The PDE.

  Since we have to find a temperature at every point (x,t) in the strip, we expect that we will need a corresponding equation at every point (x,t). The equation is the one-dimensional heat equation  

$$\d Tt = \kappa \frac{\partial^2 T}{\partial x^2}$$ (2)

The same equation appears in other areas. For example, unsteady viscous flow past a plate is governed it. Mathematically, it is classified as a ``parabolic'' PDE.