Radiation Heat Transfer

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Radiation Heat Transfer

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

Select a Suitable Geometry to meet the
industrial needs...
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How to Make Things to Look Beautiful
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How to Make Things to Look Beautiful
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Radiosity

• The radiosity of a surface is the rate at which
  radiation energy leaves a surface per unit area.

Spectral Radiosity
Total Radiosity
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Radiative Heat Transfer
Consider the heat transfer between two black
surfaces, as shown in Figure. What is the rate
of heat transfer into Surface B? To find this,
we will first look at the emission from A to B.
Surface A emits radiation as described in
This radiation is emitted in all directions, and
only a fraction of it will actually strike
Surface B. This fraction is called the shape
factor, F.
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The amount of radiation striking Surface B is
therefore
All the incident radiation will contribute to
heating of Surface B
Above equation is the amount of radiation gained
by Surface B from Surface A. To find the net
heat transfer rate at B, we must now subtract the
amount of radiation emitted by B
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The net radiative heat transfer (gain) rate at
Surface B is
Similarly, the net radiative heat transfer (loss)
rate at Surface A is
What is the relation between qA and qB ?
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Shape Factors

• Shape factor, F, is a geometrical factor which is
  determined by the shapes and relative locations
  of two surfaces.
• Figure illustrates this for a simple case of
  cylindrical source and planar surface.
• Both the cylinder and the plate are infinite in
  length.
• In this case, it is easy to see that the shape
  factor is reduced as the distance between the
  source and plane increases.
• The shape factor for this simple geometry is
  simply the cone angle (?) divided by 2p

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Geometrical Concepts in Radiation Heat Transfer
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Human Shape Factors
Wherever artificial climates are created for
human occupation, the aim of the design is that
individuals experience thermal comfort in the
environment. Among other factors thermal comfort
depends on mean radiant temperature.
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Flame to Furnace Wall Shape Factors
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Radiative Heat Exchange between Two Differential
Area Elements

• The elements dAi and dAj are isothermal at
  temperatures Ti and Tj respectively.
• The normals of these elements are at angles qi
  and qj respectively to their common normal.
• The total energy per unit time leaving dAi and
  incident upon dAj is

dwi is the solid angle subtended by dAj when
viewed from dAi.
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The monochromatic energy per unit time leaving
dAi and incident on dAj is
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• The total energy per unit time leaving dAi and
  incident upon dAj is

The monochromatic energy per unit time leaving
dAi and incident on dAj is
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The monochromatic energy per unit time leaving A
real body element dAi and incident on dAj is
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The fraction of energy leaving a black surface
element dAi that arrive at black body dAj is
defined as the Geometric configuration Factor
dFi?j.
For a diffusive surface
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Configuration Factor for rate of heat Exchange
from dAi to dAj
Configuration Factor for Energy Exchange from dAj
to dAi
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Reciprocity of Differential-elemental
Configuration Factors
Consider the products of
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Net Rate of Heat Exchange between Two
differential Black Elements
The net energy per unit time transferred from
black element dAi to dAj along emissive path r
is then the difference of i to j and j to i.
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Ib of a black element
Finally the net rate of heat transfer from dAi to
dAj is
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Configuration Factor between a Differential
Element and a Finite Area
dAi
Aj, Tj
qj
qj
qi
dAi, Ti
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Integrating over Aj to obtain
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Configuration Factor for Two Finite Areas
dAi
Aj, Tj
qj
qi
Ai, Ti
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Radiation Exchange between Two Finite Areas
The net rate of radiative heat exchange between
Ai and Aj
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Using reciprocity theorem
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Configuration Factor Relation for An Enclosure
Radiosity of a black surface i
For each surface, i
The summation rule !
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• The summation rule follows from the conservation
  requirement that al radiation leaving the surface
  I must be intercepted by the enclosures surfaces.
• The term Fii appearing in this summation
  represents the fraction of the radiation that
  leaves surface i and is directly intercept by i.

• If the surface is concave, it sees itself and
  Fii is non zero.
• If the surface is convex or plane, Fii 0.
• To calculate radiation exchange in an enclosure
  of N surfaces, a total of N2 view factors is
  needed.

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Real Opaque Surfaces

• Kichoffs Law substances that are poor emitters
  are also poor absorbers for any given wavelength
• At thermal equilibrium
• Emissivity of surface (e) Absorptivity(a)

• Transmissivity of solid surfaces 0
• Emissivity is the only significant parameter
• Emissivities vary from 0.1 (polished surfaces) to
  0.95 (blackboard)

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Complication

• In practice, we cannot just consider the
  emissivity or absorptivity of surfaces in
  isolation
• Radiation bounces backwards and forwards between
  surfaces
• Use concept of radiosity (J) emissive power
  for real surface, allowing for emissivity,
  reflected radiation, etc

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Radiosity of Real Opaque Surface

• Consider an opaque surface.
• If the incident energy flux is G, a part of it is
  absorbed and the rest of it is reflected.
• The surface also emits an energy flux of E.

Rate of Energy leaving a surface J A
Rate of Energy incident on this surface GA
Net rate of energy leaving the surface A(J-G)
Rate of heat transfer from a surface by
radiation Q A(J-G)
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Enclosure of Real Surfaces
T1,A1
T2,A1
TN,AN
J1
JN
J2
. . .
.
riGi
Ei
Gi
.
Ji
.
.
.
.
.
Ti,Ai
For Every ith surface
The net rate of heat transfer by radiation
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For any real surface
For an opaque surface
If the entire enclosure is at Thermal
Equilibrium, From Kirchoffs law
Substituting all above
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Surface Resistance of A Real Surface
Real Surface Resistance
Ebi
Black body
Ji
Actual Surface
qi
.
Ebi Ji Driving Potential
surface radiative resistance
.
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Radiation Exchange between Real Surfaces

• To solve net rate of Radiation from a surface,
  the radiosity Ji must be known.
• It is necessary to consider radiation exchange
  between the surfaces of encclosure.
• The irradiation of surface i can be evaluated
  from the radiosities of all the other surfaces in
  the enclosure.
• From the definition of view factor The total
  rate at which radiation reaches surface i from
  all surfaces including i, is

From reciprocity relation
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This result equates the net rate of radiation
transfer from surface i, Qi to the sum of
components Qij related to radiative exchange with
the other surfaces. Each component may be
represented by a network element for which
(Ji-Jj) is driving potential and (AiFij)-1 is a
space or geometrical resistance.
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Geometrical (View Factor) Resistance
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Relevance?

• Heat-transfer coefficients
• view factors (can surfaces see each other?
  Radiation is line of sight )
• Emissivities (can surface radiate easily? Shiny
  surfaces cannot)

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Basic Concepts of Network Analysis

• Analogies with electrical circuit analysis
• Blackbody emissive power voltage
• Resistance (Real Geometric) resistance
• Heat-transfer rate current

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Resistance Network for ith surface interaction in
an Enclosure
Qi