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{{short description|Simplification of a physical system into a network of discrete components}}
{{Technical|date=August 2019}}
{{Refimprove|date=August 2023}}
[[File:Ohm's Law with Voltage source TeX.svg|thumb|Representation of a lumped model
The '''lumped-element model''' (also called '''lumped-parameter model''', or '''lumped-component model''')
== Electrical systems ==
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=== Lumped-matter discipline ===
The '''lumped-matter discipline''' is a set of imposed assumptions in [[electrical engineering]] that provides the foundation for '''lumped-circuit abstraction''' used in [[Network analysis (electrical circuits)|network analysis]].<ref>Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare ([http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf PDF]), [[Massachusetts Institute of Technology]].</ref> The self-imposed constraints are:
# The change of the magnetic flux in time outside a conductor is zero. <math display="block">\frac{\partial \
# The change of the charge in time inside conducting elements is zero. <math display="block">\frac{\partial q} {\partial t} = 0</math>
# Signal timescales of interest are much larger than [[propagation delay]] of [[electromagnetic waves]] across the lumped element.
The first two assumptions result in [[Kirchhoff's circuit laws]] when applied to [[Maxwell's equations]] and are only applicable when the circuit is in [[steady state (electronics)|steady state]]. The third assumption is the basis of the lumped-element model used in [[Network analysis (electrical circuits)|network analysis]]. Less severe assumptions result in the [[distributed-element model]], while still not requiring the direct application of the full Maxwell equations.
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{{Main|Newton's law of cooling}}
'''Newton's law of cooling''' is an [[empirical relationship]] attributed to English physicist [[Isaac Newton|Sir Isaac Newton]] (1642–1727). This law stated in non-mathematical form is the following:
{{Quotation|The rate of heat loss of a body is proportional to the temperature difference between the body and its surroundings.}}
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A simplifying assumption in this ___domain is that all heat transfer mechanisms are linear, implying that radiation and convection are linearised for each problem.
Several publications can be found that describe how to generate lumped-element models of buildings. In most cases, the building is considered a single thermal zone and in this case, turning multi-layered walls into lumped elements can be one of the most complicated tasks in the creation of the model. The dominant-layer method is one simple and reasonably accurate method.<ref>Ramallo-González, A.P., Eames, M.E. & Coley, D.A., 2013. Lumped Parameter Models for Building Thermal Modelling: An Analytic approach to simplifying complex multi-layered constructions. Energy and Buildings, 60, pp.174-184.</ref> In this method, one of the layers is selected as the dominant layer in the whole construction, this layer is chosen considering the most relevant frequencies of the problem.
Lumped-element models of buildings have also been used to evaluate the efficiency of domestic energy systems, by running many simulations under different future weather scenarios.<ref>Cooper, S.J.G., Hammond, G.P., McManus, M.C., Ramallo-Gonzlez, A. & Rogers, J.G., 2014. Effect of operating conditions on performance of domestic heating systems with heat pumps and fuel cell micro-cogeneration. Energy and Buildings, 70, pp.52-60.</ref>
== Fluid systems ==
== See also ==
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