A tantalum rod of diameter 3 mm and length 120 mm is supported by two electrodes within a large vacuum enclosure. Initially the rod is in equilibrium with the electrodes and its surroundings, which are maintained at 300 K. Suddenly, an electrical current, I = 80 A, is passed through the rod. Assume the emissivity of the rod is 0.1 and the electrical resistivity is 95 × 10-8 Ω ∙ m. Use Table A.1 to obtain the other thermophysical properties required in your solution. Use a finite-difference method with a space increment of 10 mm.
(a) Estimate the time required for the midlength of the rod to reach 1000 K.
(b) Determine the steady-state temperature distribution and estimate approximately how long it will take to reach this condition.
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