Effect of a DC Field on Temperature Distribution in a Thin FGM Metal Line Subjected to Distributed Local Heating Sources

The effect of a direct-current field on the temperature distribution in a thin, non-uniform functionally graded metal line subjected to distributed local heat sources is investigated. The material properties of the metal line are assumed to vary over the span following a linear functional relationship. Bump-like heat sources of different profiles are considered to simulate the condition of distributed local heating of the metal line. The governing differential equations associated with the electrical and thermal problems are derived in terms of variable thermal and electrical conductivity of the material. The solution of the coupled boundary-value problem is then obtained using a finite-difference computational scheme. The temperature distributions in the FGM line are determined for different environmental conditions as a function of intensity of the DC field.