Hand calculation for simple short cylinder conduction and convection analysis needed.....

[gregf84]

Hello,

I created a simple Ls-Dyna FEA heat transfer conduction and convection model. This model is a simple solid short cylinder (made of solid elements). The outer surface nodes of the cylinder has a high temperature applied (163 C). A convection interface is applied to the cylinder outer surface also. The cylinder sits in air at normal room temperature with free convection. This event happens over 300 seconds (5 minutes). I ran this model to get the interior temperatures of the nodes near the center of the cylinder after 300 seconds. The analysis is not an issue but I want to find out if a hand calculation method exists for this heat transfer case. I want to compare a hand calculation to the LS-Dyna FEA analysis. Any help is appreciated.

 

[chicopee]

You'll have to set up additional nodes in the interior of the solid block and then do a numerical analysis by setting up at each node Qin-Qout= U2-U1= mCv(T2-T1)/t. At the boundaries, Qout= convective and radiative heat transfer and there will lie the problem of solving the outer node temperature because of the T^4 power from the radiation heat transfer. Work the itineration from the outer surface at one end toward the center of the solid cylinder and to the midpoint of its length in increments. I think that the increments developed from a pie shape of an incremental thickness may work out better than the heat transfer method using prismatic elements proposed in text books.

 

[prex]

It is not clear from your description what the initial temperatures are: is the full cylinder initially at 163 deg.C or what?
Anyway I think that if you want to compare with the distribution of temperatures on the CL after 300 secs, then only a finite differences approach would work. What you could compare with FEM is the average temperature of your body vs time, as this is more easily calculated by formula. The approximation depends also very much on how big (or small) is your Nusselt number.

prex
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[gregf84]

The solid cylinder is made of an epoxy adhesive. At time zero all nodes of the cylinder both exterior surface and interior nodes are at 23 C. But after 1.0 sec a uniform temperature of 163 C is applied to all exterior surface nodes on the cylinder for 5 minutes. The cylinder sits in air which is at generally at 23 C and free convection can occur. The cylinder is 50 mm in height and has a diameter of 25 mm. This is not a problem to simulate with LS-Dyna FEA software but what I need to know is if this can be hand calculated also? Thanks for your help.

 

[gregf84]

Chicopee thanks for your input but to be honest, I do not understand your approach. Can you be more detailed and/or included pictures? Also you can send me a URL link that describes your approach, if a link exists. Thanks.