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Question On Glossary Of Terms In Physics

  1. Apr 18, 2010 #1
    Hello everyone,

    Can someone please tell me what is the meaning of "lumped" term in heat transfer?

    Regards

    Huygen
     
  2. jcsd
  3. Apr 18, 2010 #2
    The idea behind the term 'lumped' is that we take a single value to represent some property or parameter that is actually distributed or variable in space.
    This idea is used in several branches of engineering to solve the controlling (differential) equations.

    In heat ransfer the assumption is that temperature within a control volume is even, at any instant. Even does not mean constant, just that there is no temperature variation within the control volume.

    This assumption allows us to use the equation

    Input minus Output = Accumulation minus Internal Generation

    in differential form with respect to time.

    So if we plunge a hot workpiece into a quenching vat and assume the temperature of the whole workpiece to be one temperature, T then the rate of cooling is found by solving the differential equation that arises from equating the heat transfer across the boundary to the rate of temperature change of the workpiece

    [tex] - hSurfaceAre{a_{workpiece}}(T - {T_{vat}})\quad = \quad Mas{s_{workpiece}}{c_{workpiece}}\frac{{dT}}{{dt}}[/tex]

    There are quite a few web presentations about this
    look up the lumped capacitanc method
    you should also look up the Biot Number.
     
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