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## Main Question or Discussion Point

I am digging back thorugh thermodynamics textbooks, and am seeing insulation values etc. but none on how to solve for time required to heat a material.

Here is the specific problem. I am trying to fgure out how long its takes to cool (or alternately heat) a concrete slab.

The slab is 8 in. with initial temp 60 degrees F. Temperature on top and bottom of slab is ambient air temp, 20 degrees.

k, concrete = 1.7 W / m - deg K

c, concrete = 750 Joules

the area of slab can be assumed to be very large (an acre? infinity?)

and the air can be assumed to not change as a result of the heat loss of the concrete.

So I have rate of heat transfer: dependent on the surface area,

H = -k A (dT / dX)

and specific heat of concrete, dependent on mass:

dQ = m c dT = Joules

t (seconds) to cool one inch thickness concrete by 22.2 deg C or K

= dQ / H = 637 seconds (this seems a little fast to me since concrete is fairly insulating material).

Does this look correct? (Assuming I have the heat capacity and conductivity of concrete correct). This would be derived into an integral to get the temp at a certain time and depth, but as a consultant would be laughed out of the room, and will simplify to some finite steps in time and thickness.

No need to get to technical! I won't get it! Thank you for your input.

Here is the specific problem. I am trying to fgure out how long its takes to cool (or alternately heat) a concrete slab.

The slab is 8 in. with initial temp 60 degrees F. Temperature on top and bottom of slab is ambient air temp, 20 degrees.

k, concrete = 1.7 W / m - deg K

c, concrete = 750 Joules

the area of slab can be assumed to be very large (an acre? infinity?)

and the air can be assumed to not change as a result of the heat loss of the concrete.

So I have rate of heat transfer: dependent on the surface area,

H = -k A (dT / dX)

and specific heat of concrete, dependent on mass:

dQ = m c dT = Joules

t (seconds) to cool one inch thickness concrete by 22.2 deg C or K

= dQ / H = 637 seconds (this seems a little fast to me since concrete is fairly insulating material).

Does this look correct? (Assuming I have the heat capacity and conductivity of concrete correct). This would be derived into an integral to get the temp at a certain time and depth, but as a consultant would be laughed out of the room, and will simplify to some finite steps in time and thickness.

No need to get to technical! I won't get it! Thank you for your input.