Transient Heat Conduction - ABS Sheet
Transient Heat Conduction - ABS Sheet
(OP)
Hello
I've been asked to provide an estimate of the core temperature of an ABS plastic sheet heated in an oven during a thermoforming process.
I have no real knowledge of the heat input to the sheet, but I do know the skin temperature is 165-175 celsius after 180s of heating.
My question is, is it possible to calculate the core temperature of this sheet (6.5 mm) from the skin temperature, heating time and material properties alone?
The oven uses radiation as its primary heating method and I have only dealt with convective heat transfer before, so I am unsure how to proceed.
Any insight would be much appreciated.
I've been asked to provide an estimate of the core temperature of an ABS plastic sheet heated in an oven during a thermoforming process.
I have no real knowledge of the heat input to the sheet, but I do know the skin temperature is 165-175 celsius after 180s of heating.
My question is, is it possible to calculate the core temperature of this sheet (6.5 mm) from the skin temperature, heating time and material properties alone?
The oven uses radiation as its primary heating method and I have only dealt with convective heat transfer before, so I am unsure how to proceed.
Any insight would be much appreciated.





RE: Transient Heat Conduction - ABS Sheet
Can you measure the surface temperature of the other side?
RE: Transient Heat Conduction - ABS Sheet
RE: Transient Heat Conduction - ABS Sheet
RE: Transient Heat Conduction - ABS Sheet
I'm afraid no closed form solution exists for your case, where the faces are much closer to a constant heat flux condition. Only a numerical solution seems too be possible: as it is a unidimensional problem it wouldn't be too difficult to write a finite difference solution in a spreadsheet.
However, if you want just an estimate, the convective solution should give you a reliable one: you could guess an equivalent heat transfer coefficient from the known surface temperature at a given time.
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RE: Transient Heat Conduction - ABS Sheet
RE: Transient Heat Conduction - ABS Sheet
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RE: Transient Heat Conduction - ABS Sheet
The problem as stated is not solvable, since the dominant heat transfer mechanism is radiation. So, we need to know the emissivity, the source temperature (at the heating elements) and the view factor.
Moreover,you cannot get a Biot number without this, since the equivalent h is
h=sigma*e*F*(Ts^4-T1^4)/(Ts4-T1)
Ts source temperature
T1 surface temperature at piece
sigma Stefan Boltzmann constant
e emissivity
Once this data is obtained, only then you can get and use the Biot number to determine if you have a "thin" slab which means the center temperature is almost equal to the surface temperature; otherwise there are a few nomographs available that can give you a good solution. I use Schneider's curves for this.
needs this I would try to upload the curves.
RE: Transient Heat Conduction - ABS Sheet
Not solvable as a closed-form, presumably, but there are lots of tools that could ostensibly iteratively solve the problem.
My bad on the form, though. I plead guilty to bad algebra, the residual should have been
(Ts+T2)*(Ts2+T22)
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RE: Transient Heat Conduction - ABS Sheet
I only say that you need e,F and Ts to get the answer.
Do we agree?
RE: Transient Heat Conduction - ABS Sheet
Ts is the temperature to solve for, assuming that you can fill in the backstory of the thermal conductance, thermal capacity, and emissivity.
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RE: Transient Heat Conduction - ABS Sheet
You cannot do the problem without
K,rho,c and source temperature of the oven,Ts, period.
BTW, I have used Ts as the source temperature and T1 the surface temperature of the specimen.
I'm now wondering if your Ts is not the same.
RE: Transient Heat Conduction - ABS Sheet
RE: Transient Heat Conduction - ABS Sheet
Assuming the source temperature is much greater than the surface temperature, (170C ) at the time of measurement, the problem is essentially constant flux into the surface at x=L and the center of the specimen by symmetry is treated as insulated.
The C& J solution is
T=FoL/k[kappa*t/L^2+.5(x/L)^2-1/6- summation of transient terms]
Fo = flux
For the problem we have
L=6.5mm=.26 "=.02 ft
k=.1BTU/HR-FT-F
Rho*c=70*.35=25
kappa=k/(rho*c)=.1/25=.004 ft^2/hr
For this problem, t=180s=1/20hr
and
kappa t/L^2=.004*1/20/.02^2=0.5
Fortuitously, for the time, 180s, the transient terms die out and we are left with a temperature distribution that is linearly rising throughout the slab with a parabolic profile
From the solution above , ignoring the transients there remains
T(0)=Fo*L/k*[kappa*t/L^2-1/6]
T(L)=Fo*L/k*[Kappa*t/L^2+1/3]
Substituting I get
T(0)/T(L)=> 0.5-.16/.8+.33=.34/.833=.408
So if T(L)=170-25=135 C, then
T(0)=.408*135=55 C
Note that Fo, the flux is not needed explicitly to get this result
For other times (kappa*t/L^2<.2) where the transient terms are significant you need to use the C&J curves to pick off T(L) and T(0) or T(x).