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 short-answer questions, covering conceptual knowledge.
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
Methods for evaluation
View factor algebra
The inside-sphere 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 partially-specular surfaces
Problem 1 (physics of radiation) (20 points).
A Ņtwo-color 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 F12 as a function of a, b and q.
b) Determine the spectral view factor F11 for the special case q = 45ū, a = Ć2 – 1, b = 1, r1s = r2s = 0.5, e1 = e2 = 0.5 (think carefully about this problem!)
Problem 3 (Radiative exchange between surfaces) (35 points).
For the configuration shown in the figure above:
a) Calculate the diffuse view factors F12d and F21d.
b) Calculate the spectral view factors F11s, F12s, F21s and F22s if surface 1 is a purely diffuse reflector but surface 2 is a purely specular reflector. Both surfaces are diffuse emitters.
c) Calculate q1 for the specularly reflecting case, in terms of e1, T1, e2 and T2 if the surroundings are at 0 K.
Problem 4 (Miscellaneous) (20 points total).
We have discussed the Ņgreenhouse 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 45ū-45ū-90ū 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, Fijs (i = 1, 2, 3; j = 1, 2, 3) in terms of the diffuse view factors Fijd for these surfaces and their images (for example Fi(j)-i, etc.) and the spectral reflectivities ris. Also draw the images where they exist.
2. a) Determine q1 for the cylinder shown with diameter 10 cm and length 20 cm. All surfaces are black (e = 1). Also determine T2.
b) If surface 2 had a heat transfer by convection on its outside surface, with T° = 500K, would T2 increase or decrease? Would q1 increase or decrease? (I intentionally didnÕt give you a value for h2; IÕm looking for an explanation of what will happen and why).