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Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Jan 19, 2016

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Louisa Bruce

solar energy

energy radiated

incoming energy

properties of energy

total radiant energy

wavelength of emitted

flux of energy wm2t

hotter objects

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Page 1: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance

Page 2: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

HEAT TRANSFER PROCESSES

• Conductive heat transfer

• Convective heat transfer

• Radiation heat transfer

Page 3: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

visiblelight

0.7 to 0.4 m

Page 4: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelight

Page 5: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelightinfrared

Page 6: Energy Balance. 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

Page 7: Energy Balance. 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

HighEnergy

LowEnergy

Page 8: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Blackbody Radiation

Blackbody radiation—radiation emitted by a body that emits (or absorbs) equally well at all wavelengths

Page 9: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Basic Laws of Radiation

1) All objects emit radiant energy.

Page 10: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Basic Laws of Radiation

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects.

Page 11: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

Page 12: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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)

Page 13: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

Page 14: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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)

Page 15: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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)

Page 16: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

We can use these equations to calculate properties of energy radiating from the Sun and the Earth.

6,000 K 300 K

Page 17: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Solar Radiation and Earth’s Energy Balance

Page 18: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Planetary Energy Balance

• We can use the concepts learned so far to calculate the radiation balance of the Earth

Page 19: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Some Basic Information:

Area of a circle = r2

Area of a sphere = 4 r2

Page 20: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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).

Page 21: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:

Incoming energy = outgoing energy

Ein = Eout

Ein

Eout

Page 22: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much solar energy reaches the Earth?

Page 23: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much solar energy reaches the Earth?

As energy moves away from the sun, it is spread over a greater and greater area.

Page 24: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 25: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

So = L / area of sphere

Page 26: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 27: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

Page 28: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Each planet has its own solar constant…

Page 29: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 30: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 31: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much energy does the Earth emit?

300 K

Page 32: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much energy does the Earth emit?

Eout = E x (area of the Earth)

Page 33: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much energy does the Earth emit?

Eout = E x (area of the Earth)

E = T4

Area = 4 re2

Page 34: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much energy does the Earth emit?

Eout = E x (area of the Earth)

E = T4

Area = 4 re2

Eout = ( T4) x (4 re2)

Page 35: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

(m)

1000 100 10 1 0.1 0.01

Earth Sun

Hotter objects emit more energy than colder objects

Page 36: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

(m)

1000 100 10 1 0.1 0.01

Earth Sun

Hotter objects emit more energy than colder objects

E = T4

Page 37: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

(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

Page 38: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much energy does the Earth emit?

Eout = E x (area of the Earth)

Eout

Page 39: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 40: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much solar energy reaches the Earth?

Ein

Page 41: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 42: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 43: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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…

Page 44: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 45: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much solar energy reaches the Earth?

Ein = So re2

BUT THIS IS NOT QUITE CORRECT!

**Some energy is reflected away**

Einre

Page 46: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

How much solar energy reaches the Earth?

Albedo (A) = % energy reflected away

Ein = So re2 (1-A)

Einre

Page 47: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 48: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:

Incoming energy = outgoing energy

Ein = Eout

Eout

Ein

Page 49: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

Ein = So re2 (1-A)

Eout

Ein

Page 50: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

Ein = So re2 (1-A)

Eout = T4(4 re2)

Eout

Ein

Page 51: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

So re2 (1-A) = T4 (4 re

2)

Eout

Ein

Page 52: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

So re2 (1-A) = T4 (4 re

2)

Eout

Ein

Page 53: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

So (1-A) = T4 (4)

Eout

Ein

Page 54: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Energy Balance:Ein = Eout

So (1-A) = T4 (4)

T4 = So(1-A) 4

Eout

Ein

Page 55: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

Page 56: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

T4 = So(1-A) 4

For Earth:

So = 1370 W/m2

A = 0.31 = 5.67 x 10-8 W/m2K4

Page 57: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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)

Page 58: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 59: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Expected Temperature:

Texp = 254 K

(oC) = (K) - 273

Page 60: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Expected Temperature:

Texp = 254 K

(oC) = (K) - 273

So….

Texp = (254 - 273) = -19 oC

Page 61: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Is the Earth’s surface really -19 oC?

Page 62: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

Is the Earth’s surface really -19 oC?

NO. The actual temperature is warmer!

The observed temperature (Tobs) is 15 oC

Page 63: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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)

Page 64: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 65: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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

Page 66: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

Page 67: Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer.

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.

This extra warmth is what we call the GREENHOUSE EFFECT.


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