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Ronin, you're right. Depth is an issue. Heat is lost on all sides, the heat flux at the surface depends on depth.
The thermal conduction resistance for a long, isothermal tube (the heating element) can be expressed at 1/Sk, where k is the thermal conductivity of the concrete and S is known as the shape factor.
For a tube radiant heating system buried in concrete, S=(2*pi*L)/(cosh^-1)(2z/D) where L is the length of tube, z is the depth, D is the tube diameter, and cosh^-1 is the inverse hyperbolic cosine func. If the depth z is greater that 3D/2 (should be...) then that can be reduced to a easier to work with form of (2*pi*L)/(ln(4z/D) - 2 pi * length divided by the natural log of (4*depth / diameter of tube)....
With that out of the way, you can see how diameter effects the thermal resistance network, R(t,cond)=1/Sk
And the ultimate heat flux equaling q = Sk(delta T) .. the delta T being the temp difference between the surface of the heating pipe and the top surface of the slab. This, ultimately, would be expressed in watts/square meter.
Whew. I think I got all that right, I may have misquoted a figure somewhere in that but the idea is yes, the depth of the pipe has a relationship on the heat flux through the top surface of the slab, the deeper you go the worse it gets obviously.. and if I was even more bored than I was I'd plot that out non-dimensionally so we could see the relationship more clearly..
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M
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