Heat Transfer:
Radiation Heat Transfer
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Objectives
Module 6: Radiation Heat Transfer
Page 2

Understand the basics of radiation heat transfer.

Examine surface properties linked to radiation heat exchange.

Study radiation exchange between two bodies.

Understand radiation heat transfer to ambient.

Identify the considerations for numerically solving radiation heat
transfer problems.

Study two examples:
 Radiation heat loss from a sphere inside an enclosure
 Radiation heat loss to the night sky
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Understanding Radiation Heat Transfer
Module 6: Radiation Heat Transfer
Page 3






Does not require the presence of matter.
All matter emits radiation.
Radiation may be considered propagation of
electromagnetic waves, photons or quanta.
Thermal radiation is that portion of electromagnetic radiation that is
generated by the thermal motion of charged particles in matter.
In contrast to conduction and convection, radiation reaches its
maximum efficiency in the absence of matter.
Radiation may be considered a surface phenomenon where the
wavelength of radiation can be given by:
  c/ f
© 2011 Autodesk
Where:
c = phase speed / Speed of light
f = frequency of the wave
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Understanding Radiation
Module 6: Radiation Heat Transfer
Page 4
Image: Courtesy NASA
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Surface Properties
Module 6: Radiation Heat Transfer
Page 5

Emissivity (Є) represents the efficiency of a body for emitting
radiation.

Absorptivity (α), Reflectivity (ρ) and Transmissivity (τ) respectively
represent the portion of radiation that is absorbed, reflected and
transmitted by an object.
α+ ρ+ t =1
Glass Cover
Glass cover: High transmissivity, low reflectivity
Absorber plate: high absorptivity, low reflectivity
Absorber Plate
Solar Collector
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Radiation Exchange between Two Bodies
Section 6 – Thermal Analysis
Module 6: Radiation Heat Transfer
Page 6

Net Radiation exchange between two bodies depends upon two
factors:
Temperatures of the bodies
 View Factor



The View Factor for simple shapes can be found analytically.
Complex shapes require numerical analysis.
In the example at right, body B sees all of body A,
but body A cannot see all of body B.
B
If body A is very close to body B:
The view factor from A to B is almost 1
 The view factor from B to A is <1

A
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Example of View Factors
Module 6: Radiation Heat Transfer
Page 7
figure 1
figure 2
View factors for perpendicular rectangles with a common edge (figure 1) and
coaxial parallel disks (figure2).
Images courtesy of Fundamentals of Heat Transfer, F.P. Incropera and D.P. DeWitt, John Wiley and
Sons.
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Radiation Heat Transfer to Ambient
Module 6: Radiation Heat Transfer
Page 8



Radiation heat loss to ambient (at absolute zero) occurs when a
second body is not present in proximity to the body radiating heat.
For example, the dark side of the earth radiating heat to space.
Radiation heat lost to ambient is easier to calculate as it is assumed
that heat is being lost through radiation but not being received.
Radiation heat lost to ambient can be calculated through the Stefan
Boltzman Law:

The heat “Q” transmitted from an area can be given as
Q  A(Ts  T
4
4
ambient
)
where
watt
  5.67 10 ( 2 4 )
m K
  emissivity
8
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Consideration for Numerically
Solving Radiation




Module 6: Radiation Heat Transfer
Page 9
For radiation problems using FEA, large numbers of mesh cells are
extremely difficult to solve and in some cases unfeasible.
The reason is cell to cell shape factor calculations that are memory
intensive and computationally expensive (see bottom figure).
Radiation surfaces, or those surfaces that take part in radiation heat
exchange, should be pre-defined by the user. Any surfaces that have
negligible parts to play can be ignored.
In general, larger nonlinear effects, like radiation, require smaller
relaxation parameters to avoid divergence.
C
To estimate the radiation heat loss from surface “A” in a 2D box,
view factors from A to B, A to C, and A to D would have to be
calculated. Similarly to find the net heat exchange, view factors for
all combinations e.g C-B, B-D would have to be calculated.
D
B
A
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Example: Radiation Heat Loss
from a Sphere Inside an Enclosure
Section 6 – Thermal Analysis
Module 6: Radiation Heat Transfer
Page 10
Spherical object made of
ceramic contained inside a
ceramic box.
Sphere is at 60ºC
Heat source face is 150ºC
Ambient is at -80ºC
A video presentation is available for this module that covers setting up,
solving and viewing results for this example.
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Additional Example:
Radiation Loss to Night Sky


Section 6 – Thermal Analysis
Module 6: Radiation Heat Transfer
Page 11
Radiation heat loss to the night sky on a clear night is much higher
than on cloudy nights.
Frost on a windshield indicates radiation heat loss to the night sky.
Q  A(T )
4
Notice that as radiation heat is being lost to
space at temperature of absolute zero, the above
expression is the simplified version of the one
observed earlier in the slide “Radiation Heat
Transfer to Ambient”.
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Summary
Module 6: Radiation Heat Transfer
Page 12

Radiation heat transfer is usually neglected at small temperatures;
however, it becomes the major mode of heat transfer at high
temperatures.

For instance, molten metal loses more heat through radiation than
convection and conduction combined.

Radiation heat exchange can be calculated between two bodies or
between the body and ambient.

The former is complex because of the involvement of view factors.

The view factors indicate how much two radiating bodies “see” one
another.
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community
Section 6 – Thermal Analysis
Summary
Module 6: Radiation Heat Transfer
Page 13

Thus the more surfaces participating in heat exchange, the more
complex the problem becomes as view factor calculations increase
the computation time.

The calculation of heat loss to ambient is relatively straight forward.

Surface properties such as emissivity play a major role in determining
radiation heat loss.

Similarly, properties such as absorptivity, reflectivity and
transmissivity are also important for calculations.
© 2011 Autodesk
Freely licensed for use by educational institutions. Reuse and changes require a note indicating
that content has been modified from the original, and must attribute source content to Autodesk.
www.autodesk.com/edcommunity
Education Community