## Boundary and Initial Conditions

**Boundary and Initial Conditions**

As for another **differential equation**, the solution is given by **boundary** and **initial conditions**. With regard to the boundary conditions, there are several common possibilities that are simply expressed in mathematical form.

Because the heat equation is second order in the spatial coordinates, to describe a heat transfer problem completely, **two boundary conditions** must be given **for each direction** of the coordinate system along which heat transfer is significant. Therefore, we need to specify four boundary conditions for two-dimensional problems, and six boundary conditions for three-dimensional problems.

Four kinds of boundary conditions commonly encountered in heat transfer are summarized in following section:

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