rays
Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultravioletvisiblelightinfraredmicrowaves x-rays
HighEnergy
LowEnergy
Blackbody Radiation
Blackbody radiation—radiation emitted by a body that emits (or absorbs) equally well at all wavelengths
Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects.
Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object.
Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.
This is the Stefan Boltzmann Law
E = T4
E = total radiant energy emitted per unit time per unit surface area(W/m2)
T = temperature (K) = 5.67 x 10-8 W/m2K4 (a constant)
Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.
3) The hotter the object, the shorter the wavelength () of emitted energy.
Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.
3) The hotter the object, the shorter the wavelength () of emitted energy.
This is Wien’s Law
max 2828 m T(K)
Stefan Boltzmann Law.
F = T4
F = flux of energy (W/m2)T = temperature (K) = 5.67 x 10-8 W/m2K4 (a constant)
Wien’s Law
max 2828 m T(K)
We can use these equations to calculate properties of energy radiating from the Sun and the Earth.
6,000 K 300 K
Planetary Energy Balance
• We can use the concepts learned so far to calculate the radiation balance of the Earth
Energy Balance:
The amount of energy delivered to the Earth is equal to the energy lost from the Earth.
Otherwise, the Earth’s temperature would continually rise (or fall).
How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and greater area.
How much solar energy reaches the Earth?
As energy moves away from the sun, it is spread over a greater and greater area.
This is the Inverse Square Law
So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e) and the Sun and the Sun’ luminosity.
How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re)
Einre
How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re)
Ein = So (W/m2) x re2 (m2)
Einre
How much energy does the Earth emit?
Eout = E x (area of the Earth)
E = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
(m)
1000 100 10 1 0.1 0.01
Earth Sun
Hotter objects emit at shorter wavelengths.
max = 2828/T
Hotter objects emit more energy than colder objects
E = T4
How much energy does the Earth emit?
Eout = E x (area of the Earth)
E = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
Eout
How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).
Einre
How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).
Ein = So x (area of circle)
Einre
So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.
Remember…
How much solar energy reaches the Earth?
We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).
Ein = So x (area of circle)
Ein = So (W/m2) x re2 (m2)
Einre
How much solar energy reaches the Earth?
Ein = So re2
BUT THIS IS NOT QUITE CORRECT!
**Some energy is reflected away**
Einre
How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
Ein = So re2 (1-A)
Einre
How much solar energy reaches the Earth?
Albedo (A) = % energy reflected awayA= 0.31 today
Ein = So re2 (1-A)
Ein = So re2 (0.69)
reEin
T4 = So(1-A) 4
If we know So and A, we can calculate the temperature of the Earth. We call this the expected temperature (Texp). It is the temperature we would expect if Earth behaves like a blackbody.
This calculation can be done for any planet, provided we know its solar constant and albedo.
T4 = So(1-A) 4
For Earth:
So = 1370 W/m2
A = 0.31 = 5.67 x 10-8
T4 = (1370 W/m2)(1-0.31) 4 (5.67 x 10-8 W/m2K4)
T4 = So(1-A) 4
For Earth:
So = 1370 W/m2
A = 0.31 = 5.67 x 10-8
T4 = (1370 W/m2)(1-0.31) 4 (5.67 x 10-8 W/m2K4)
T4 = 4.23 x 109 (K4)
T = 254 K
Is the Earth’s surface really -19 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15 oC
Calculate the average temperatures of Mars and Venus applying the Simple Global Temperature Model:
Planet Venus Earth MarsDistance from Sun(106 km
108 150 218Solar Constant (W/m2 )
2620 1370 589
Albedo (%) 76 31 25Atmospheric Pressure (atm)
90 1 0.006
Effective Temperature(K)Surface Temperature(K)
Planet Venus Earth MarsDistance from Sun(106 km
108 150 218Solar Constant (W/m2 )
2620 1370 589
Albedo (%) 76 31 25Atmospheric Pressure (atm)
90 1 0.006
Effective Temperature(K)
229 254 210
Surface Temperature(K)
750 288 218
Is the Earth’s surface really -19 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15 oC
The difference between observed and expected temperatures (T):
T = Tobs - Texp
T = 15 - (-19)
T = + 34 oC
T = + 34 oC
In other words, the Earth is 34 oC warmer than expected based on black body calculations and the known input of solar energy.