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Heat Transfer by RadiationInstitute of Fluid Dynamics & ThermodynamicsOtto von Guericke-University MagdeburgGermany 39106Dr. Ing. Ashok Kumar NallathambiPavan Kumar Penumakala M.TechProf. Eckehard Specht1

References: Heat and mass Transfer by Incropera, CengelOVGU, Magdeburg2

Radiation

Radiation does not require medium(solid or fluid) Radiation can happen two bodies separated by the medium colder than both the bodies Radiation is a volumetric phenomenon. However, the radiation emitted from interior molecules is strongly absorbed by adjoining molecules. Therefore, it is approximated as surface phenomenon.

All substances with temperature above absolute zero level continuously emit radiation due to vibrational and rotational motions of molecules, atoms, and electrons of a substance. Waves and Particles Theory Ref: Incropera, CengelOVGU, Magdeburg3

Transport of Radiative Energy Particle Theory / Quantum Theory [Max Planck, 1900] : propagation of collection of particles known as photons or quanta

Plancks constant

Wave Theory [Maxwell, 1864] : propagation of electromagnetic waves with a speed of light

Combining both naturesRef: Incropera, Cengel

OVGU, Magdeburg4

Spectrum of Electromagnetic Radiation

Ref: Incropera, CengelShort Waves Cosmic rays, Gamma rays, X-rays, UV Long Waves micro-waves, radio waves

Visible light 0.38 0.78 m

Thermal radiation little UV, visible and Infrared raysOVGU, Magdeburg5

Thermal Radiation

Spectral distribution - Magnitude of radiation varies with wavelength Directional distribution - Magnitude of radiation varies with directionBoth magnitude of radiation at any wavelength and spectral distribution vary with nature and temperature of emitting surfaceRef: Incropera, CengelOVGU, Magdeburg6

Radiation IntensityRef: Incropera, Cengel

Plane Angle

Solid Angle

steradianradianOVGU, Magdeburg7

Radiation IntensityRef: Incropera, Cengel

Solid Angle

Solid AngleSolid angle associated with entire hemisphere

Full sphereOVGU, Magdeburg8

Radiation IntensityRef: Incropera, Cengel

OVGU, Magdeburg9

Ref: Incropera, Cengel

Radiation IntensityOVGU, Magdeburg10

Radiation IntensityRef: Incropera, Cengel

Total Emissive Power

For diffuse emitter ( a surface for which intensity of emitted radiation is independent of direction)

Spectral Emissive PowerTotal Emissive PowersteradianOVGU, Magdeburg11

Irradiation (incident radiation)Ref: Incropera, Cengel

For diffuse irradiationSpectral IrradiationTotal IrradiationOVGU, Magdeburg12

Radiosity (total radiation leaving the surface = emitted + reflected)Ref: Incropera, Cengel

Diffuse reflector & diffuse emitterSpectral RadiosityTotal Radiosity

OVGU, Magdeburg13

Blackbody RadiationA blackbody absorbs all incident radiation, regardless of wavelength and directionFor a prescribed temperature and wavelength, no surface can emit more energy than a blackbodyAlthough the radiation emitted by a blackbody is a function of wavelength and temperature, it is independent of direction. Therefore, the blackbody is a diffuse emitter.

Complete absorptionDiffuse emission fromaperatureDiffuse radiation of inner surfacesBlackbody Cavity

Blackbody radiation exists within the cavity irrespective of whether cavity surface is highly reflecting or absorbing.Ref: IncroperaOVGU, Magdeburg14

Planck DistributionRef: Incropera

Planck, 1959

Universal Planck ConstantBoltzmann ConstantSpeed of light

Blackbody is a diffuse emitter. Therefore,Blackbody spectral intensity

BLACKBODYOVGU, Magdeburg15

Planck DistributionRef: Incropera

Wiens DisplacementLaw

BLACKBODYOVGU, Magdeburg16

Stefan-Boltzmann LawRef: Incropera

Plancks Blackbody emissive power distribution,

Total emissive power

Stefan-Boltzmann Law

Stefan-Boltzmann constantTotal Emissive power of a blackbody is only a function of Temperature.

Total emissive intensityBLACKBODYOVGU, Magdeburg17

Emission from Real SurfacesRef: Incropera

OVGU, Magdeburg18

Ref: Incropera

Spectral, directional emissivityTotal, directional emissivity

Spectral, hemispherical emissivityEmission from Real Surfaces

Total, hemispherical emissivity

OVGU, Magdeburg19

Ref: IncroperaEmission from Real Surfaces

Directional distributions of total, directional emissivity

Absorption, Reflection and Transmission

Opaque : Transmission is zero , absorption and reflection are Surface phenomenon For a Radiation Balance on the medium,The surface absorption and reflcetion are responsible for the perception of color

Due to selective reflection and absorption of the Irradiation that is incedent from the sun or source of light.

Red : Preferentially absorbs blue,green and yellow and reflects red.

Green : Preferentially absorbs blue, red and yellow and reflects green. color is due to emission at a high temperature (incandescent )

At Room Temperature, emission falls in IR region

Balance of Radiation :

Dividing each term of the relation by G

For Opaque surface

Absorptivity :The Absorptivity is a property that determines the fraction of irradiation absorbed by a surface.

Spectral, directional absorptivitySpectral, hemispherical absorptivityTotal, hemispherical emissivity

The dependence of Temperature is small for most spectral radiative properties.

Reflectivity : The Reflectivity is a property that determines the fraction of irradiation reflected by a surface.

Spectral, directional Reflectivity

Spectral, hemispherical absorptivity

Total, hemispherical emissivity

Diffusive and Specular ReflectionTransmissivity : Spectral, hemispherical Transmissivity

Total, hemispherical Transmissivity

Special Considerations: They are always positive and lies between 0 and 1

Non Reflecting surface

Perfect Reflector, does not absorb or transmit

Opaque surface

Perfect Transparent

Non absorbing surface (also called white surface)

Perfectley absorbing surface (called black if it is dissusive) Kirchhoff's Law :

Radiative Exchange in an isothermal enclosureA large isothermal enclosure of surface Temperature Ts forms a black body cavity.Regardless of its orientation, the irradiation expereinced by any body in the cavity is diffusive and equal to emission from a black body at Ts

Under steday state , Thermal equilibrium must exit between the bodies and enclosure.

Applying energy balance to a control surface on body1,

Gray Surface:

The spectral, directional emissivity and absorptivity are equal

The first condition corresponds to the major assumption required for the Kirchhoffs Law

Radiation Exchange Between surfaces : This Exchange strongly depends on the surface geometries and orientations.The surfaces are seperated by non participating medium , which has no effect on radiationShape Factor / View Factor

The View Factor Fij is defined as the fraction of radiation leaving the surface i that is intercepted by surface j

View Factor : Fij is The fraction of radiation that leaves Ai and is intercepted by Aj

Similarly, Fji is The fraction of radiation that leaves Aj and is intercepted by Ai

Reciprocity Relation :

Shape Factor Relations:

Reciprocity Relation :

Symmetry Rule :

Summation Rule :

Superposition Rule :

Compute the Shape factors between different surfaces of the configurations shown in the below figure12

123

12

35Radiation Exchange between surfaces in an enclosure :

The surfaces - Opaque Diffusive Gray

Net Radiation Exchange at a surface:

Net Radiation Exchange between surfaces:

The total rate at which radiation reaches surface i from all surfaces inluding i is Driving potential Surface radiative resistance

From the reciprocity relation,

And substituting in,From summation rule,

Each component may be represented by a network element for which,

is driving potential and

is a space or geometrical resistance.

At node i,Blackbody Radiation Exchange : Large surroundings , Real surfaces, that are coated with high emissivity finishes, may be treated as hypothetical black surfaces. The absorptivity of a black surface is unity , no reflcetion and radiosity is solely of emitted energy.

Reduces to Example

Solution

Two surface enclosure: The simple enclosure of two surfaces that exchange radiation only with each other.

The net work reprsentation of enclosure is

Example 1.Emissivities of two large parallel plates maintained at 800 C and 300 C are 0.3 and 0.5 respectively. Find the net radiant heat exchange per square meter for these plates. 2. A pipe carrying steam having an outside diameter of 20cm runs in a large room and is exposed to air at a temperature of 30 C. The pipe surface temperature is 400 C. Calculate the loss of heat to surroundings per metre length of pipe due to thermal radiation. The emissivity of pipe surface is 0.8 what would be the loss of heat due to radiation if the pipe is enclosed in a 40cm diameter brick conduit of emissivity 0.91?Radiation combined with Convection:

An approximate method for calculating the total heat transfer by both convection and radiation is by the linear super position of heat fluxes due to these modes.

hc is the convective heat transfer coefficient and hr is the radiative heat transfer coefficient