Midterm Exam Study Guide
October 22, 2009
Format of the exam
The midterm exam will be open book. You may use any reference materials you
want, but no laptop computers. The
exam will have both analytical/numerical problems and shortanswer questions,
covering conceptual knowledge.
Material covered
The exam may cover any material through the end
Chapter 6. This material includes:
Fundamentals of thermal
radiation
Basic laws of
thermal radiation
Emissive power,
radiative intensity, radiative heat flux
View factors
Definition
Summation rule
Methods for
evaluation
Area integration
View factor
algebra
Crossedstrings
The insidesphere
and unit sphere
Radiative exchange
between diffuse surfaces
Radiative exchange
between black surfaces
Radiative exchange
between gray, diffuse surfaces
Electrical network
analogy
Specular view
factors
Enclosures with
partiallyspecular surfaces
Radiation shields
Problem 1 (physics of radiation) (20
points).
A Òtwocolor pyrometerÓ is a device that measures
the surface temperature of an object assuming it behaves as a gray body
(emissivity doesnÕt matter as long as itÕs independent of wavelength) without
needing a reference object. It
works by looking at the ratio
of intensities at two different wavelengths. For the following measurements, determine the temperature of
the test object:
Measurement wavelength 1: 3.5 µm, intensity = 0.504 (units donÕt
matter)
Measurement wavelength 2: 5 µm, intensity = 1 (in same units as
above)
Problem 2 (view factors) (25 points).
For the object shown in the figure:
a)
Determine the diffuse view factor F_{12} as a function of a, b
and q.
b)
Determine the spectral view factor F_{11} for the special case q = 45û, a = Ã2 – 1, b = 1, r_{1}^{s} = r_{2}^{s} = 0.5, e_{1} = e_{2} = 0.5 (think carefully about this
problem!)


Problem 2 
Problem 3 
Problem 3 (Radiative exchange between
surfaces) (35 points).
For the configuration shown in the figure above:
a)
Calculate the
diffuse view factors F_{12}^{d} and F_{21}^{d}.
b)
Calculate the
spectral view factors F_{11}^{s}, F_{12}^{s}, F_{21}^{s}
and F_{22}^{s} if surface 1 is a purely diffuse reflector but
surface 2 is a purely specular reflector.
Both surfaces are diffuse emitters.
c)
Calculate q_{1}
for the specularly reflecting case, in terms of e_{1}, T_{1}, e_{2} and T_{2} if the surroundings
are at 0 K.
Problem 4 (Miscellaneous) (20 points total).
We have discussed the Ògreenhouse effectÓ in
class, which causes the interior of an enclosure to reach a temperature higher
than that of the surrounding air when sunlight passes though a window of the
enclosure. Answer and explain
briefly the following questions
about this effect:
a.
Would running a fan
inside the enclosure to increase the convective heat transfer coefficient
between the interior air and the wall of the enclosure increase or decrease the
temperature inside the enclosure?
Extra problems (not on any previous
midterm):
1.
For the following 45û45û90û
triangular enclosure, surfaces 1 and 2 have a specular component to their
reflectivity but surface 2 is a purely diffuse reflector. All surfaces are diffuse emitters. List all 9 specular view factors, F_{ij}^{s}
(i = 1, 2, 3; j = 1, 2, 3) in terms of the diffuse view factors F_{ij}^{d}
for these surfaces and their images (for example F_{i(j)i}, etc.) and
the spectral reflectivities r_{i}^{s}. Also draw the images where they exist.
2.
a) Determine q_{1} for the
cylinder shown with diameter 10 cm and length 20 cm. All surfaces are black (e = 1).
Also determine T_{2}.
b) If surface 2 had a heat transfer by convection
on its outside surface, with T_{°} = 500K, would T_{2} increase
or decrease? Would q_{1}
increase or decrease? (I intentionally
didnÕt give you a value for h_{2}; IÕm looking for an explanation of
what will happen and why).