In this article we have presented a modified form of traditional fuzzy finite element method. Here the involved fuzzy numbers are changed into intervals through α -cut. Then the intervals are transformed into crisp form by using some transformation. Crisp representations of intervals are defined by symbolic parameterization. The traditional interval arithmetic is then modified using the crisp representation of intervals. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element method converts the governing differential equation into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methodes) have been used to solve distribution of temperatures in a conduction-eonvection system for a test problem. Here we have considered both Triangular Fuzzy Number (TFN) and Trapezoidal Fuzzy Number (TRFN) for uncertain parameters involved in the system. Finally the obtained results are compared and it has been seen that the proposed methods are reliable and may be applicable to other heat and mass transfer problems.