Thermodynamics question?

Question

I need to calculate the gap between the panes of an insulating window. Panes are 3mm thick, emissivity=absorbtivity=0.9, separated by air space at 1 atm. Outside air is -20 C, outside surface of window is -16 C, inside surface is 21 C, inside air is 25 C. k glass = 1.4, k air = 0.024, h = 5 for inside and outside convection. Neglect radiation in the air gap.

I'm assuming that it's conduction, not convection, in the gap, because there's no movement to the air, and because convection doesn't require a gap distance. But I have no idea how to find the gap distance, because the only equations we've been taught involve the gradient of a thermal conductivity equation, which we aren't given here. So I don't know where to apply the thickness of the window panes, or how to solve for the gap.

If someone could help me out with just a formula to use, I'd appreciate it. I've hit up Google, but can't find anything. Thanks.

UNG · Accepted Answer

Key equation:

heat flux from inner air to inner surface of glass
= heat flux through inner glass pane
= heat flux through air gap
= heat flux through outer glass pane
= heat flux from outer surface of outer pane to outside air.

If T1 = temperature of inner air
T2 = temperature of inside surface of window
T3 = temperature of gap side of inner pane
T4 = temperature of gap side of outer pane
T5 = temperature of outside surface of window
T6 = temperature of outside air
t_g = thickness of each glass pane
t_gap = thickness of air gap
then

h_in(T1-T2) = k_glass(T2-T3)/t_g = k_air(T3-T4)/t_gap = k_glass(T4-T5)/t_g = h_out(T5-T6)

Solve for T3, T4, and t_gap.  Everything else is known.

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Thermodynamics question?

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