Question

In heat transfer, if we neglect the lumped capacity system approach and use the heat diffusion equation to solve transient conduction problems, why do they consider infinite and semi infinite geometries?

and what are the differences between infinite and semi infinite for spheres/plates or cylinders?

Answer 1

Infinite Body: A plate whose thickness is small relative to the other dimensions can be modeled as an infinitely large plate, except very near the outer edges. But the edge effects on large bodies are usually negligible.

Thus, a large plane wall such as the wall of a house can be modeled as an infinitely large wall for heat transfer purposes.

A long cylinder whose diameter is small relative to its length can be analyzed as an infinitely long cylinder.

Semi Infinite Body: This idealized body is used to indicate that the temperature change in the part of the body in which we are interested (the region close to the surface) is due to the thermal conditions on a single surface.

The earth, for example, can be considered to be a semi-infinite medium in determining the variation of temperature near its surface.

Also, a thick wall can be modeled as a semi-infinite medium if all we are interested in is the variation of temperature in the region near one of the surfaces, and the other surface is too far to have any impact on the region of interest during the time of observation.