Temperature Across Concrete Barrier

Assuming a steady state is reached, T = T_c + 350d/44; where:
T = temperature at distance d into the concrete from the colder side, and
T_c = temperature on the colder side.

Or, even simpler, 350/44 degrees per inch.

Thank you. That will give me the straight line gradient which will be good for all practical purposes, however, what I am looking for is to plot a curve across the thickness which will depend on co-efficient of thermal condtivity for concrete and Delta T.

It would be interesting to see an FEA-type simulation. If one side of the barrier is warmed (or cooled) quickly, there will be a steep gradient through a small but increasing thickness of the barrier, with the "heel" of the curve progressing through the barrier until the steady state is reached.

Exactly! The curve will become flatter as it goes from high to low temp across the section and at a certain thickness it will become completely flat and there will be no heat transfer beyond that.

For a plane wall, a temperature step ( + or -) and for constant thermal diffusibility there are already equations and a FEA simulation is not required.

To answer the previous question the temperature gradient can be determined wiyj help of conductivity if the heat flow/area unit is known. Since the total temperature drop is known what was suggested is totally sufficient provided that the wall is plane or that the ratio R/t is big for a round wall.