A numerical study of cylindrical electric furnace performance using the finite element method

Abstract

Described is a development of a new finite element-method-based numerical technique to carry out the steady-state thermal analysis of a cylindrical electric furnace. Such furnaces are in common use for the continuous melting of glass rods. Our aim was to use an iterative technique in which components of the furnace were visited sequentially and which would require less memory and would serve as an alternative to creating a global matrix encompassing the entire solution domain. A finite element method code was written in C++ to accomplish this.

The code was first used in a test case involving a thermally connected system consisting of three cylindrical sectors. Then upon running the code for a full furnace assembly it was found that although the approach was valid, the iterative technique took much longer to converge than had been anticipated. Attempts were made to speed up the convergence and to reduce the time required for executing a single iteration. While some modest improvement was achieved, convergence could not be speeded up to a sufficient degree to make this new approach practical using current generation computers.

It was concluded from this research that though the new approach is theoretically valid, it can not be practically implemented until significant improvements in machine speed or new, more efficient algorithms are available. The new approach, however, is a viable option for users who have time to wait for a converged solution but who do not have the resources to buy an expensive workstation.