Estimate thickness of an object based on radiative heat flux decay curve

[SimoneSk]

Dear all,
I have a slab of unknow thickness, with a starting temperature of 1400 K, emplaced over cold ground at a temperature of 285 K (air temperature assumed to be the same and held constant). I do have measures of its cooling curve in terms of radiative heat flux (in Watt) loss at the surface through time. I also know the area of this slab, and parameters like specific heat capacity, conductivity, density, etc... What I need, is to provide an estimate of the thickness of the slab, based on how quickly the curve decay (or ~reaches ambient temperature). Is there a way to retrieve thickness information based on the above data? If so, could you provide guidance on how to achieve it? Thanks a lot in advance

 

[jrmichler]

Is this homework? If so, we can move it to a homework forum.

I do have measures of its cooling curve in terms of radiative heat flux (in Watt) loss at the surface through time.

That covers the heat loss upward. The heat loss downward is a function of the thermal conductivity, specific heat, and density of the ground and the heat transfer coefficient between the slab and the ground. Any moisture in the ground will increase the heat transfer by evaporation and condensation similar to, for example, heat pipes.

Now, add the assumption that heat transfer through the thickness is enough to keep the top and bottom surfaces of the slab at the same temperature. The total heat loss is the sum of the heat loss up and heat loss down, both of which are a function of the slab temperature. The thermal mass (specific heat times mass) is the thermal mass that results in the measured cooling curve. From the thermal mass, calculate the thickness.

Have fun, it sounds like an interesting problem.

Last minute edit: Mass and heat transfer per unit area is a better approach than total mass and total area.

 

[SimoneSk]

Hi @jrmichler , thanks for getting back. No, this is not homework. Is more a curiosity of mine.
I am aware (please correct me if I am wrong), that a way to retrieve the thickness would be apply:
Volume = (E_tot) ./ (Rho.*(Cp .* D_T)), where, simplyfying, E_Tot = E_Rad + E_Conv + E_Cond, namely the total energy loss by the hot body moving from T initial to T ambient (where E_Rad, E_Conv, and E_Cond are terms for heat loss by radiation, convection and conduction, respectively). Rho is the density of the material, Cp is the specific heat capacity, and D_T = 1400 - 285.
With the volume retrieved, and knowing the area, the thickness is solved!

The point is, I do not have information about E_Conv or E_Cond.
Now (sorry I should have specified this at the beginning), I only have information about the cooling curve up to a certain point, let say until when the surface temperature of the hot body is 400 K (see below). I wonder if there is a way to use the radiative heat flux decay up to a certain point in time, to estimate the thickness, given the other available parameters.