Calculating heat transmission loss in a thick glass

Hi.

Do anybody here knows, if and how much and how quick a thick tempered (60 degrees celcius) glass (85mm) of size 500mm * 500mm looses it temperature?

What I want to know, is the temperature profile "out-of-plane" inside the 50-100mm thick glass and related to time.

The glass is surrounded by air of ambient temperature (20 degrees celcius).

I know there are several programs out there, who could answer this question, such as COMSOL 3.5, ANSYS Multiphysics, NAFEMS etc. But I don't have acces to these fancy software packages.

Did anyone here made some calculations related to the above?

How much heat energy/temperature do a thick window as described above loose within 5, 10 and 15 minutes surrounded by ambient temperature?

Thanks in advance

Frank Nielsen
IknowalittleAsked:
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IknowalittleConnect With a Mentor Author Commented:
WOW!!!

I just found this site with experts a few days ago and posted my first question at that same time.

I must say, that I'm really impressed!

I had very qualified and quick answer. I will certainly be a fixed member of this site. Hopefully I can also offer ansers to other people in the future.
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I just have a few additional questins related to the solution presented.

1) I think, the initial temperature used in the calculation is not 60 degrees celcius, but 50 degrees celcius?

    This is ok, because we had four different glasses at four different temperatures for testing, one of these four temperatures was 60 degrees celcius and another was 51 degrees celcius.

So I'm happy with the solution as it is. It shows me what I wanted to se, that the temperature decreased (a lot) within the first ten-fifteen minutes.

2) What program did you use for this calculation?

3) What is your background? Do you study or?


Best regards

Frank Nielsen
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InteractiveMindCommented:
Do you happen to know the temperature of the glass at a particular time t>0?
If so, then we could work it out using Newton's law of cooling
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InteractiveMindCommented:
(I've requested that this question is reopened, as I did not actually answer the question. The real experts will hopefully be along soon.)

Authors comment:

"No, sorry. We didn't had any equipment to measure the temperature of the glas.

The glass was originally put into a climate chamber for 24 hours at temperature 60 degrees celcius. It was then removed from the chamber and was supposed to be used for some specific purpose with an expected temperature of the thick glass at 60 degrees. But I could put my fingers and my whole hand on one side of the glass after approx. 10 minutes, and it didn't felt uncomfortable at all to do this; I could keep my hand on the glass without problems, and it didn't felt like 60 degrees at all, not even 50 degrees. Maybe it is just the outer layers of the glass who loosed its temperature (quickly) ? Hope to hear more from you."
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aburrCommented:
did the author not say that the temperature was 60 degrees at t = 0?
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"What I want to know, is the temperature profile "out-of-plane" inside the 50-100mm thick glass and related to time."

If I understand your question, the answer to this part is no.
The edges will be at a different temperature than the interior.
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The glass will begin cooling immediately and will always be below 60 degrees. It will approach 20 degrees. (rapidly at first, then more slowly) The rest of your questions can be answered with more info about the exact type of glass. (Info needed - heat capacity and thermal conductivity.)
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Darrell ThomasConnect With a Mentor Commented:
aburr is correct with "rapidly at first, then more slowly.  Also, the core of the glass remains warmer than the edges for quite some time.  I ran the dimensions and physical properties to get the attached graphs of Temp distro in K.  Table below is in C.

Time(s)     Edge temp(C)    Core temp(C)
60              39                     47
300            45                     37
600            41                     36
900            39                     33

Arrows on graph represent heat flux.

Assumptions:
initial condition: 60C (converted to Kelvin),
boundary conditions: 20C (converted to Kelvin)
model:  Conduction/convection partial differential equation (parabolic)
geometry:  antisymmetric about the 500mm axis, i.e. looked at glass on 500x85 2D plot
physical properties:  (Appendix I of Ozisik's "Heat Conduction (2ed):
density of glass 2700 kg/m^3
C_p= 0.84 kJ/kgC
k= 1.3 W/mC
took a "reasonable guess at the convection coefficient (remember, it's not a physical property, but rather a constant of proportionality, and neglected radiation.



one.jpg
five.jpg
ten.jpg
fifteen.jpg
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Darrell ThomasConnect With a Mentor Commented:
Oops.. typed in edge and core backwards... the core is always warmer than the edge here.  

Time       Edge     Core
01 min      39            47
05 min      37            45
10 min      36            41
15 min      33            39

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IknowalittleAuthor Commented:
Nothing to write here
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Darrell ThomasCommented:
1)  No, the model started at 60.  You lose 10 degrees in the first 60 seconds.  There is one unknown value (convective heat transfer coefficient) in which I took a reasonable guess.  I.e. was there wind blowing on it?  was the air still?  etc... the heat transfer between the glass and air is governed by this coeffiient (and the temp difference).  This means the answer is +/- 10% or so.

2) I used a PDE (partial differential equation) solver in Matlab.  There are other open source solvers (scilab, octave, LISA, etc.. as you mentioned above.  I just stumbled across this problem last night and told myself, "I know how to do that! Let me help this guy out!"  Drop me a note if you need anything else.  darrellthomas67 at gmail dot com.

3)  Right now I'm in the Air Force, but I'm getting ready to retire soon.  Now I have to figure out what I want to do when I grow up :).  For study, I have a Master's in Mechanical/Aerospace engineering.
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IknowalittleAuthor Commented:
No, sorry. We didn't had any equipment to measure the temperature of the glas.

The glass was originally put into a climate chamber for 24 hours at temperature 60 degrees celcius. It was then removed from the chamber and was supposed to be used for some specific purpose with an expected temperature of the thick glass at 60 degrees. But I could put my fingers and my whole hand on one side of the glass after approx. 10 minutes, and it didn't felt uncomfortable at all to do this; I could keep my hand on the glass without problems, and it didn't felt like 60 degrees at all, not even 50 degrees. Maybe it is just the outer layers of the glass who loosed its temperature (quickly) ? Hope to hear more from you.
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