The boundary conditions.

  In the example, the temperature is given at all four boundaries as  

$$T(y,0)=100, \quad T(y,\ell) = 0, \quad T(x,0) = T(x,h)$$ (16)

Such a problem, with boundary conditions around a closed boundary, is called a boundary value problem (BVP).

In contrast, the previous unsteady heat conduction and convection equation problems were examples of initial-boundary value problems (IBVP). There, one of the independent variables was physically a time. The initial conditions in time were given at a starting time, none at a later time. The solution did not depend on what occurs at later times. In contrast, the temperature inside the plate depends on the temperature of all the boundaries.