Lumped System Analysis Interior temperatures of some bodies remain essentially uniform at all times during a heat transfer process. The temperature of such bodies are only a function of time, T = T(t). The heat transfer analysis based on this idealization is called lumped system analysis.
What do you mean by lumped system?
A lumped system is one in which the dependent variables of interest are a function of time alone. In general, this will mean solving a set of ordinary differential equations (ODEs) A distributed system is one in which all dependent variables are functions of time and one or more spatial variables.
What is the lumped heat capacity method?
The lumped thermal capacity model is the simplest transient heat conduction approach. In this model, the temperature of the solid body is a function of the time only, which means that the temperature is assumed to be spatially independent (uniform).
What is meant by a semi infinite solid?
Semi-infinite solid: An idealized body that has a single plane surface and extends to infinity in all directions. The earth can be considered to be a semi-infinite medium in determining the variation of temperature near its surface.
Which material is suitable for lumped analysis?
Therefore, small bodies with high thermal conductiviy are good candidates for lumped system analysis, especially when they are in medium that is a poor conductor of heat (such as air or another gas) and motionless.
What is lumped system analysis when it is applicable?
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.
What does lumped in mean?
To put or categorize someone or something in the same manner or group as someone or something else, especially in a careless, hasty, or indiscriminately. Just because I’ve dabbled in drugs and alcohol doesn’t mean I deserve to be lumped in with those degenerates.
What do you mean by lumped heat capacity body?
The lumped-heat-capacity method of analysis is used in which no temperature gradient exists. This means that the internal resistance of the body (conduction) is negligible in comparison with the external resistance (convection). i.e small h and large k.
Can the earth or thick walls be considered semi-infinite media with respect to heat transfer?
Can the Earth and thick walls be considered semi-infinite media with respect to heat transfer? Yes, both can be considered semi-infinite media. Thus a large value of Fourier number indicates faster propagation of heat through body.
