This seems a bit generic. What do you mean by an analogy?Anything more specific?
If I understand your question correctly this may be helpful.
You can envision a control volume around an empty pipe with a slow moving fluid such as molasses entering it. When fluid starts to flow the pipe is filling more and more with fluid. So more fluid is entering the control volume than is leaving it.
Picture now beside the pipe there is a solid bar that is cold and being heated from one end. This is analogous to transient state heat conduction because when heating begins there is more energy entering the bar then is leaving it. In this case the "flow" is of energy not fluid.
Eventually the fluid will reach the end of the pipe and the flow through the control volume will be steady. Similarly at steady state the energy entering the rod control volume will be equal to the energy leaving it.
Of course, the fluid flow is driven by a pressure difference and the heat conduction is driven by a temperature difference.
All analogy’s have their limits but I found this a useful way to imagine it.
Electrical analogy for transient heat conduction in solids.
http://nvlpubs.nist.gov/nistpubs/jres/61/jresv61n2p105_A1b.pdf
Dear Aashray
Robert Smusz 's answer (above) is probably one of the best. The electric analogy seem to be a suitable approach for your problem. From own experience I can state that a carefully built analog provides good and reliable results for steady state problems.
Transient problems might be investigated as well. The crutial point is that you have to add sufficient capacitors to simulate the thermal inertia which is manually more difficult in reality that it appears at first (theoretical) glance. How good your result is mostly depends on the quality of your hardware model.
Due to the availability of computing power these techniques became more and more obsolete. If you do not have a suitable finite element program available, a good approach is to build up an analog electric network (a mesh out of resistors and capacitors against grount added at the meshpoints) in a computer program.
Some additional hints you might find in
Eckert, E. R. G. & Drake, R. M. jr.:
Analysis of Heat and Mass Transfer.
McGraw-Hill, 1972, ISBN 0-07-085200-6
If you search the net you'll probably find articles dealing with heat transport in electrical components etc.
Regards
Nikolaus Hannoschöck
I think Dave Stanier analogy is beter if you want to get an overall picture of the transient and I found Smusz 's answer pretty technical. I rather recommend
Lienhard&Lienhard (2005) "A HEAT TRANSFER TEXTBOOK" 5th chapter.
It´s correct, clear and plenty of examples.
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