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1 Heat Transfer: Radiation Heat transfer occurs by three mechanisms: conduction, convection, and radiation. We have discussed conduction in the past two lessons. In this lesson, we will discuss radiation. We will start by looking again at the electromagnetic spectrum. Figure 1: Equipment for Heat Transfer: Radiation black metal sheet white metal sheet E glass normal glass heat lamp (halogen light) with stand normal lamp (regular lightbulb) propane torch temperature probes or thermocouple Objectives [At the end of this lesson students will be able to...] describe the concept of radiation heat transfer and the equation governing this process. explain how this concept can be applied in our daily life and in space technologies. Start-up questions 1. How does heat (or energy) come to us from the sun? 2. What is in the space between planet earth and the sun? 3. Do all bodies produce heat? 4. Do you know how night vision goggles work? Heat Transfer: Radiation -- Page 1 of 6

5 Q emitted = P/A = σt 4 so that T = [Q emitted / σ] ¼ = {500 W/m²/[ W/(m² K 4 )]} ¼ = K We were asked for C, so convert from K to C: T = = 34 C 2. You work part time as a contractor building houses (to supplement your teaching income). Your client asks you what difference there is (if any) between using a light color roof and a dark color roof in the south where the summer is very hot (we all know that). The homeowner wants to use very dark shingles with an emissivity of The roof has a 6.0"-thick fiberglass insulation and the attic temperature is always maintained at 80.0 F (26.7 C= K). Thermal conduction through the roof to the attic and radiative loss are the main sources of heat transfer. Determine the equilibrium temperature in the day time for the shingles if the solar power is 1.0 kw/m². Solution: Energy absorption rate = 1.0 kw/m² 0.90 = 9.0 kw/m². Heat loss through conduction = (0.040 W/m K) / ( m) T = 0.26 (T- 300) W/m² Heat loss through radiation = σt 4 = W/(m² K 4 ) T 4 = T 4 W/(m² K 4 ) Balancing heat absorption and loss yields: 900 = 0.26T T T T = 0 (NOW WHAT DO WE DO????) You can either go and consult a mathematician to solve the equation or make some approximations. If we are lucky, we can get pretty close to the correct answer. Assume that the T 4 term is small compared to the other two terms (this is true for small T). Then the solution is simply T = 3760 K. This is a pretty high temperature and violates the assumption of small T. Actually if we substitute this solution into the original full equation, we have: This certainly is not equal to zero. Another assumption is that 0.26T is small; then we have as an approximation of the equation: T = 0 or T = 364 K (a much more reasonable assumption). To check, we can substitute this solution back into the original equation and we have: which indicates that our answer is a little high, but no more than about 10% off. Quite acceptable in this approximation. Heat Transfer: Radiation -- Page 5 of 6

6 Homework After teaching high school science for 20 years, you decided to change your career and became a space thermal scientist for NASA. You were charged with the design of a solar panel in space (the only heat transfer there is radiation, no heat conduction at all). Your solar panel receives 1.0 kw/m² of solar energy and its emissivity (also its absorptivity) is 0.60 (or 60.%). The solar energy is received on only one side at a time, but emission occurs on both sides. Determine the equilibrium temperature of the panel. Repeat the calculation for an emissivity of 0.30 and see what you find. Heat Transfer: Radiation -- Page 6 of 6

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