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Newton's law of cooling

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I am trying to model a cilinder at 200 ºC that its cooling following the Newton's Law of cooling.

What I want is to model how the temperature decrease with time. I need help., Someone can help me to model this?

Thank you.

5 Replies Last Post 28 mai 2012, 06:34 UTC−4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 23 mai 2012, 13:16 UTC−4
Hi

the simplest is to select 2D-axi or 3D, Heat Transfer physics and time dependent solver, draw your cylinder geometry , give it a material data property of your choice.
Define the initial conditions to be 200[degC]

Then you need to say what kind of heat exchange you have, how is the cylinder "cooling" ? one way is all surrounded by air (a cylinder floating in air) and then a good engineering book would tell you that the heat exchange follows a rule with typically Power = h*Area*(T-T0) with h = 5 [W/m^2K] and lets say T0=20°C ambient temperature

Then you need to set the time series, the default range(0,0.1,1) this is in seconds, far too short if your object is large.

You can estimate the time by calculating the total energy stored in Joules = Volume*rho*Cp*(T-T0), estimate the total cylinder surface Area exchanging heat, and then with h*Area*(T-T0) you have the power loss, and the ratio of these two values give you roughly the half life of your temperature, so take three times this duration, perhaps it's 3 hour, so add to your range(0,0.1,1)*3[h] and off you go: solve

--
Good luck
Ivar
Hi the simplest is to select 2D-axi or 3D, Heat Transfer physics and time dependent solver, draw your cylinder geometry , give it a material data property of your choice. Define the initial conditions to be 200[degC] Then you need to say what kind of heat exchange you have, how is the cylinder "cooling" ? one way is all surrounded by air (a cylinder floating in air) and then a good engineering book would tell you that the heat exchange follows a rule with typically Power = h*Area*(T-T0) with h = 5 [W/m^2K] and lets say T0=20°C ambient temperature Then you need to set the time series, the default range(0,0.1,1) this is in seconds, far too short if your object is large. You can estimate the time by calculating the total energy stored in Joules = Volume*rho*Cp*(T-T0), estimate the total cylinder surface Area exchanging heat, and then with h*Area*(T-T0) you have the power loss, and the ratio of these two values give you roughly the half life of your temperature, so take three times this duration, perhaps it's 3 hour, so add to your range(0,0.1,1)*3[h] and off you go: solve -- Good luck Ivar

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Posted: 1 decade ago 24 mai 2012, 06:28 UTC−4
Hi, Ivar

Thank you for your answer.

I have other questions,

Where do I "say" to the software that the cylinder is surrounding by air?

In "heat transfer in solids" Do I have to specify a physics or boundary conditions to make the simulation of cooling?

how can I plot Temperature (x axis) vs time (y axis).

Thank you.

Best Regards.
Hi, Ivar Thank you for your answer. I have other questions, Where do I "say" to the software that the cylinder is surrounding by air? In "heat transfer in solids" Do I have to specify a physics or boundary conditions to make the simulation of cooling? how can I plot Temperature (x axis) vs time (y axis). Thank you. Best Regards.

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 24 mai 2012, 07:13 UTC−4
Hi

in HT physics (Heat Transfer) set set the T initial to your initial cylinder temperature, add a Convective Cooling BC, select all boundaries, set your h i.e. 5 [W/m^2/K] and set your ambient air temperature (or leave it to the default 20°C. select the time of time solver running, as you have a cooling type dcay, you could use a time range of the type

2^{range(0,1,16)}*1[min]

then solve, thats all ...

Then for the postprocessing, it is nicer to either look at the temperature in °C or to substract the ambient air temperature, and plot T-20[degC]

--
Good luck
Ivar
Hi in HT physics (Heat Transfer) set set the T initial to your initial cylinder temperature, add a Convective Cooling BC, select all boundaries, set your h i.e. 5 [W/m^2/K] and set your ambient air temperature (or leave it to the default 20°C. select the time of time solver running, as you have a cooling type dcay, you could use a time range of the type 2^{range(0,1,16)}*1[min] then solve, thats all ... Then for the postprocessing, it is nicer to either look at the temperature in °C or to substract the ambient air temperature, and plot T-20[degC] -- Good luck Ivar

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Posted: 1 decade ago 28 mai 2012, 05:53 UTC−4
Hi, Ivar.

I have tried to do what you said in your previous mail.

But I have some problems.

How can I take the data to plot Temperature versus time?
Where are the solutions data?
In the solution, I only see the cylinder at the same temperature, I would like to see the evolution from high temperature (120ºC) to ambient Temperature, Is this possible?

Could you recommend me any book or tutorial in pdf format to understand a lear to use the comsol 4.2a software?

Thank you.

Regards.
Hi, Ivar. I have tried to do what you said in your previous mail. But I have some problems. How can I take the data to plot Temperature versus time? Where are the solutions data? In the solution, I only see the cylinder at the same temperature, I would like to see the evolution from high temperature (120ºC) to ambient Temperature, Is this possible? Could you recommend me any book or tutorial in pdf format to understand a lear to use the comsol 4.2a software? Thank you. Regards.

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 28 mai 2012, 06:34 UTC−4
Hi

if you have a time dependent solver selected with a time range of the type range(0,0.1,1) (or whatever you have) then you can access the time data in the main plot node as a pull down selection item. By default you have the LAST time step of the solver. You can also make player movie plots of 2D or 3D data

Now if you want to look at a particular variable over time the easiest is to estimate the variable in a "Results - Derived Variable" node (right click add a global or integration or average node and get your variable defined). Do not forget that most variables are fields and are in units of densities so these must be integrated or averaged over the appropriate Boundries (in 2D-axi you often need to add the loop length 2*pi*r, or in 2D the "depth" else you have "per meter " results)

To learn COMSOL you have many videos on the COMSOL web site, you have excellent COMSOL training courses, the conferences and the workshops. then there are several books (search for "books" on the main web site)

--
Good luck
Ivar
Hi if you have a time dependent solver selected with a time range of the type range(0,0.1,1) (or whatever you have) then you can access the time data in the main plot node as a pull down selection item. By default you have the LAST time step of the solver. You can also make player movie plots of 2D or 3D data Now if you want to look at a particular variable over time the easiest is to estimate the variable in a "Results - Derived Variable" node (right click add a global or integration or average node and get your variable defined). Do not forget that most variables are fields and are in units of densities so these must be integrated or averaged over the appropriate Boundries (in 2D-axi you often need to add the loop length 2*pi*r, or in 2D the "depth" else you have "per meter " results) To learn COMSOL you have many videos on the COMSOL web site, you have excellent COMSOL training courses, the conferences and the workshops. then there are several books (search for "books" on the main web site) -- Good luck Ivar

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