1. Multi-Dimensional Transient Conduction
So far we have only examined transient behavior in which conduction takes place in only one direction.
There are many instances when heat tranfer (via conduction) is significant in more than one direction.
Examples: A Short Cylinder, a Rectangular Bar
In such cases, when multi-dimensional conduction has to be taken into account, the transient behavior of the system can be analyzed by superposing the solution of simpler geometries.
E.g. A Short Cylinder can be viewed as the inersection of a Plane Wall and an Infinite Cylinder.
. Then the temperature distribution for the Short Cylinder is the product of the distributions a Plane Wall and an Infinite Cylinder.

2. Multi-Dimensional Transient Conduction Various Configurations