Direct Solar Radiation and electric heater intensity's...?
Question:
Assume that the heater radiates uniformly in all directions. Explain your work. Good luck! :)
Answer:
First, your initial assumtion is incorrect. I believe the solar radiation on a clear day is closer to 1000W/m^2.
Secondly, we don't know how much of the 1kw input power to your heater is converted to convective heat, and how much is converted to infrared radiation. For the purposes of this problem, I will assume the heater is in a vacuum and all 1000w of power is converted to IR and visible radiation.
Be that as it may, the infrared radiation is emitted equally in all directions, so the distance we determine will be located on a sphere centered on the heater. We want 100W of radiation to fall on 1 square meter.
The solution is simple: Determine the radius of a sphere with surface area 10 m^2. Each of those 10 square meters of the sphere will have 100W on it, and by definition, a radiation intensity of 100W/m^2.
Since the surface area of a sphere is 4 * pi * r^2 the solution is
10=4*pi*r^2
-or-
r=sqrt(10/4pi)
so r = 0.8m
As with many of this type of problem, the math is not so difficult as just learning to look at the problem in the right "light" (so to speak).
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