Lumped-element model: Difference between revisions

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== Thermal systems==

A '''lumped-capacitance model''', also called '''lumped system analysis''',<ref>{{cite book | last = Incropera |author2=DeWitt |author3=Bergman |author4=Lavine | title = Fundamentals of Heat and Mass Transfer | url = https://archive.org/details/fundamentalsheat00incr_869 | url-access = limited | edition = 6th | year = 2007 | isbn = 978-0-471-45728-2 | publisher = John Wiley & Sons | pages = 260–261[https://archive.org/details/fundamentalsheat00incr_869/page/n267 260]–261}}</ref> reduces a [[thermal system]] to a number of discrete “lumps” and assumes that the [[temperature]] difference inside each lump is negligible. This approximation is useful to simplify otherwise complex [[differential equation|differential]] heat equations. It was developed as a mathematical analog of [[electrical capacitance]], although it also includes thermal analogs of [[electrical resistance]] as well.

The lumped-capacitance model is a common approximation in transient conduction, which may be used whenever [[heat conduction]] within an object is much faster than heat transfer across the boundary of the object. The method of approximation then suitably reduces one aspect of the transient conduction system (spatial temperature variation within the object) to a more mathematically tractable form (that is, it is assumed that the temperature within the object is completely uniform in space, although this spatially uniform temperature value changes over time). The rising uniform temperature within the object or part of a system, can then be treated like a capacitative reservoir which absorbs heat until it reaches a steady thermal state in time (after which temperature does not change within it).