  Traditional finite element method is a well-established method to solve
various problems of science and engineering. Different authors have used
various methods to solve governing differential equation of heat conduction
problem. In this study, heat conduction in a circular rod has been considered
which is made up of two different materials viz. aluminum and copper. In
earlier studies parameters in the differential equation have been taken as
fixed (crisp) numbers which actually may not. Those parameters are found in
general by some measurements or experiments. So the material properties are
actually uncertain and may be considered to vary in an interval or as fuzzy and
in that case complex interval arithmetic or fuzzy arithmetic has to be
considered in the analysis. As such the problem is discretized into finite
number of elements which depend on interval/fuzzy parameters. Representation of
interval/fuzzy numbers may give the clear picture of uncertainty. Hence
interval/fuzzy arithmetic is applied in the finite element method to solve a
steady state heat conduction problem. Application of fuzzy finite element
method in the said problem gives fuzzy system of linear equations in general.
Here new methods have also been proposed to handle such type of fuzzy system of
linear equations. Corresponding results are computed and has been reported
here.
