Thermal conductivity of the glass problem

[PhysWiz2009]

Homework Statement

I have plate of glass pressed between a hot plate on top and a insulating surface below. The idea is to be able to predict the temperature of the glass plate and the thermal gradient through the plate as well at any time. I know the hot plate is at 400 deg F, that it is an 1800 Watt unit, and that the heating surface is 16X20 in. The glass is a 12 inch circle that is 3mm thick. Thermal conductivity of the glass k = 1.2 W/mK and the specific heat capacity c = 0.83 kJ/kgK also the mass of the glass is 521.23g. This problem has me stumped! Any help would be greatly appreciated.

Homework Equations

I've tried Q/$$\Delta$$t = -k_t*A*$$\Delta$$T/$$\Delta$$x
But doesn't seem to work

The Attempt at a Solution

 

[mgb_phys]

You need to know about the insulating surface.
If you assume it is perfectly insulating then there is no heat flow once the glass as reached the same temperature as the hot-plate.
If it is a cold sink (assume infinite heat capacity) then you need to know it's temperature.

Is this a textbook type question or real life ?

 

[PhysWiz2009]

It's a real life lab situation. The insulator is a foam so it isn't perfect but is still pretty good.

 

[mgb_phys]

Then it's dominated by the conduction through the 'insulator' - you need to know the thermal conductivity+thickness of the insulating material and the temperature and heat capacity of what's on the other side (if it's just air this is going to get tricky!)

The other problem is that thermal conductivity across an interface between solids is proportional to the pressure - so you need to know how hard the glass is sandwiched between them.