GR9677 #75



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Comments 
lrichey 20111105 12:08:50  maybe I'm just stupid... but could someone explain why I can keep .8 in terms of meters and 4 in terms of mm?
titanqq 20121012 05:12:23 
you get the variables k_A/B and k_B/A to divide one by one. This means, it doesn't matter in what terms you take it, they just must be taken both in 1 terms

  redmomatt 20110924 06:52:22  The problem can be solved without knowing Fourier's Law specifically.
Since we are given conductivities in watts/meter C, the ratios will be independent of these quantities. Given that the only variable then is the thickness of the pane, we take the limiting case to see how heat flow is affected; a monumentally thicker piece of glass will have a lower heat flow through it, given the same conditions. So, we can see that heat flow is inversely proportional to thickness.
Thus, we can simply divide the conductivity by the thickness, and then divide A by B, obtaining (.8/4)/(.025/2) = .2/.0125 = 80/5 = 16 .   walczyk 20110403 06:18:57  why is it that the temperature differentials are equal? I'm not really sure what it signifies. Temperature per length... shouldn't the temperature be larger per distance for one of the walls/windows?
walczyk 20120929 16:30:28 
I see, delta T is T_outdoor  T_indoor, which is the assumed the same for each case.

  carle257 20100405 00:26:17  You can also think of it like a resistance problem. A is 32 times more conductive to heat, but double the length. Thus the thermal resistance is proportional to conductivity*area/length = 32/2 = 16.   jw111 20081105 15:07:59  Fourier's Law is very similar to V=IR
for
V ~ temperature difference
I ~ heat flow
R ~ heat resistance = inverse of conductivity
here ra = 1/0.8 and rb = 1/ 0.025, thus
Ra = ra*4, Rb = rb*2
then Ia/Ib = Rb/Ra = 16.   bat_pesso 20071031 14:02:21  dimensional analyses:
heat flow A = 0.8/4mm
heat flow B = 0.025/2mm
A/B = (0.8x2)/(0.025x4) = 16/1
FortranMan 20080902 17:10:17 
provided you remember how area is involved in Fourier's law, otherwise you might get alarmed with meters^2 popping up

 

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