Conductive Heat Transfer
Conductive Heat Transfer
(OP)
We need to calculate how long it takes for an aluminium plate to assume the same temperature as the heated air in an oven. To a first approximation it may be assumed that the amount of heat available for the heated air in the oven is effectively infinite compared to the mass of the aluminium plate. Assuming the plate is 12"x12"x1" and loses no heat through conduction to the outer wall of the oven how long will it take before the aluminium is soaked through to the same temperature as the heated air inside the oven? Typically the oven and the plate start at a temperature of 22°C and then the aluminium plate is heated using air which is heated in the oven at the rate of 1°C/minute controlled by an electronic controller.
Thanks very much
Thanks very much





RE: Conductive Heat Transfer
TTFN
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RE: Conductive Heat Transfer
Thanks again though - I appreciate your input.
RE: Conductive Heat Transfer
If the air temperature of the oven were constant the plate temperature would asymptotically tend to Tamb:
T(t)=Tamb - (Tamb - Ti)*exp[-A*h*t/(m*cp)]
Being :
Tamb = ambient/oven temperature
Ti = starting temperature
A = plate exposed area
h = heat transfer coefficient (convection + radiation)
m = plate mass
cp = aluminium specific heat.
t = time
Now the problem could be a bit more tricky as your Tamb is not constant but varies at the rate of 1°C/minute.
RE: Conductive Heat Transfer
I really appreciate your help on this one.
RE: Conductive Heat Transfer
If both the down side and the upper side of the plate are exposed to still air (natural convection) I would consider approx 6 W/(m^2*K). This value takes into account also the radiative contribute.
RE: Conductive Heat Transfer
RE: Conductive Heat Transfer
TTFN
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RE: Conductive Heat Transfer
Then, when the oven reaches steady-state, the response of the system is that is a first-order system to a steady input...i.e. the temperature of the plate will asymptotically approach that of the oven.
You should be able to model the temperature of the plate to a high degree of accuracy in this piece-wise manner.
Good luck,
Dave
RE: Conductive Heat Transfer
MCpdT/dt=hA(To+at-T)
where Tamb= T0+at
t= time
a= ramp rate 60 deg C/hr
MCp/hA= time constant of system
The solution is:
T=(T0+aMCp/hA)*exp-(t(hA/MCp)+at-aMCp/hA
After heating the oven to its final temperature Tf, at time s, the temperature of the aluminum is Tal<Tf so the ODE becomes for t>s (part2)
MCpdT/dt=hA(Tf-T)
and the solution to this part is
T=Tal+(Tf-Tal)exp-[(hA/MCp)(t-s)]
RE: Conductive Heat Transfer
The last equation should read
T=Tf-(Tf-Tal)exp-[(hA/MCp)(t-s)] or
T=Tal +(Tf-Tal){(1-exp-[(hA/MCp)(t-s)]
which shows that the aluminum reaches Tal after the ramp rise of oven temperature and then goes asymtotically toward Tf
RE: Conductive Heat Transfer
T(t) = (aMCp)/(hA)*[exp(-hAt/(MCp)) -1 ] + T0 + at
RE: Conductive Heat Transfer
Ione,
Thanks for the correction.
Have to pay more attention to the particular solution.