RubberDucky

You need to design a double plane window that is comprised of two 5mm thick slabs of window glass (mean thermal conductivity 0.84 W/(mk)) with a gap of stagnant air (mean thermal conductivity 0.02W/(mk)) in between them. The room temperature is 298k, outside temperature is -15c. The heat transfer coefficients of the window with the air on the inside and outside are 10W/(m^2k) and 80W/(m^2k) respectively.
a) Determine what spacing should be made between the glass in order to have heat loss rate less than 100W/(m^2k)
b)If we wanted to replace the composite window with a single plane of glass, what thickness would be required.

I'm struggling to get set up here. I have a solid interacting with a fluid, so I know I need to track down that equation, but part of the problem is I don't have a text book. Our professor has hand-written notes that are used as the class text (not joking). His writing isn't the best. I don't know what I need to get going. Please help.

Woody

I think you are worrying unnecessarily about the solid interacting with the fluid.
A key point is that the air is "stagnant", in other words it is not moving.
(It is a feature of double glazing that that the spacing should be fairly close to prevent significant convection currents developing).

So I think you can just treat the air (in this case) the same way as you would a solid with the appropriate thermal conductivity and heat transfer.

studiot

Well said Woody.

RubberDucky

That helps a little bit. Well maybe it helps a lot, but I'm still unsure. So I have h=heat trans coeff. and resistance due to convection =(T_s-T_f)/q_x=1/(Ah) where T_s is solid temp, T_f is fluid, q_x is flux, A is cross-sec area, and h is heat trans coeff. Now as far as stagnant air goes, I have that inside the glass, but what about the exterior temperature? Can I disregard the "fluid outside" and treat the outside piece of glass as the -15c, because that seems like a problem. I don't know that it is, I'm just thinking that if the inside is some temp, 1, the air gap is temp 2 at inner glass interface, temp 3 at outer glass interface, and outside is temp 4 , then the outside glass isn't actually at temp 1 until / if the system is at equilibrium. As I said, can I make that assumption, and simply disregard air inside and outside? like: (T1-T4)/q_x=Rk_1+Rk_2+Rk_3?

RubberDucky

Wait, Rk_x will be delta x/(k_x*A) and I don't have an area. AHHHH someone please point me in some direction. Please, for the sake of my sanity. That or take me out to the shed and put me out of my misery.

Woody

To me this looks like a simultaneous equation problem.
As you say the temperature change across each of the three sections (glass, air, glass) depends on the width of the air gap.
So you know the 2 temperatures on the outside surfaces of the two panes of glass, but not the two temperatures of the surfaces of the glass in contact with the air in the gap.
Try setting up separate equations for each stage and just enter the the two unknown temperatures as unknown temperatures T1 and T2 (for now).
Similarly with the third unknown, the width of the air gap, W.
Hopefully the mathematical relationship between these values will become apparent, and hence the solution.

I haven't looked at this in detail, (so I can't guarantee I'm correct) but this is how I would proceed.

Although it is not explicitly stated, I am sure that you can assume equilibrium conditions.
There is no indication of any time dependency anywhere in the question (and the problem would start to get silly complicated if it we don't assume equilibrium).
Make sure you convert your -15C to Kelvin.

RubberDucky

Thanks, for the reply. I'll see what comes from it.