Help with Steady State Heat Transfer Problem

[Diego Saenz]

Hello everyone,

I have this setady state, heat transfer problem; I hope you can help me with it.
I have flux source of 400 W/m² (a lamp), and i want to calculate the heat flux passing through a surface arbitrarily placed and oriented in the space. There is air in between. How can i do this?

I thought that I could use ∫∫(-k∇T)*(n dS)
But i don't know what ∇T is...

Thanks.

 

[mikeph]

That will give you the answer once you've found T. Finding T involves solving the heat equation with a local heat source. You'll need some more boundary conditions to do this, e.g. what are the temperatures of the walls?

If your geometry is simply you can solve for T analytically then differentiate to find your heat flux through a surface.

If not, you'll need some software.

 

[Diego Saenz]

Hi mikeph,

My surface is simple, is a square. Is it possible to use this information to solve for T? Can you explain how can I do this?

Thanks

 

[mikeph]

If the heat source is inside the surface then it's just 400 W/m^2, this is from energy conservation using the steady state assumption.

If you have a constant temperature distribution then the heat being added inside the box (400) must equal the heat leaving through the walls, otherwise the temperature of the box would have to increase which would introduce a time variation.

 

[Diego Saenz]

I really appreciate your help mikeph.
But I have problems visualizing the solution, could you provide simple example?