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

Transfer of Heat Transfer of Heat 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 molecular nergy of thermal motion is transferred by molecular collision along the objectcollision along the object”.

Physics Department

Helwan University

Physics Department

Helwan University

Linear Flow of HeatLinear Flow of Heat

Quantity of heatgained or lost by a substance

Q Time (t) Area Area ((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

• 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 A A && 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

• H = Q/t = - K AA . dT/dr = - K (4(4 r r22)). dT/dr H . dr/ rr22 = - 44 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 of HeatRadial Flow of Heat

Q

Physics Department

Helwan University

Physics Department

Helwan University

• Integrating,

H[(1/r1) - (1/r2)] = - 4 K (T2 – T1)

= 4 K (T1 – T2)

2

1

2

1

r

r

T

T2

dTK4r

drH

2

1

2

1

TT

r

rTK4

r1

H

)TT(rr4)rr(H

K2121

12

Physics Department

Helwan University

Physics Department

Helwan University

Radial Flow of HeatRadial Flow of Heat

Cylindrical Flow of HeatCylindrical Flow of Heat

• The quantity of heat flowing per second across the element is given by:

H = Q/t = -KAA .dT/dr but AA= 2 r L

H = -2 K r L (dT/dr) H . dr/r = -2 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

• Integrating,

2

1

2

1

T

T

r

r

dTLK2r

drH

2

1

2

1

TT

rr TLK2rlnH

]TT[LK2]rr

[ln

]TT[LK2)rlnr(lnH

211

2

1212

)TT(L2rr

lnHK

21

1

2

Physics Department

Helwan University

Physics Department

Helwan University

Cylindrical Flow of HeatCylindrical Flow of Heat

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) & = 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

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.

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 A T4 where: 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

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.

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Helwan University

Physics Department

Helwan University

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 perfect polished surface, emissivity e = 0.

Physics Department

Helwan University

Physics Department

Helwan University

• 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

• 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

• 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 → e1 = a1 & e2 = a2 → emissivity & absorptivity of same surface are equal.

Physics Department

Helwan University

Physics Department

Helwan University

Prevost's Theory of ExchangesPrevost's Theory of Exchanges

EB1EB2

Ritchie’s experiment

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

Natural Radiation

• There is almost no overlap: # solar spectrum (0.25 3.0 m) with # thermal radiation (2 nm 100 m)• 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.

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

VISVISNNIRIRIRIR

VISVISNNIRIRIRIR

Cooling Cooling LoadLoad

Heating Heating LoadLoad

GlassGlass

Physics Department

Helwan University

Physics Department

Helwan University

VISVIS++NNIRIR

Electromagnetic SpectrumElectromagnetic Spectrum

NNIRIR++IRIR

VISVIS

IRIR

ThermalThermal

ThermalThermal

Heat Mirror: PrinciplesColdHot

HotCold

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.

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

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.