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May 29, 2008, 10:07 
radiation from sun

#1 
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If I wanted to calculate how hot (worse case scenerio) a piece of metal just outside the earth's atmosphere would get due only to the sun's radiation I used:
q = sigma * emiss * (Tsun^4  Tmetal^4) knowing q = 1367 W/m^2 Tsun  6000K assuming emiss = 1 for black body I am getting a really hot piece of metal  4236K did I miss something? 

May 29, 2008, 10:31 
Re: radiation from sun

#2 
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I think I am missing a view factor..


May 29, 2008, 14:46 
Re: radiation from sun

#3 
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Is your piece of metal actually a black body? Surely some of the radiation will be reflected...


May 29, 2008, 15:06 
Re: radiation from sun

#4 
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I'm doing worse case scenerio, so I am treating it as a black body. I am having trouble computing a view factor because of the distance from the sun..any suggestions?


May 29, 2008, 15:22 
Re: radiation from sun

#5 
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Hmmm not sure on the mechanics of actually calculating the view factors (I let the CFD code I use do it for me!). How is the piece of metal cooled?


May 29, 2008, 15:25 
Re: radiation from sun

#6 
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it is not cooled at all..i am just trying to figure out how hot it would get if it was in direct sunlight basically at the same distance the earth is. So, I know how much energy gets to the earth from the sun, the sun's temp, the area of the metal piece, and the diameter of the sun. But, the view factor is throwing me off.


May 29, 2008, 15:48 
Re: radiation from sun

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j = sigma T^4, using T = 6000K is the radiative power per square metre on the surface of the Sun. Bear in mind that there is some 1.4x10^11m between the surface of the Sun and that piece of metal...
The 1367W/m^2 is the heat energy supplied by the Sun at the Earth's surface. You need an equation that defines the temperature rise that will be obtained by the metal conducting 1367J of energy (assuming complete absorption of the Sun's Energy). 

May 29, 2008, 16:18 
Re: radiation from sun

#8 
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using q*A=sigma*emiss*T^4 and knowing the area (A) of the plate I can solve for T, which gives me around 350K, which is reasonable. I know the equilibrium temp is of the earth is roughly 270K, so this sounds better.


May 29, 2008, 17:23 
Re: radiation from sun

#9 
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So it receives heat from the sun but has no mechanism to pass that heat on thus achieving continuity, ummmm....


May 30, 2008, 03:42 
Re: radiation from sun

#10 
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The piece of metal emits black body radiation. The view issue seems simple enough. Assume that the sun emits radiation isotropically.
R : distance from sun to object P_s : total power emitted by sun P_a : power absorbed by object P_e : power emitted by object A : crosssectional area of object facing the sun S : total surface area of object so we have P_a = P_s A /(4 \pi R^2) P_e = S \sigma T^4 The steady state condition is P_a = P_r. Suppose the object is spherical with radius r. Then A = \pi r^2 and S = 4 \pi r^2 so \sigma T^4 = P_s / (16 \pi R^2) putting in numbers gives about 280 K. 

June 3, 2008, 04:30 
Re: radiation from sun

#11 
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let sun temperature be Ts and Radius of earth orbit be d and radius of earth be R ... then assuming thermal equilibrium betweem earth and sun u will get
{sigma*4*pi*Rsun^2*Ts^4/(4*pi*d^2)}*pi*R^2=sigma*4*pi*R^2*Te^4 This would give you the temperature of earth... now your steel metal piece is in thermal equilibrium with the sun and earth... so u need to find thermal resistance between metal and sun and metal and earth... all r in sries.. then u need to find the potential(temperature) using series law of resistances... to figure out the resistances see any book on heat transfer(radiation) ... it will depnd on the shape and orientation of ur metal piece. 

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