Radiation as a Mode of Heat Transfer in Textiles and Clothing

Dr. Kausik Bal

KHT, TUL

Radiation is the energy emitted by matter in the form of electro-magnetic waves.

Thermal radiation is energy emitted by matter that is at a finite temperature above the

absolute zero. Unlike conduction or convection, it does not require any medium of transfer.

What is thermal radiation?

Radiation in Nature: The Sun

Coronal Mass Ejection as viewed by the Solar Dynamics Observatory on June 7,

2011. Credit: NASA/SDO

Distance to Earth: 149,600,000 km (light travels from the Sun to Earth in about 8 minutes and 19 seconds.)

Surface temperature: 5,778 K

Mass: 1.98930 kg

Radius: 695,500 km

Radiation in Nature: Heating of Earth Surface

Radiation in Nature: Heating of Earth Surface

Radiation in Nature: Heating of Earth Surface

Heating of Earth Surface: Global Warming

http://earthobservatory.nasa.gov/Features/GlobalWarming/page2.php

Solar Energy Spectrum

Solar Constant = 1.36 kW/m2 (amount of incoming solar radiation per unit area on a plane perpendicular

to the rays at a distance of 1 astronomical unit [AU]).

The speed of radiation

Electromagnetic waves are characterized by their frequency (ν) [Hz] and wavelength

(λ) [m] where

λν =𝑐0𝑛

n = index of refraction of the medium

(n = 1 for air)

𝑐0 = 3 × 108 [ 𝑚 𝑠] is the speed of light (or the EM wave) in vacuum

Radiation at interface of two media

𝐴𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑣𝑖𝑡𝑦 = α

𝑅𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑖𝑡𝑦 = ρ

𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑣𝑖𝑡𝑦 = τ

α + ρ + τ = 1

For opaque surface, τ = 0 and hence, α + ρ = 1

Irradiation = Radiation flux

incident on a surface

(denoted by G)

SUN

Incident solar

radiation 100%

Reflected

radiation 8%

Transmitted

radiation 80%

Absorbed

radiation 12%

Outward transfer of

absorbed radiation 8%

Inward transfer of

absorbed radiation 4%

Blackbody

Blackbody is a hypothetical (or theoretical) surface which is a perfect absorber of

electromagnetic radiation, i.e., for the surface of blackbody, absorptivity α = 1.

A blackbody absorbs all the radiation that falls on it, converts it into internal energy

(heat), and then re-radiates this energy into the surroundings. The re-radiated thermal

energy, known as blackbody radiation, has a continuous spectrum governed solely by

the body's temperature.

Emissivity of a surface

(Total hemispherical) Emissivity ε 𝑇 =𝐸 𝑇

𝐸𝑏 𝑇is the ratio of the total radiation energy

emitted by the surface at a given temperature over all wavelengths in all directions to the

same emitted by a blackbody at the same temperature.

By definition, the emissivity of a blackbody is maximum and equals to unity.

All real surfaces have emissivity less than unity and are known as grey body. In the

extreme case, a white body is a hypothetical surface which does not absorb any

wavelength of radiation incident upon it at any direction.

Materials Temperature (°C) Typical emissivity

Commercial aluminium sheet 100 0.09

Pure highly polished gold 100 0.02

Brick (Building) 1000 0.45

Concrete 0 - 100 0.94

Smooth glass 0 - 200 0.95

Graphite 0 - 3600 0.7 – 0.8

Human skin 36 0.985

Wood (Oak, sanded) 93 0.82

Opaque plastics (any colour) 25 0.95

www.transmetra.ch

Stefan – Boltzmann Law

𝐸𝑏 𝑇 = σ𝑇4 [ 𝑊 𝑚2]

σ = 5.670 × 10−8 [ 𝑊 𝑚2𝐾4 ] is Stefan-Boltzmann constant

Example:

1. What is the radiation flux emitted by human skin? (Take ε = 0.95)

Solution: Skin temperature = 305 [K], hence, the radiative heat flux is:

𝐸 𝑇 = 305 = 0.95 × 5.670 × 10−8 × 3054 = 466 𝑊 𝑚2

2. Calculate the radiation flux from a wall with ε = 0.64 which is at 20°C.

Solution: Wall temperature = 293 [K], hence the radiative heat flux is:

𝐸 𝑇 = 293 = 0.5 × 5.670 × 10−8 × 2934 = 267 𝑊 𝑚2

The total radiation flux emitted by a blackbody at temperature T is a function of its

temperature only

Therefore, for a real surface (grey body with surface emissivity ε, the total radiation flux

emitted is E 𝑇 = εσ𝑇4.

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.

ε 𝑇 = α 𝑇

T

T(ε, α)

E(T)

Wien’s Displacement Law

λ𝑚𝑎𝑥𝑇 = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑊𝑖𝑒𝑛′𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 2897768.5 𝑛𝑚.𝐾

Planck’s Law of blackbody radiation

𝐸𝑏λ λ, 𝑇 =𝐶1

λ5 𝑒𝐶2λ𝑇 − 1

𝑊 𝑚2 . μ𝑚

𝐶1 = 2𝜋ℎ𝑐02= 3.742 × 108 𝑊μ𝑚4 𝑚2

𝐶2 = ℎ𝑐0𝑘 = 1.439 × 10

4 μ𝑚.𝐾

ℎ = 6.6256 × 10−34 𝐽. 𝑠

𝑘 = 1.3805 × 10−23 𝐽 𝐾

Planck’s constant

Boltzmann’s constant

Radiation Geometry I: Solid angle

2D 3D

𝑑ω =𝑑𝑆

𝑟2= sin 𝜃 𝑑𝜃𝑑φ

dS

φ

θr

Unit of solid angle: sr (steradian)

Intensity of radiation

The Radiation Intensity 𝐼𝑒 θ, φ is defined as the rate at which radiation energy 𝑑𝑄𝑒is emitted in the θ, φ direction per unit area normal to this direction and per unit

solid angle about this direction.

𝐼𝑒 𝜃, φ =𝑑𝑄𝑒

𝑑𝐴 cos𝜃 sin 𝜃𝑑𝜃𝑑φ 𝑊 𝑚2. 𝑠𝑟

Emissive power

The radiation flux for emitted radiation is the emissive power E, i.e., the rate at which

radiation energy is emitted per unit area of the emitting surface.

𝐸 =

ℎ𝑒𝑚𝑖𝑠𝑝ℎ𝑒𝑟𝑒

𝑑𝐸 = φ=0

2𝜋

𝜃=0

𝜋 2𝐼𝑒 𝜃, 𝜑 cos 𝜃 sin 𝜃 𝑑𝜃𝑑𝜑 𝑊 𝑚2

In case of diffusely emitting surface, 𝐸 = 𝜋𝐼𝑒 𝑊 𝑚2

Therefore, in case of a blackbody, the following is valid:

𝐼𝑏 𝑇 =𝐸𝑏 𝑇

𝜋=𝜎𝑇4

𝜋 𝑊 𝑚2 . 𝑠𝑟

Irradiation

The intensity of incident radiation 𝐼𝑖 𝜃, 𝜑 is defined as the rate at which radiation energy 𝑑𝐺 is

incident from the 𝜃, 𝜑 direction per unit area of the receiving surface normal to this direction and

per unit solid angle about this direction. When incident radiation is diffused, 𝐼𝑖 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.

𝐺 =

ℎ𝑒𝑚𝑖𝑠𝑝ℎ𝑒𝑟𝑒

𝑑𝐺 = φ=0

2𝜋

𝜃=0

𝜋 2𝐼𝑖 𝜃, 𝜑 cos 𝜃 sin 𝜃 𝑑𝜃𝑑𝜑 𝑊 𝑚2

The radiation flux incident on a surface from all directions is called irradiation (G).

For diffusely incident radiation, 𝐺 = 𝜋𝐼𝑒 𝑊 𝑚2

Radiosity

The rate at which radiation energy leaves a unit area of a surface in all directions is termed as

Radiosity (J).

𝐽 = φ=0

2𝜋

𝜃=0

𝜋 2𝐼𝑒+𝑟 𝜃, 𝜑 cos 𝜃 sin 𝜃 𝑑𝜃𝑑𝜑 𝑊 𝑚2

G

J

E

𝐺𝑟𝑒𝑓

Radiation Geometry II: View factor

Surface 3

Surface 2

Surface 1

Point source

𝑑𝜔 21

𝐴 1

𝐴 2𝑛 1

𝑛 2

𝑑𝐴 1

𝑑𝐴 2

𝜃 1

𝜃 2

𝑟

𝐹𝑖𝑗 =1

𝐴𝑖 𝐴𝑖

𝐴𝑗

cos 𝜃𝑖 cos 𝜃𝑗

𝜋𝑟2𝑑𝐴𝑖 𝑑𝐴𝑖

Exposure to radiation: Buildings and vehicles

Exposure to radiation: Outdoors

Radiation heat transfer

𝑇1 𝑇2

𝑄1

𝑄2

𝐴1 𝐴2 Net radiation transfer from surface 1 to 2 (both black) is:

𝑄12 = 𝐴1𝐹12𝜎 𝑇14 − 𝑇2

4 𝑊

Net radiation transfer from non-black surface i is:

𝑄𝑖 =𝐴𝑖𝜀𝑖1 − 𝜀𝑖

𝐸𝑏𝑖 − 𝐽𝑖

Electrical analogy: 𝑄𝑖 =𝐸𝑏𝑖−𝐽𝑖

𝑅𝑖where, 𝑅𝑖 =

1−𝜀𝑖

𝐴𝑖𝜀𝑖is Surface Resistance

When the two surfaces are diffuse, opaque and grey, net

radiation heat transfer from surface i to surface j:

𝑄𝑖𝑗 =𝐽𝑖−𝐽𝑗

𝑅𝑖𝑗where 𝑅𝑖𝑗 =

1

𝐴𝑖𝐹𝑖𝑗is Space Resistance

𝐸𝑏𝑖

𝑅𝑖

𝐽𝑖

𝑅𝑗

𝐽𝑗

𝐸𝑏𝑗𝑅𝑖𝑗

𝑄𝑖𝑗

http://www.kostic.niu.edu/352/_352-posted/Heat_4e_Chap13-Radiation_HT_lecture-PDF.pdf

Radiation shielding

Reflecting surfaces and coating

Surface Absorptivity

Aluminum, dull/rough polished 0.4 - 0.65

Aluminum. polished 0.1 - 0-40

Asbestos Cement, old 0.83

Black matt 0.95

Chromium plate 0.20

Iron, galvanised old 0.89 - 0.92

Grey paint 0.95

Light gren paint 0.95

Limestone 0.33 - 0.53

Red clay brick 0.94

White paint 0.89

For opaque materials, practically there is no transmission 𝜏 = 0 of radiation incident

on its surface. Hence, in such cases, ρ = 1 − 𝛼

Scattering

It is the process in which electromagnetic radiation or particles are deflected or

diffused. Such deflection can be due to the presence of other particle (s) or due to

localized non-uniformities of the medium.

Generally speaking, in case of waves (e.g. EM waves), the interaction with a matter

may cause two types of reflections from the surface where the wave is incident, one is

specular reflection and another is diffused reflection. The second type is a common

example of scattering.

In case of light (EM wave) scattering from a small particles, scattering is categorized in

three domains based on a dimensionless parameter.

Rayleigh Scattering: 𝛼 ≪ 1Mie Scattering: 𝛼 ≈ 1Geometric Scattering: 𝛼 ≫ 1

D Here, 𝛼 =𝜋𝐷

λ

Thermal radiation and textiles

Radiation, emitted by a hot surface may pass through the straight

pores (holes) across the textile.

Radiation, while passing through a textile, may be scattered by

the solid fibres or yarn.

Radiation incident on fibres, yarns or fabric surface may partly

be absorbed.

The fibres, yarns or fabric itself may emit radiation as a grey

body which depends on its temperature and emissivity.

Some fibres may allow the radiation to be transmitted through

them by refraction

In case of special fibres (e.g., metallic) or in case of textiles with

reflective coating (e.g. metallic coating), a significant amount of

incident radiation may be reflected back by specular reflection.

Research on the thermal radiation in textiles

Theoretical prediction of radiation through woven (and/or knitted fabric) in the

light of the fabric structure.

Theoretical prediction of radiation through nonwovens and random fibrous

assemblies.

Development of measurement techniques with fabrics in single and multiple

layers.

Development of measurement techniques with clothing.

Empirical and semi-empirical modelling of insulation from thermal radiation in

respect of protection from heat stress.

Empirical and semi-empirical modelling of radiation transfer and shielding in case

of UV protection.

Empirical analysis of structure – property relations to find total effective thermal

resistance.

Interaction of thermal radiation with fibres and yarns

Considering the typical diameter of textile fibres which has a range 10−6 [𝑚] - 10−4 [𝑚], and the wavelength of thermal radiation being between 10−7 [𝑚] and 10−3 [𝑚].

Therefore, fibres can cause scattering of thermal radiation and such scattering is

often considered to be in the Mie Scattering regime.

Yarns have typical diameters in the range 10−5 [𝑚] - 10−3 [𝑚], and therefore

such yarns as a solid material can also cause scattering of thermal radiation and

such scattering is also often considered to be in the Mie Scattering regime.

Some researchers have developed models of radiation

heat transfer in fibrous materials such as nonwovens

assuming that there is no scattering.

1. B. Farnworth, Mechanism of heat flow through clothing insulation, Textile Research Journal, Vol. 53 (12), 1983.

2. X. Wan; J. Fan, Heat transfer through fibrous assemblies incorporating reflective interlayers, International Journal of heat & Mass Transfer, Vol.

55, 2012.

3. D. Bhattacharjee & V. K. Kothari, A theoretical model to predict the thermal resistance of plain woven fabrics, Indian Journal of Fibre & Textile

research, Vol. 30 (3), 2005.

Modelling thermal radiation transfer through fabrics

In situation where the total heat transfer by conduction through fabric is much higher

than the heat transfer by radiation, the total thermal conductivity (or resistance) can be

considered as a linear sum of the individual components due to conduction and radiation.

λ𝑒𝑓𝑓 = λ𝑐𝑜𝑛𝑑 + λ𝑟𝑎𝑑

In such cases, it is assumed that it is possible to express the radiative heat flux in terms

of the temperature gradient at steady state which resembles Fourier’s law of thermal

conductivity.

𝑞𝑟𝑎𝑑 = λ𝑟𝑎𝑑 𝑇1 − 𝑇2

Where λ𝑟𝑎𝑑 = 4𝜎𝑇𝑚3 𝜀1

−1 + 𝜀2−1 − 1 and 𝑇𝑚 = 𝑇1 + 𝑇2 2

In case of nonwovens or similar low density fabrics, the radiation is given as

λ𝑟𝑎𝑑 =4ℎ𝜎𝑇𝑚

3

2𝜀 − 1

𝑒0.188ℎ ν−1 𝜇

𝑟√𝜋

ℎ = thickness

ν = (idealized) portion of fibres

oriented vertically

𝜇 = filling coefficient of the fabric

1. M. Boguslawska-Baczek; L. Hes, Determination of heat transfer by radiation in textile fabrics by means of method with known emissivity of

plates, Journal of Industrial Textiles, 2013.

Radiation heat transfer through clothing

• Clothing acts as a barrier to radiation heat transfer

between skin and environment.

• The insulation or protection provided by the clothing can

reduce heat stress and discomfort and can even be a life

saver when the clothed human is exposed to very intense

thermal radiation.

Intense solar radiation (dry deserts and snow-capped

mountain peaks)

Fire-fighting

Furnace-work

Space-travel

Very limited models exist for the radiation heat transfer through clothing, some empirical

and some semi-analytical and almost all approximate.

1. E. A. D. Hartog; G. Havenith, Analytical study of the heat loss attenuation by clothing on thermal manikins under radiative heat loads,

International Journal of occupational Safety and Ergonomics, Vol. 16 92), 2010.

Protection Vs. Comfort: Clothing for radiative environments

The requirements of protection and comfort are

often contradictory. It may be obvious to give

more weightage to protection in case of short

duration use, but comfort becomes more

important for longer duration of continuous use

and performance.

Thank you for your attention. For further discussion, please contact by email: kb.iitd@gmail.com