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

  • I
  • Thread starter Thread starter SimoneSk
  • Start date Start date
  • Tags Tags
    Heat Thickness
AI Thread Summary
To estimate the thickness of a slab with an unknown thickness cooling from 1400 K to ambient temperature, one can analyze the radiative heat flux decay curve. The heat loss includes contributions from radiation, convection, and conduction, but the user lacks data on convection and conduction losses. The cooling curve data can be used to calculate the thermal mass, which is essential for determining the thickness. By applying the formula for volume based on total energy loss and known parameters like density and specific heat capacity, thickness can be derived if sufficient cooling curve data is available. The discussion emphasizes the importance of understanding heat transfer dynamics in this estimation process.
SimoneSk
Messages
6
Reaction score
0
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
 
Science news on Phys.org
Is this homework? If so, we can move it to a homework forum.
SimoneSk said:
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.
 
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.

exa3.png
 
I need to calculate the amount of water condensed from a DX cooling coil per hour given the size of the expansion coil (the total condensing surface area), the incoming air temperature, the amount of air flow from the fan, the BTU capacity of the compressor and the incoming air humidity. There are lots of condenser calculators around but they all need the air flow and incoming and outgoing humidity and then give a total volume of condensed water but I need more than that. The size of the...
Thread 'Why work is PdV and not (P+dP)dV in an isothermal process?'
Let's say we have a cylinder of volume V1 with a frictionless movable piston and some gas trapped inside with pressure P1 and temperature T1. On top of the piston lay some small pebbles that add weight and essentially create the pressure P1. Also the system is inside a reservoir of water that keeps its temperature constant at T1. The system is in equilibrium at V1, P1, T1. Now let's say i put another very small pebble on top of the piston (0,00001kg) and after some seconds the system...
Back
Top