Heat transfer from inside to outside

[JSBeckton]

An insulation system is to be selected for a furnace wall at 1000 deg C using first a layer of mineral wool blocks (k=.091 W/m-c) followed by fiberglass boards (k=.0425 W/m-c). The outside of the insulation is exposed to an environment with h= 15 W/m^2-c and temp of 40 deg C. Claculate the thickness of each material such that the interface between to insulators is not greater than 400 deg C and the outside surface is not greater than 55 deg C. What is the heat loss per unit square meter?

I have been going over this question that sounded pretty simple at first, but I soon realized that I have no idea where to start. I cannot calc the overall heat loss because I don't know the thicknesses, and I can't calc the thicknesses because I don't know the overall heat loss. Catch 22? I'm sure that it has something to do with solving equations simo but cannot figure out where to start w/o any additional info, can anyone help me out?

Thnaks
Josh

 

[Cyrus]

Did you make a thermal resistance network?

 

[JSBeckton]

Not sure what you mean by that but if you are referring to the resistances between the inside and outside:

Temp inside->
R conduction from mineral blocks ->
Temp interface ->
R conduction from fiberglass ->
R convection from fiberglass ->
Temp outside

Where do I begin?

 

[Cyrus]

(1) Draw a picture and upload it to www.imageshack.cc[/URL]

 

[Integral]

You have 2 equations.

1. The temp difference between the interior and the interface, the interior material thickness and conductivity.

2. The Temp difference between the interface and the exterior, the exterior material thickness and conductivity.

Solve.

 

[JSBeckton]

I tried that but I have 3 unknowns:

1) Thickness of mineral blocks
2) Thickness of fiberglass
3) Heat flow per unit area.

I uploaded my work here

[URL=http://imageshack.us][PLAIN]http://img126.imageshack.us/img126/1482/img020yu7.jpg[/URL][/PLAIN]

 

[JSBeckton]

Let me know if you can't read it and I will try again.

 

[Integral]

A 3rd equation would be the one relating the total thickness, the total resistance and the internal and external temperatures.

You are also given the temperature of the environment, this could give you a net heat loss with an assumption on the mechanism, ie pure radiative loss or perhaps a convective loss. With either you would need to know something about the emissivity of your final surface.

 

[JSBeckton]

Thanks, I think that I figured it out.