The paper deals with problems of convergence when solving partial differential equations by computers. Practical experiences are given concerning calculations of heat transfer through solving temperature and velocity fields in vertical cooling ducts of transformer windings. This problem leads to a system to two elliptic simultaneous partial differential equations with boundary conditions of Dirichlet's or Neumann's type. For solving the net-point method and the overrelaxation method with constant as well as variable value of the overrelaxation coefficient was used. In the paper there are many examples together with the convergence of their solutions for different procedures of solution and different values of the overrelaxation coefficient.