4 - Transient Heat Conduction

Question 1

When is lumped system analysis applied?

Answer 1

When interior temperature of the body remains essentially uniform at all times during a heat transfer process.
Temperature can be taken to be a function of time only, T(t).
High convection heat transfer coefficient (h) and thermal conductivity (k).

Question 2

How does the temperature of a lumped system change with time?

Answer 2

Temperature of the body approaches the ambient/environment temperature (Tinfinity) exponentially.

Question 3

When does heat transfer to or from a body reach its maximum value?

Answer 3

When the body reaches the environment temperature.

Question 4

When is lumped system analysis applicable?

Answer 4

Biot number is less than or equal to 0.1

Question 5

Which bodies are most likely to satisfy the criterion for lumped system analysis?

Answer 5

Small bodies
High thermal conductivities
Low convection coefficients

Question 6

What is the Fourier number?

Answer 6

A measure of heat conducted through a body relative to heat stored (i.e. a larger Fourier number indicates faster propagation of heat through a body).

Question 7

Define semi-infinite solid

Answer 7

An idealised body that has a single plane surface and extends to infinity in all directions.

Question 8

When can a body be modelled as a semi-infinite solid?

Answer 8

A thick wall if we are only interested in the variation of temperature in the region near one of the surfaces, and any other surface is too far to have any impact on the region of interest during the time of observation.
For short periods of time, most bodies can be modelled as this since heat does not have sufficient time to penetrate deep into the body.