METHOD OF MODELING THERMAL PROBLEMS USING A NON-DIMENSIONAL FINITE ELEMENT METHOD

The method of modeling thermal problems using a non-dimensional finite element method is a computerized method for modeling thermal systems that relies on the variational principle. The variational principle specifies the total potential of the system, given by a scalar quantity Π, which is defined by an integral form for a continuum problem. The solution of the continuum problem is a function that makes Π stationary with respect to the state variables. The governing equation of the problem is used to calculate the potential Π. The non-dimensional form of the potential is obtained by insertion of the defined non-dimensionless parameters. The element non-dimensional stiffness matrix and the non-dimensional load vectors are then obtained by invoking the stationarity of the non-dimensional potential Π with respect to a non-dimensional temperature vector {θ}.