fundamentals of thermal radiation - eth z · building physics: theory and applications |jonas...

| | Building physics: Theory and Applications

Fundamentals of thermal radiation

Dr. Jonas Allegrini

24.10.2018 Jonas Allegrini 1

Master in Integrated Building Systems: Building Physics

2

INTRODUCTION


What are the modes of heat transport

1. Conduction 2. Convection 3. Radiation

24.10.2018 3

This lecture…

Jonas Allegrini


Effects on the atmospheric conditions (daylight, outside temperatures, …)

Effect on the thermal behaviour of the building: Absorption of thermal radiation by materials (building envelope,

environment,…) Transmittance of solar radiation through glazing

Effects on humans Effects thermal comfort Glare

24.10.2018 4

Why is radiation important for buildings?

Source: http://www6.knmi.nl/research/CKO/doc/EMIC/ReferenceRun/ttr.html

Jonas Allegrini

| | Building physics: Theory and Applications 24.10.2018 5

5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies 9. Atmospheric and solar radiation 10. Solar gains through transparent components 11. Solar radiation on an opaque wall

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation

Jonas Allegrini


Radiation doesn’t require a medium Energy transfer by radiation is fastest (speed of light) Radiation can occur in liquids, gases, and solids

24.10.2018 7

5.1. Introduction radiation

Hot object in a vacuum chamber loses heat by radiation only

Vacuum chamber

Hot object

Jonas Allegrini


?

Radiation can occur between two hotter bodies even if low air temperatures are in between

24.10.2018 8

5.1. Introduction radiation

Radiation reaches earth surfaces after going through low temperatures

Jonas Allegrini


• Radiation is heat transfer by electromagnetic waves. • Thermal radiation is electromagnetic waves (including light) produced by objects

because of their temperature

10-2 < λ < 0.38 µm UV radiation (UV) 0.38 < λ < 0.76 µm visible light (L) 0.76 < λ < 103 µm IR radiation (IR)

5.2. Thermal radiation

Electromagnetic spectrum

24.10.2018 9 Jonas Allegrini


Energy spectrum of radiation


• Electromagnetic waves have same general features, but differ significantly in their behavior



Energy spectrum of radiation


Thermal radiation 0.1 to 100 µm



• Light is the visible portion of electromagnetic spectrum (0.4 and 0.76 µm) • Half of solar radiation (0.3 and 3 µm) is light





Long wave & Short wave radiation

• All surfaces with a temperature > 0K radiate heat

• Resultant radiative heat transfer is

only possible between surfaces at different temperature



Exchanging heat by thermal radiation is a continous phenomenon All bodies in the environment emit and receive thermal radiation Thermal radiation takes several forms Short wave Long wave

24.10.2018 14

Summary - Thermal radiation in the environment

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation

Jonas Allegrini


5.3. Blackbody radiation

• A body at a temperature above zero Kelvin emits radiation • Amount of radiation energy emitted from a surface depends on:

• material of the body, • condition of surface, and • surface temperature

• A black body is a perfect emitter which serves as a standard • Is defined as a perfect emitter and absorber

of radiation • A blackbody emits radiation energy

uniformly in all directions per unit area normal to direction of emission

Jonas Allegrini



The radiation energy emitted by a blackbody is expressed by

𝑀𝑀𝑏𝑏 𝑇𝑇 = 𝜎𝜎𝑇𝑇4 (𝑊𝑊/𝑚𝑚2)

𝜎𝜎 = 5.670 ∙ 10−8 (𝑊𝑊/𝑚𝑚2) Black body constant (Stefan-Boltzmann constant)

Emittance

𝑀𝑀𝑏𝑏 𝑇𝑇 = 5.67 ∙ (𝑇𝑇

100)4

Jonas Allegrini



Spectral blackbody emissive power

Example of spectralemissive power of incandescent light bulb

Jonas Allegrini




Mbλ

(W/m

²nm

)

Max Planck (1858-1947)

Jonas Allegrini




Mbλ

(W/m

²nm

)

Planck’s law

Mc h

expch

k T-

b

2 -5

λ

π λ

λ

=

2

1

c = speed of light (m/s) h = Planck constant (6.6 10-34 J.s) k = Boltzmann constant (1.3810-23 J/K)

W/m.Hz.rad

Wien’s law: λMT = 2898 (λM in µm)

Jonas Allegrini


If the sun was a perfect black body, what would be its temperature?

How much energy is radiated from a black body at room temperature (20°C)?

How much energy is absorbed by a blackbody at room temperature?

24.10.2018 21

Questions

Jonas Allegrini


If the sun was a perfect black body, what would be its temperature?

How much energy is radiated from a black body at room temperature (20°C)?

How much energy is absorbed by a blackbody at room temperature?

24.10.2018 22

Questions

Jonas Allegrini

𝑀𝑀𝑏𝑏 𝑇𝑇 = 𝜎𝜎𝑇𝑇4 𝑀𝑀𝑏𝑏 𝑇𝑇 = 5.67 ∙ (𝑇𝑇

100)4 M

c h

expch

k T-

b

2 -5

λ

π λ

λ

=

2

1

c = speed of light (m/s) h = Planck constant (6.6 10-34 J.s) k = Boltzmann constant (1.3810-23 J/K)

W/m.Hz.rad

λMT = 2898 (λM in µm)


If the sun was a perfect black body, what would be its temperature? 5700 K

How much energy is radiated from a black body at room temperature? 418 W/m2

How much energy is absorbed by a blackbody at room temperature? 418 W/m2

24.10.2018 23

Questions

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions

Jonas Allegrini


Radiation intensity Radiation is emitted by all parts of a plane surface in all directions into the hemisphere above the surface The quantity that describes the magnitude of radiation emitted (or incident) in a specific direction in space is the radiation intensity IR

24.10.2018 25

5.4. Definitions

dAi

dAj Aj

φi

φj

Jonas Allegrini


5.4. Definitions

Plane angle: Solid angle:

24.10.2018 26

α r

l

[rad] rl

=α

[rad] 22 ππα ==rr

Arc length for full circle:

t)(Steradian [sr] 2rdS

=ω

Solid angle for a sphere:

[sr] 442

2

ππω ==rr

r

dS

Jonas Allegrini


Radiation intensity IR

The quantity that describes the magnitude of radiation emitted (or incident) in a specific direction in space is the radiation intensity IR

24.10.2018 27

5.4. Definitions

dAi

dωi

iiiR d

dqddA

dIωω

=Φ

=2 Radiant heat

flow rate

Solid angle

Jonas Allegrini


Incident radiation All surfaces emit radiation, but they also receive radiation emitted or reflected by other surfaces. The radiation flux incident on a surface from all directions is called irradiation E.

24.10.2018 28

5.4. Definitions

dA

E

Jonas Allegrini


Radiosity Surfaces emit radiation as well as reflecting it. This quantity is called the radiosity. The calculation of radiation heat transfer between surfaces involves the total radiation energy streaming away from a surface with no regard for its origin

24.10.2018 29

5.4. Definitions

Radiosity

Emission

Reflected portion of irradiation

Irradiation

Jonas Allegrini


Summary

24.10.2018 30

5.4. Definitions

Quantity Definition and units

Radiant heat QR The amount of heat, which is emitted or received as electromagnetic waves. Unit: Joule (J)

Radiant heat flow ΦR The amount of radiant heat per unit of time. Unit: Joule per second J/s= Watt (W)

Radiant heat flow rate qR The radiant heat flow per unit of surface Unit: Watt per m2 (W/m2)

Radiation intensity IR The radiant energy, which is emitted in a specific direction Unit: Watt per m2 . rad

Emittance M Emitted radiant heat flow rate

Irradiation E Incoming radiant heat flow rate

Radiosity M’ Emitted and reflected radiation rate

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties

Jonas Allegrini


Four containers were filled with warm water. Which container would have the warmest water after ten minutes (material properies are the same for the inside and outside surfaces)?

5.5. Radiative properties

Shiny metal Dull metal Dull black Shiny black

• The shiny metal container would be the warmest after ten minutes because its shiny surface reflects heat radiation back into the container so less is lost.

• The dull black container would be the coolest because it is the best at emitting heat radiation.

Jonas Allegrini


Absorption Absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. Absorption in the material only in a very thin layer d = 10-6 m (metal) d = 10-4 m (others)

24.10.2018 33


Jonas Allegrini


Absorption The absorption coefficient α Is the ratio of total-absorbed to the incident radiation

24.10.2018 34


E⋅= αRaq

E

qRa

Jonas Allegrini


Reflection The reflection coefficient ρ also called the albedo when considering surfaces in the environment Is the ratio of total-reflected to the incident radiation

24.10.2018 35


E⋅= ρRrq

E qRr

Jonas Allegrini



High albedo materials

Why are houses often painted white in hot countries?

Jonas Allegrini



The albedo, or reflection coefficient of different surface materials in the built environment

Jonas Allegrini


Transmission The transmission coefficient τ Is the ratio of total-transmitted to the incident radiation

24.10.2018 38


E⋅= τRtq

E

qRt

Jonas Allegrini



Absorptivity, Reflectivity, Transmissivity

Absorption factor: Reflection factor: Transmission factor:

RiRa qq=α

RiRr qq=ρ

RiRt qq=τ

α ρ τ+ + = 1 Conservation of energy (temperature is constant)

τ

α ρ

Jonas Allegrini

Riq

Rrq

Rtq

Raq


Emittance M The emission coefficient ε is the ratio of total-emitted radiation of a grey body to the emitted radiation of a black body

24.10.2018 40


bM⋅= εM E M

Jonas Allegrini


Emissivity Represents the ratio of the radiation emitted by the surface at a given temperature, to the radiation emitted by a blackbody at the same temperature. Real materials are colored bodies -> for simplification they are assumed to be grey

24.10.2018 41


bMM

=ε

Grey surface, ε=constant

Blackbody, ε=1

Real surface, ελ

T = const. 0 λ

ελ

1

ε

Jonas Allegrini


Classification of radiating bodies Black body α=1, ρ=0, τ=0 White body α=0, ρ=1, τ=0 Grey body α=constant <1

independent of temperature/wavelength or incidence angle

Colored body: α=dependent on tempearture/wavelength or incidence angle

24.10.2018 42


Grey surface, ε=constant

Blackbody, ε=1

Real surface, ελ

T = const. 0 λ

ελ

1

ε

Jonas Allegrini


Kirchhoff ’s law The total hemispherical emissivity of a surface at temperature T is equal to its total hemispherical absorptivity for radiation coming from a blackbody at the same temperature. The emissivity of a surface at a specified wavelength, direction, and temperature is always equal to its absorptivity at the same wavelength, direction and temperature.

24.10.2018 43


)()( TT λλ αε =

Jonas Allegrini


Characteristics of grey bodies Difference between the radiative properties of grey bodies between shortwave and longwave radiation:

24.10.2018 44


Shortwave radiation: solar radiation

1=++ SSS τραLongwave radiation: ambient radiation

1=++ LLL τρα

Jonas Allegrini


Four containers are close to a heat source. Which container would have the warmest water after ten minutes (material properies are the same for the inside and outside surfaces)?


Shiny metal Dull metal Dull black Shiny black

• The black container would be the warmest, since it absorbs more energy. • The shiny metal would be the coolest, due to low absorption.

Jonas Allegrini



Example materials in the built environment Long wave radiation and undercooling




Example materials in the built environment Absorption & Emission

Jonas Allegrini



Example materials in the built environment Metal foil

Jonas Allegrini


The Greenhouse Effect Incoming energy is short wave radiation Outgoing radiation is long wave (infrared) radiation

24.10.2018 50


Spectral transmissivity of low-iron glass at room temperature for different thicknesses

Jonas Allegrini



Materials

Materials εL (300K) αS (6000K)

Polished metal <0.1 0.3 Concrete, mortar >0.85 0.6-0.65 Brick 0.9 0.4-0.7 Wood 0.86 0.35 Glass 0.94 <0.15 Bituminous membranes 0.92 0.9 White finishes 0.92 0.35 Black finishes 0.95 0.92

Jonas Allegrini


Real surfaces are simplified to grey bodies Conservation of energy – absorption, reflection, and transmission There are differences between the radiative properties of grey bodies in shortwave

and longwave radiation

24.10.2018 52

Summary of radiative properties

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer View factors Reciprocity The summation rule The superposition rule

Jonas Allegrini


The view factor Radiation heat exchange between surfaces depends on the orientation of surfaces relative to each other. This dependence on orientation is accounted for by the view factor. Fij= the fraction of the radiation leaving surface i that strikes surface j directly

5.6. Radiation heat transfer

dAi

φi

φj

dAj

dωi

r Φ𝑏𝑏𝑏𝑏→𝑗𝑗 = 𝐴𝐴𝑏𝑏𝐹𝐹𝑏𝑏𝑗𝑗𝑀𝑀𝑏𝑏𝑏𝑏

Emittance W/m2

View factor Surface m2

Radiant heat flow

Jonas Allegrini


Reciprocity The reciprocity relation for view factors allows one to calculate F21 if one already knows F12, using the areas of the two surfaces A1 and A2

24.10.2018 55


𝐴𝐴1𝐹𝐹12 = 𝐴𝐴2𝐹𝐹21

Jonas Allegrini


Surrounding surfaces When a surface A1 is totally surround by the surface A2, the view factor F12=1 Using reciprocity then we find:

24.10.2018 56


𝐹𝐹21 =𝐴𝐴1𝐴𝐴2

Jonas Allegrini


An example A small spherical body of 0.1 m radius is located in a cubical enclosure with a side length of 4 m, calculate the view (angle) factors between the enclosure and the spherical body. 24.10.2018 57


Jonas Allegrini


An example Since all radiation from the small body reaches the enclosure surface then Using the reciprocity relationship

24.10.2018 58


𝐹𝐹𝑏𝑏−𝑒𝑒 = 1

𝐴𝐴𝑏𝑏𝐹𝐹𝑏𝑏−𝑒𝑒 = 𝐴𝐴𝑒𝑒𝐹𝐹𝑒𝑒−𝑏𝑏

𝐹𝐹𝑒𝑒−𝑏𝑏 = 𝐴𝐴𝑏𝑏𝐹𝐹𝑏𝑏−𝑒𝑒𝐴𝐴𝑒𝑒

= 4𝜋𝜋 .1 216∗4∗4

= 0.00131

Jonas Allegrini


Self viewing surfaces For a convex surface, no radiation can leave the surface and then hit it later, because radiation travels in straight lines. Hence, for convex surfaces, F11=0 For concave surfaces, this doesn‘t apply, and so for concave surfaces F11>0


Jonas Allegrini


Summation rule The entire radiation leaving any surface of an enclosure is intercepted by the surfaces of the enclosure. The sum of the view factors from surface i of an enclosure to all surfaces of the enclosure, including itself, must equal unity.


11

=∑= →

n

j jiF

Jonas Allegrini


Superposition rule If view factors for given geometries are not available, the sum or difference of some geometries with known view factor from a surface i to a surface j is equal to the sum of the view factors from surface i to the parts of surface j.


∑=

=n

kikij FF

1

A1 Ak

Ai

An

Aj

Jonas Allegrini


from Cengel textbook

Sichtbarkeitsfaktoraus-drücke für einige unendlich lange (2-D) Geometrien


View factor relations


| | Building physics: Theory and Applications from Cengel textbook

View factor between two aligned parallel rectangles of equal size.




from Cengel textbook

View factor between two perpendicular rectangles with a common edge.



| | Building physics: Theory and Applications [Ali-Toudert, 2005]

Sky view factor




5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies

Jonas Allegrini


5.7. Radiative exchange between black bodies

112121 bb MFA=Φ →

Black body 1=α radiative exchange

A1 A2

221212 bb MFA=Φ →

212112 bb MFA=Φ →

( )21121

122112

bb

bbb

MMFA −=Φ−Φ=Φ →→

Jonas Allegrini


Mb1 − Mb2 = CbT1

100

4

−T2

100

4

[ ]2121 TTFCMM Tbbb −=−

FT =4

104 Tm12

T1

100

2

+T2

100

2

FT ≈4

100Tm

100

3

Tm =T1 + T2

2

Temperature factor (FT)


𝑀𝑀𝑏𝑏 𝑇𝑇 = 5.67 ∙ (𝑇𝑇

100)4




FT ≈4

100Tm

100

3

Tm =T1 + T2

2( )2111212 θθ −=Φ AFFC Tbb

Black body constant = 5.67

W/m2K4 Temperature

factor

View factor Surface m2

A1 A2 Temperatures

in Kelvin

Jonas Allegrini


View factors of different configurations including rules and simplifications Black body radiation exchange

24.10.2018 70

Summary

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies

Jonas Allegrini


E ρ E

M

Radiosity M’

1

5.8. Radiative exchange between grey bodies

Reflected radiation

Emitted radiation

111'1 EMM ρ+=

1111'1 EMM b ρε +=

Radiosity of one grey body:

Emitted radiant heat flow rate:

11' EMqR −= (W/m2)




( )21112 θθ −=Φ AFFC rTbb

Black body constant = 5.67

W/m2K4 Surface m2

Temperature factor K3

Radiative factor

A1 A2

Radiative exchange between two grey bodies

Jonas Allegrini



2

1

2

2

121

1 11

AA

F

Fr

ερ

ερ ++

=

Reflection coefficient

Ratio of surfaces

Emission coefficient

View factor

A1 A2

Radiative exchange between two grey bodies

Jonas Allegrini



2

1

2

2

121

1 11

AA

F

Fr

ερ

ερ ++

=

Two parallel surfaces A1=A2, F12=1

2

2

1

1 1

1

ερ

ερ ++

=rF

1111

21

−+=

εε

rF

2

2

1

1 1111

εε

εε −++−

=rF

ερ −= 1

Jonas Allegrini


5.8. Radiative exchange between grey bodies Two parallel surfaces A1=A2

1111

21

−+=

εε

rF

11121

−+=

εε

Tbr

FCh

)( 21112 θθ −=Φ AFFC rTb

)( 21112 θθ −=Φ Ahr

Heat transfer coefficient for radiation W/m2

Jonas Allegrini


5.8. Radiative exchange between grey bodies Surrounded surface (surrounding is infinite: e.g. sky and wall)

1ε=rF

Tbr FCh 1ε=

0/ 21 ≈AAA1

A2

)( 21112 θθ −=Φ Ahr

Heat transfer coefficient for radiation W/m2

Jonas Allegrini



Example: Two very large parallel plates are maintaned at uniform temperatures T1=800K and T2= 500K and have emissivities ε1= 0.2 and ε2= 0.7. Determine the net rate of radiation heat transfer between the two surfaces per unit surface area of the plates

Jonas Allegrini



Example: Two very large parallel plates are maintaned at uniform temperatures T1=800K and T2= 500K and have emissivities ε1= 0.2 and ε2= 0.7. Determine the net rate of radiation heat transfer between the two surfaces per unit surface area of the plates

( )2112 θθ −=Φ= rTb FFCA

q111

1

21

−+=

εε

rF FT ≈4

100Tm

100

3

( )500800...67.512 −= rT FFq184.0

17.0

12.0

11 =

−+=rF 985.10=tF2/343812 mWqb ≈

Jonas Allegrini


5.8. Radiative exchange between grey bodies Application example: Average surface film coefficients for heat transfer – Inside environment

0=++ radLconvcond qqqθsi θj θi

θsk

Jonas Allegrini



)( siicici hq θθ −=θsi

Convective surface film coefficient

)(,sii

sijjcici hh

θθθθ

−

−=

θj θi Convective

heat flow rate

5.3=cih W/m2K

2.1=cih W/m2K

vertical surfaces

horizontal surfaces

Application example: Average surface film coefficients for heat transfer – Inside environment

Jonas Allegrini



24.10.2018 82


)( siririri hq θθ −=θsi

Radiant surface film coefficient

∑

∑=

k

skkri A

A θθθj θi Radiant heat

flow rate

θsk LiTbri FCh ε=

95.0≈TF9.08.0 ≤≤ Liε

5.4=rih W/m2K

Jonas Allegrini



θsi θj θi

θsk

8≈ih W/m2K vertical surfaces

rci hhh +=

5.3=cih W/m2K vertical surfaces

5.4=rih W/m2K

Outside environment

2523−≈ih19=cih4=rih

W/m2K


Jonas Allegrini


5.8. Radiative exchange between grey bodies Values surface coefficients W/(m2K) from SIA



Radiative exchange between grey bodies Simplification methods (radiative factor, temperature factor) Application example – all modes of heat transfer together

24.10.2018 85

Summary

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies 9. Atmospheric and solar radiation

Jonas Allegrini


5.9. Atmospheric and solar radiation

The solar energy reaching the earths atmosphere is called the total solar irradiance (solar constant) whose value is 1367 W/m2

http://www.greenrhinoenergy.com/solar/radiation/extraterrestrial.php

1367 W/m2

Jonas Allegrini


The sun is the main source of energy (exceeding geothermal energy by a order of 4 magnitudes).

24.10.2018 88

Solar radiation

Source: Solar radiation – radiative transfer; Institute for atmospheric and climate science, ETH Zurich

Jonas Allegrini


Source: Klimagerechtes Bauen




The total solar irradiation on a surface with angle b, consists of a direct and diffusive part. We consider the diffusive radiation of the sky to be isotropic.

Direct radiation

Diffuse radiation from the sky

Diffuse radiation from the ground





The total irradiation depends highly on weather conditions especially on the cloudiness



5.9. Atmospheric and solar radiation The total irradiated solar energy depends on the time of the year

(summer vs winter), the orientation and the inclination of the surface. Example of a South oriented surface

Low sun altitude during winter

21th december 21th december 21th june



5.9. Atmospheric and solar radiation The total irradiated solar energy depends on the time of the

year (summer vs winter), the orientation and the inclination of the surface.

Example of vertical surfaces with different orientation




South Facing Facades For a predominately South facing facade, effective solar shading can be achieved using a fixed horizontal solar shading system. During the day in both summer and spring/autumn, a fixed horizontal system projecting out from the window can be designed to shade the building during office hours. In the winter such a device cannot stop direct rays of the sun penetrating the building since the sun is much lower. However the heat gain and solar glare is greatly reduced in winter and therefore this may not considered to be a major problem.

summer

winter

Spring / autumn



east west


East or West Facing Facades With a predominantly East or West facing facade, a fixed system will not perform well throughout the whole day as the altitude of the sun is much lower. Sunlight will pass directly under most horizontal shading systems as shown in the illustration below. To overcome this problem, effective solar shading can be achieved using a movable solar shading system



5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies 9. Atmospheric and solar radiation 10.Solar gains through transparent components

Jonas Allegrini


97

STEsingle glazing

Transparent component

irradiation EsT : the total solar

irradiation including direct and diffuse parts on the transparent component (W/m2)

5.10. Solar gains through transparent components



STE

STS Eρ

One part of the irradiation is reflected with ρS the reflection coefficient

one part is transmitted, with τS the transmission coefficient

one part is absorbed, with αS the absorption coefficient

reflection


irradiation

STS Eαabsorption

STS Eτtransmission

single glazing




STS Eα

STE Due to absorption the

glass pane heats up and releases heat by convection and radiation to the environment according to the heat transfer coefficient hi for inside and he for outside


absorption

irradiation

single glazing




STE The total heat admission through

glass is the sum of the radiation transmitted through

glass the inward convective /radiative

flow from the heated glass due to absorbed solar radiation

the heat flow due to outdoor-indoor temperature differences


irradiation

STS Eτtransmission

STS Eαabsorption

θi θe

single glazing




STE


irradiation

STS Eτtransmission

STS Eαabsorption

θi θe

Solar heat gain coefficient or G-value is the fraction of incident solar

radiation admitted through a window, both directly transmitted and absorbed and subsequently released inward. SHGC is expressed as a number between 0 and 1. The lower a window's solar heat gain coefficient, the less solar heat it transmits.


single glazing



STE

STS Eτ


irradiation

ie

SiS hh

hg+

+=ατ

Overall solar heat gain coeffcient for single glazing or ‘g’ value

transmission

STS Eαabsorption




STE

STS Eτ


irradiation

transmission

STS Eαabsorption

5.10. Solar gains through transparent components 1. Direct solar gains

STSsd Eq τ=

2. Indirect solar gains

STie

Sisi E

hhhq

+=

α

STs Egq =

Total solar gain



STE

STS Eτ


irradiation

Transmission coefficient for double glazing

transmission

21

21

1 ρρτττ

−=S

1 2 5.10. Solar gains through transparent components


| | Building physics: Theory and Applications 24.10.2018 105 Jonas Allegrini


Floated glass

Low E glass

τS ρS αS εL

0.826 0.075 0.099 0.837

0.583 0.302 0.115 0.09

λ (W/mK)

glass

0.8

Glass



| | Building physics: Theory and Applications Wellenlänge

Lich

tdur

chlä

ssig

keit



U = 5.76 W/m2K

g = 0.826+0.026 = 0.85

d = 4 mm

hi = 8, he = 23 W/m²K

ei hd

h

U 111

++=

λλ= 0.8 W/mK


Example 1:


ie

SiS hh

hg+

+=ατ


U = 5.76 W/m2K

g = 0.826+0.026 = 0.85

he = 100 W/m²K

Inside surface of reflective glass

hi = hci + hri = ?

Outside surface of reflective glass

he = hce + hre = ?

Example 1: hi = 8, he = 23 W/m²K

λ= 0.8 W/mK Very windy weather:

Use a reflective foil:



U = 5.76 W/m2K

g = 0.826+0.026 = 0.85

he = 100 W/m²K U=7.1 W/m²K

Inside surface of reflective glass

hi = hci + hri = 3.5 + 4.5 U=2.99 W/m²K

Outside surface of reflective glass

he = hce + hre = 19 + 4 U=5.5 W/m²K

Example 1: hi = 8, he = 23 W/m²K

λ= 0.8 W/mK Very windy weather:

Use a reflective foil:



1R

=λg Nu

d+

Cb FT

1ε1

+1ε2

−1U =

11hi

+ R +1he

U-value

Nu = 1.2

FT = 0.9

Floated glass

Low E glass

τS ρS αS εL

0.826 0.075 0.099 0.837

0.583 0.302 0.115 0.09

λ (W/mK) 0.025 0.017 0.009

air argon krypton glass

0.8

Double glass



U = 5.76 W/m2K

g = 0.85

d = 4 mm

U = 2.9 W/m2K

g = 0.69 + 0.06 = 0.75

15 mm



5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies 9. Atmospheric and solar radiation 10. Solar gains through transparent components 11.Solar radiation on an opaque wall

Jonas Allegrini


5.11. Solar radiation on an opaque wall

Jonas Allegrini

skθeθ

seθ

STS Eα

We assume all the environment on the air temperature θe

The sky has a

temperature θsk The sun irradiates with αS·EST

The surface wall

temperature equals θse



Jonas Allegrini

Shortwave radiation:

Longwave radiation

to environment and sky

Convection:

STSS Eq α=

( )seecec hq θθ −=

skθeθ

seθ

STS Eα



Jonas Allegrini

The temperature of the sky is normally lower than the air temperature, which is referred to as undercooling

)1(21 cesk −−= θθ

where c is the cloudiness c= 0 : clear sky c= 0.87 : cloudy

skθeθ

seθ

STS Eα



Jonas Allegrini

We replace the environment with solar radiation, longwave radiation and convection

by an equivalent environment with only convective heat transport with the environment on an equivalent temperature

STS Eα

skθ

eθseθ

*eθ

seθ

)( *seeeLcs hqqq θθ −=++

equivalent temperature



Jonas Allegrini

2cos1 ω+

=sskF

e

TssksskLSTSee h

cFFE )1(120* −−+=

εαθθ

3

1002

1004

+

≈ssk

Tssk

TT

F

Absorption coefficient and solar irradiation

Temperature factor for sky and surface

Sky view factor

Longwave emission

coefficient of the environment SHOULd BE SURFACE

Temperatures in Kelvin !

cloudiness

Heat transfer coefficient

outside

Inclination of the wall, 0 for a roof, 90° for

a wall

Solar radiation Longwave radiation

Convection



Example 1:

Jonas Allegrini

A bituminous flat roof, with a U value of 0.2 W/m2K is exposed to an environment with air temperature of 5°C during night. There are no clouds. The absorption coefficient of the roof is 0.6. The emission coefficient of the environment is 0.9. The heat transfer coefficient is 23 W/m2K . The temperature factor is 0.77.

Determine the surface temperature of the roof



Example 1:

Jonas Allegrini

K m W h c E C C K m W U C

e L ST S

e sk e i

² / 23 0 9 . 0 0 6 . 0 21 5 ² / 2 . 0 20

= = = = = ° − = ° = = ° =

ε α θ θ θ θ

77.0=TsskF °= 0ω

A bituminous flat roof, with a U value of 0.2 W/m2K is exposed to an environment with air temperature of 5°C during night. There are no clouds. The absorption coefficient of the roof is 0.6. The emission coefficient of the environment is 0.9. The heat transfer coefficient is 23 W/m2K . The temperature factor is 0.77.

The data:



Example 2:

Jonas Allegrini

A bituminous flat roof, with a U value of 0.2 W/m2K is exposed to an environment with air temperature of 20°C and a solar irradiation of 800 W/m2. There are clouds. The absorption coefficient of the roof is 0.8. The emission coefficient of the environment is 0.9. The heat transfer coefficient is 23 W/m2K.The temperature factor is 0.77.

Determine the surface temperature of the roof



Example 2:

Jonas Allegrini

KmWhcmWECCKmWUC

eLSTS

eskei

²/2385.09.0²/8008.02120²/2.020=====

°−=°==°=εα

θθθθ

77.0=TsskF °= 0ω

A bituminous flat roof, with a U value of 0.2 W/m2K is exposed to an environment with air temperature of 20°C and a solar irradiation of 800 W/m2. There are clouds. The absorption coefficient of the roof is 0.8. The emission coefficient of the environment is 0.9. The heat transfer coefficient is 23 W/m2K.The temperature factor is 0.77.

The data:



Jonas Allegrini

The equivalent temperature during night is 1.4°C due to the cold sky.

The surface temperature is 1.5°C and lower than the air temperature 5°C, thus undercooling occurs.

The equivalent temperature during daytime is 47.3°C due to the solar radiation.

The surface temperature is 47.0°C and much higher than the air temperature 20°C.

CC

s

e

°=°=

5.14.1*

θθ

CC

s

e

°=°=

0.473.47*

θθ


sun is the main source of energy It is essential to take the position of the sun into account, while planning a building Selection of glazing influences the comfort inside the building and the amount of heat

transmitted to inside Solar radiation and the sky influences the outside surfaces of buildings

24.10.2018 127

Summary

Jonas Allegrini


5. Radiation 1. Introduction to radiation 2. Thermal radiation 3. Blackbody radiation 4. Definitions 5. Radiative properties 6. Radiation heat transfer 7. Radiative exchange between black bodies 8. Radiative exchange between grey bodies 9. Atmospheric and solar radiation 10. Solar gains through transparent components 11. Solar radiation on an opaque wall

Jonas Allegrini

fundamentals of thermal radiation - eth z · building physics: theory and applications |jonas...

Documents