What is lumped system analysis? When is it applicable?

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written 8.4 years ago by

teamques10 ★ 68k

All solids have finite thermal conductivity and there will be always a temperature gradient inside the solid whenever heat is added or removed.
However, for solids of large thermal conductivity with surface areas that are large in proportion to their volume like plates and thin metallic wires, the thermal resistance can be assumed to be small or negligible in comparison with the convective resistance at the surface.
The process in which the internal resistance is assumed negligible in comparison with its surface resistance is called the Newtonian heating or cooling process.
The temperature in this process is considered to be uniform at a given time.
Such an analysis is called Lumped parameter analysis because the whole solid, whose energy at any time is a function of its temperature and total heat capacity is treated as one lump.
We can apply the lumped parameter analysis if βi<1. (βi=Biot Number).

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