1. Heat TransferHeat Transfer
Heat is transferred from one place or body to another by
means of one or more of three mechanisms:
1) Conduction (heat transfers but material not),
2) Convection (heat transfer by material transfer),
3) Radiation (no material).
• In practical situation any two or all three may be
operating at the same time.
Physics Department
Helwan University
Physics Department
Helwan University
2. Transfer ofTransfer of
HeatHeat
by Conductionby Conduction• Heat conduction in materials
= result of molecular collisions.
• As one end of the object is heated, molecules move faster
and faster.
• As molecules collide with their slower-moving neighbors,
some of their energy to these molecules whose
speeds increase.
• “EEnergy of thermal motion is transferred by molecularnergy of thermal motion is transferred by molecular
collision along the objectcollision along the object”.
Physics Department
Helwan University
Physics Department
Helwan University
3. Linear Flow ofLinear Flow of
HeatHeat
Quantity of heat
gained or lost
by a substance
Q ∝ Time (t)
∝ AreaArea ((AA))
∝ Temperature difference (T2-T1)
∝ 1/1/ LengthLength (d)d)
Physics Department
Helwan University
Physics Department
Helwan University
AA
dd
• Then:
Q ∝ t AA (T2-T1) / d
Q = K t AA (T2-T1) / d
* k is proportionality constant :
= “thermal conductivity”
= characteristic of the material.
T2 T1
4. • Rate of heat flow = Quantity of heat flow per unit time:
H = Q/t = K AA [[(T2
-T1
)/ d]]
= (T2
-T1
) / (d / k AA)
= - K AA . dT/dr
* temperature gradienttemperature gradient.
** thermal resistance.
• Rate of heat flow is:
1- directly proportional to cross-sectional area AA && to
“temperature gradient” [[(T2
-T1
)/ d]]
2- inversely proportional to thermal resistance (d / k AA).
Physics Department
Helwan University
Physics Department
Helwan University
Linear Flow of HeatLinear Flow of Heat
AA
dd
HH T1T2
5. • H = Q/t = - K AA . dT/dr
= - K (4(4ππ rr22
)). dT/dr
H . dr/ rr22
= - 44ππ K. dT
•Heat is conducted through the specimen
from the inner to the outer shell.
•Specimen is contained between two thin
spherical shells of radii r1
and r2
.
•Heating element at the center of shells.
Radial Flow ofRadial Flow of
HeatHeat
Q
Physics Department
Helwan University
Physics Department
Helwan University
6. • Integrating,
H[(1/r1
) - (1/r2
)] = - 4π K (T2
– T1
)
= 4π K (T1
– T2
)
∫ ∫π−=
2
1
2
1
r
r
T
T
2
dTK4
r
dr
H
[ ] 2
1
2
1
T
T
r
r
TK4
r
1
H π−=
−
)TT(rr4
)rr(H
K
2121
12
−π
−
=
Physics Department
Helwan University
Physics Department
Helwan University
Radial Flow of HeatRadial Flow of Heat
7. Cylindrical Flow ofCylindrical Flow of
HeatHeat
• The quantity of heat flowing per second
across the element is given by:
H = Q/t = -KAA .dT/dr
but AA= 2 π rL
H = -2 π K r L (dT/dr)
H . dr/r = -2 π K L dT
•Cylindrical tube of length L, inner
radius r1
and outer radius r2
.
L
Q Q
•Heat is conducted radially
across the wall.
Physics Department
Helwan University
Physics Department
Helwan University
8. • Integrating,
∫∫ π−=
2
1
2
1
T
T
r
r
dTLK2
r
dr
H
[ ] [ ] 2
1
2
1
T
T
r
r
TLK2rlnH π−=
]TT[LK2]
r
r
[ln
]TT[LK2)rlnr(lnH
21
1
2
1212
−π=
−π−=−
)TT(L2
r
r
lnH
K
21
1
2
−π
=
Physics Department
Helwan University
Physics Department
Helwan University
Cylindrical Flow of HeatCylindrical Flow of Heat
9. Transfer of Heat by ConvectionTransfer of Heat by Convection
• Convection is process whereby: “heat is
transferred by the mass movement of
molecules from one place to another”.
• Convection involves movement of
molecules over large distances.
• “Natural convection” occurs as well and
one familiar example is that hot air rises.
• V/T = constant (at constant pressure) &
ρ = m/V,
• If temperature of given mass of air
increases, volume must also increases by
same factor and then its density decreases
making it buoyant.
Physics Department
Helwan University
Physics Department
Helwan University
Heat source
H
H
H
C C
10. Breezes Over Land MassesBreezes Over Land Masses
• During day, air above water
will be cooler than that over
land →low pressure area over
land breezes blowing
from water to land.
• During night water cools off
more slowly than land → air
above water is slightly
warmer than over land →
creates low pressure area over
water breezes will blow
from land to water .
Physics Department
Helwan University
Physics Department
Helwan University
• Water has larger heat capacity than land → holds heat better &
takes longer time to change its temperature.
11. Transfer of Heat by RadiationTransfer of Heat by Radiation
• Convection and conduction require the presence of matter.
• Radiation consists essentially of “electromagnetic waves”
transferee to over empty (or nearly empty) space.
• Infrared (IR) radiation is mainly responsible for heating earth.
• Rate at which object radiates energy is given by Stefan-Boltzmann
equation:
∆Q/∆t = e σ A T4
where: σ is a universal constant called the Stefan-Boltzmann constant.
T is absolute temperature in Kelven.
e is emissivity which is characteristic of material.
• If object surrounded by environment at temperature T2 →
Physics Department
Helwan University
Physics Department
Helwan University
12. Emissivity and AbsorptivityEmissivity and Absorptivity
• Definitions:
1. “Emissive power” (E) of a surface is: “energy emitted
per second per square centimeter of the surface”.
1.1. “Dark and rough” surfaces correspond to high
emissive powers.
1.2. “Light and polished” surfaces correspond to low
emissive powers.
1.3. Surface corresponds to maximum emissive power
at same conditions, is known as perfect black body.
1.4. Perfect polish surface is one whose emissive power
is zero.
Physics Department
Helwan University
Physics Department
Helwan University
13. Emissivity and AbsorptivityEmissivity and Absorptivity
• Definitions:
2. “Emissivity” "e" of surface is: “ratio between the
energy emitted from the surface es to that emitted from a
perfect black body eb at the same conditions”:
e = es / eb
2.1. Take time interval of one second & area of one cm2
of either surface: e = Es / Eb
where Es is emissive power of surface & Eb is emissive
power of perfect black body.
2.2. For perfect black body, emissivity e = 1, while for
Physics Department
Helwan University
Physics Department
Helwan University
14. • Definitions:
3. “Absorptivity” (a) of a surface is: “ratio between the
energy absorbed by the surface as and that incident ei on
it in the same time interval”:
a = as / ei
4. Kirchoft's Law (1859): “At any temperature the ratio of the
emissive power and the absorptive power of all bodies is constant
and is equal to the emissive power of a perfectly black body”.
Thus,
e1 / a1 = e2 / a2 = constant = Eb = 1
→ General rule that emissivity & absorptivity of same surface have
equal values.
Physics Department
Helwan University
Physics Department
Helwan University
Emissivity and AbsorptivityEmissivity and Absorptivity
15. • Several bodies of different materials: Each emits amount
of energy & at same time receives some of energy emitted
by other bodies.
• After considerable time interval steady state is reached
[each body emits radiation at exactly same rate at which
absorbs it] → good emitter should also be good absorber
& bad emitter should also be bad absorber.
• Emissivity & Absorptivity of same surface are equal.
• “Temperature of each body arrives to constant steady” →
“emissivity and absorptivity of same surface are equal”
→ Prevost's theory of exchanges.
Physics Department
Helwan University
Physics Department
Helwan University
Prevost's Theory of ExchangesPrevost's Theory of Exchanges
16. • Dark surface of cube B: Thermal radiation emitted / second, EB1 = e1 Eb
• Polished surface of cube B: Thermal radiation emitted / second, EB2 = e2 Eb.
• Polished surface of the cube C: Thermal radiation incident, EB1 = e1 Eb,
Thermal radiation absorbed / second, ac = EB2 a2= (e1 Eb) a2,
• Dark surface of cube A: Thermal radiation absorbed / second, aA = EB2 a1= (e2 Eb) a1,
• Experiment shows that cubes A & C absorb equal thermal radiation, therefore,
aC = aA
e1 Eb a2 = e2 Eb a1→ e1 / a1= e2 / a2
• For perfect black body e = a = 1 → e1 / a1 = e2 / a2 = ……= e/a = 1 →
Physics Department
Helwan University
Physics Department
Helwan University
Prevost's Theory of ExchangesPrevost's Theory of Exchanges
EB1EB2
Ritchie’s experiment
17. Solar EnergySolar Energy
• Sun is largest source of renewable energy & this energy is abundantly available
in all parts of earth.
• Sun is in one of the best alternatives to non-renewable sources of energy.
• Biggest share of solar energy reaching earth is absorbed at surface.
• Amount that actually reaches surface varies according to weather conditions,
amount of particulate matter & water vapor in air, time of day, season of year,
earth’s distance from sun.
Physics Department
Helwan University
Physics Department
Helwan University
18. Natural Radiation
• There is almost no overlap:
# solar spectrum (0.25 < λ < 3.0 µm) with
# thermal radiation (2 nm < λ < 100 µm)
• Optical properties change with Wavelength.
Wavelength selection is possible.
Physics Department
Helwan University
Physics Department
Helwan University
Coatings which have
spectral selective
properties.
Electromagnetic Spectral region:
1) Visible (VIS) 0.3-0.77 μm,
2) near–infrared (NIR), 0.77–2.0μm
3) infrared (IR), 2.0 – 100 μm.
19. Spectral (Solar) Selective Coatings
They are classified to two categories:
1. Transmission–Reflection type:
a) high transmission to VIS/solar spectrum and good
reflection to thermal radiation (IR) Heat MirrorsHeat Mirrors.
b) good reflection to solar spectrum and high transmission
to thermal radiation CCold Mirrorsold Mirrors.
2. Absorption–Reflection type:
high absorption to solar spectrum and good reflection to
heat waves (IR) Black absorbersBlack absorbers.
Physics Department
Helwan University
Physics Department
Helwan University
21. Heat Mirror
Electromagnetic spectrum has three regions :
a) Visible (VIS) 0.3-0.77 μm,
b) near – infrared (NIR), 0.77 – 2.0 μm
c) infrared (IR), 2.0 – 100 μm.
• Heat mirror is defined as a wavelength selective
coating exhibiting high transmittance to VIS and/or
Solar radiation and good reflectance to IR radiation.
22. Solar EnergySolar Energy
• Solar PondsSolar Ponds: One way to tap solar energy is through use of solar ponds =
large-scale energy collectors with integral heat storage for supplying thermal
energy.
• Principle: as water or air is heated → become lighter & rise upward.
• Ordinary pond: sun’s rays heat water & heated water within pond rises → top →
loses heat into atmosphere → pond water remains at the atmospheric temperature.
• Water is very poor conductor of heat → if this circulation can be stopped → heat
can be trapped in bottom of lake.
• Solar pond: Natural tendency of hot water to rise to surface is restricted by
dissolving salt in bottom layer of pond making it too heavy to rise.
Physics Department
Helwan University
Physics Department
Helwan University
3) Bottom storage zone or Lower Convective Zone
zone is very hot, 70°– 85° C, & is very salty.
1) Top zone is surface zone or Upper Convective Zone
at atmospheric temperature & has little salt content.
2) important gradient zone or Non-Convective Zone
23. Solar EnergySolar Energy
• Solar PondsSolar Ponds: One way to tap solar energy is through use of solar ponds =
large-scale energy collectors with integral heat storage for thermal energy.
• Solar pond collector has major advantages:
1) The heat storage is massive, so energy can be extracted day and night → source of
'base load' solar power → no batteries or other storage needed.
2) Solar ponds can have very large heat collection area at low cost.
3) Major production potential is during peak electrical power demand in mid
summer.
Physics Department
Helwan University
Physics Department
Helwan University
• Heat is extracted by heat exchanger at
bottom of pond.
• Heat energy can power engine,
provide space heating or produce
electricity via low-pressure steam
turbine.
• Heated saltwater can be pumped to
location where heat is needed.
• After heat is used, water can be
returned to solar pond & heated again.
