Well, in principle it must follow Newtons law, but it would depend on the environment, if it is open, if it is in a cooled room, the external humidity, etc... But my suggestion is to determine it experimentally. Just record the temperature during heating and cooling in adequate time intervals and then you can fit the data to get the cooling rate of your own furnace. We did the experiment once for teaching, see the attached file.

Regards

Well, in principle it must follow Newtons law, but it would depend on the environment, if it is open, if it is in a cooled room, the external humidity, etc... But my suggestion is to determine it experimentally. Just record the temperature during heating and cooling in adequate time intervals and then you can fit the data to get the cooling rate of your own furnace. We did the experiment once for teaching, see the attached file.

Regards

Thank you Dr. Caballero-Briones for your detailed response and for sharing the experimetal data!

I agree with Dr. Briones. I worked from 650°C to 1000°C. I observed for the tube furnace when the temperature difference between the enivornment and the temperature i am working with is huge the furnace cooled down very fast. In my opinion firstly you fix the temperature you will work, after determine the cooling rate the way Dr. Briones suggested you. And if you want to control heating rate and cooling rate of your furnace then you may install a digital temperature controller.

Best just to measure it, it depends on too many factors to calculate it (mainly: optical vs resistive heating, size, and quality of thermal insulation).

You really need to be careful. If you seek constant cooling rate, you will not achieve it by just letting furnace cool down. Lower the temperature gets, slower the cooling rate will be. Then it also depends on sample you have in furnace. Small furnace volume with proportionally large sample will behave differently.

In general heat flux will be under Stefan's law proportional to T to the power of 4.

This is a question to hand to a chemical engineer who has had a heat transfer course. It is a problem in unsteady-state convection. Radiation is probably minimal unless your room is in a vacuum or the oven is at a 1000 oC or more. The key parameters are the Biot and Fourier numbers of your system. The cooling rate is a non-linear function of time. Think the second law of diffusion, generate a rough plot of dimensionless concentration versus dimensionless time + distance + diffusion coefficient, translate concentrations to temperatures and use thermal diffusivity in place of diffusion coefficient, and you will have a first approximation to the answer, at least under the assumption that your oven is isotropic in properties throughout.

Or, you can just do the experiments.

:-)

Edit: I meant to say this requires use of the Heisler charts.

http://en.wikipedia.org/wiki/Heisler_Chart

Thank you all for your valuable comments and clarifications!

I tried to dive into Heisler Chart, but I am lost when trying to calculate Fourier and Biot Numbers. 

Please give your opinion, how to achieve intermediate cooling i.e. Rapid Cooling (3-6econds) from 800C to 500C. What is the best way to achieve it?

@S Abbas: The Fo and Bi numbers are set by the geometry and conditions of the system. Absent the specific information that is demanded for these two dimensionless numbers, any answers someone might give to your question are nothing more than wild speculation. For example ... Suppose that you want cool down in 15 s. OK, turn off the oven very quickly. Suppose that you want cool it down in 15 days. OK, pull the plug very, very slowly. Those are my "opinions" based on your request.

Here is exactly what you need ...

h - convection coefficient of the surrounding air

k - effective thermal conductivity of the oven

V/A - volume to external area ratio of the oven

alpha = k/\rho Cp - effective mass density and specific heat capacity of the oven

You can get h from Perry's Handbook or other references. You can estimate k, \rho, and Cp for the oven by taking the main material that comprises it and using those values. You might assume a brick or ceramic or insulation. You can determine V/A by geometry.

See what you find from this. Follow up directly for additional help.

Cooling rate can be derived from the Stefan-Boltzman law. Cooling times will go like 

1 / (temperature)^3 ....... You can easily work it out.

With convection, the T-t profiles are mapped in a Heissler chart, not by Newton's or Stefan-Boltzman's law (both of which have no idea about convection).

Why don't you just turn it off an measure the cooling rate?  I will of course be faster if you purge with an appropriate cool material like N2 ,steam or even  water

I measured by "turn off" method (see attachment), but factors such as RT, with or without crucible, single or multiple elements etc. are so many factors which cannot be controlled so easily. My analysis of furnaces is in line with what was highlighted by Mr. David Bombač in initial comments.

Syed,  That is a very interesting result.  It appears it is much more complicated than expected.  No the question is "how important is it to figure out what is really happening". I will speculate that the specific heat of the crucible is high enough to dominate the cooling behavior of the entire furnace and that there is quite a bit of other interesting stuff going on probably water or other substances evaporating/condensing and absorbing/desorbing and causing uneven cooling.  An alternate theory is that the accuracy of your measurement can account for a lot of the scatter. 

It is time to ask yourself what is the purpose/goal of this question and how well do you have to answer the question to satisfy that goal. You could just put a sign on the oven that say it may be hot for X hours after use.  Or you could gather more detailed data and explain every bump in the curve.

@S Abbas: Further questions must be addressed:

• As near as I see, you are showing rates INSIDE the furnace, correct?
• What is rate? Is it dT/dt? Or something else?
• Are the axes scales the same in all graphs? Can the figures for each furnace be overlapped?
• Are the starting points the same for each experiment?
• Is the rate calculated at a defined point in heating or cooling (instantaneous), or is it calculated from start to end (as an average)?

So many questions are tied up in the figures. First principle interpretations will be muddled at best. Finally, as R Manner notes ... What is your goal?

I also request, rather than continuing to hijack the original post from M Zaki with questions rather than answers, please start your own thread on this topic as related to YOUR research work. You can properly reference this thread in your new posting.

@S Abbas: Your entire problem really is NOT a continuation of the original post. The original post is a basic question about cooling a furnace when it is turned off. Your post is an entire thesis on how to manage heating and cooling rates for an object inside a furnace.

I cannot demand. However, for the sake of clarity to this post and respect to its originator (M R Zeka), I recommend that you move your entire discussion above to a new thread.

Following is the thread

https://www.researchgate.net/post/How_to_calculate_rate_of_heat_transfer_from_the_object_and_Rate_of_heat_transfer_into_the_system