Content deleted Content added
my best attempt to deal with this long, complex, and convoluted sentence Tag: Reverted |
Link suggestions feature: 3 links added. |
||
| (10 intermediate revisions by 5 users not shown) | |||
Line 1:
{{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 ==
Line 16 ⟶ 13:
=== 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.
Line 54 ⟶ 51:
==== Thermal purely resistive circuits ====
A useful concept used in heat transfer applications once the condition of steady state heat conduction has been reached, is the representation of thermal transfer by what is known as thermal circuits. A thermal circuit is the representation of the resistance to heat flow in each element of a circuit, as though it were an [[electrical resistor]]. The heat transferred is analogous to the [[electric current]] and the thermal resistance is analogous to the electrical resistor. The values of the thermal resistance for the different modes of heat transfer are then calculated as the denominators of the developed equations. The thermal resistances of the different modes of heat transfer are used in analyzing combined modes of heat transfer. The lack of "capacitative" elements in the following purely resistive example, means that no section of the circuit is absorbing energy or changing in distribution of temperature. This is equivalent to demanding that a state of steady state heat conduction (or transfer, as in radiation) has already been established.
Line 89 ⟶ 87:
{{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.}}
Line 162 ⟶ 160:
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 ==
| |||