A computational study of the impact of the Wiedemann-Franz-Lorenz law on the thermal response of nichrome cylinders

摘要

This paper reports an investigation of the impact of temperature-dependent electrical and thermal conductivities ( as governed by the classical Weidemann-Franz-Lorenz law) on the thermal response of nickel-chromium ( nichrome) alloy cylinders. The relationship between the conductivities and temperature for nichrome is seen to be quite well characterized by a quadratic dependence. This relationship is incorporated into the heat conduction equation and the thermal response of an electrically heated, cylindrical specimen cooled by free convection is studied. It is seen that the temperature dependent response of the cylinder consistently reaches an average steady state temperature and a time to steady state that are lower than the temperature-independent case, e. g. by about 30% and 25%, respectively, for a thin disc. It is also demonstrated that if the temperature dependence of conductivities were ignored when determining these properties from test data, the assumption translates into an under-prediction of temperature by about 25 degrees C at certain locations in the cylinder; the implications of these errors are discussed.