The effect of stringent boundary conditions on the solution of a transient heat conduction problem

A notation system is proposed for the writing of the finite difference equations related to a conduction heat transfer problem in a composite medium with variable thermal properties. An example is worked out with Euler explicit, Euler implicit and Crank-Nicolson methods. Special care is taken of the conductivity expression and an analysis shows the importance of using mean conductivity values around the nodes especially when stringent Dirichlet boundary conditions are imposed.