FYKOS Year 35 Series 3 Problem 5 — blacksmith's · FYKOS 35 #35.3.5

Physics · thermodynamics

Problem

Gnomes decided to forge another magic sword. They make it from a thin metal rod with radius R=1 cmR=1\,\mathrm{cm}, one end of which they maintain at the temperature T1=400 ∘\mathupCT_1 = 400\,\mathrm{^\circ\mskip-2mu\mathup{C}}. The rod is surrounded by a huge amount of air with the temperature T0=20 ∘\mathupCT_0 = 20\,\mathrm{^\circ\mskip-2mu\mathup{C}}. The heat transfer coefficient of that mythical metal is α=12 W⋅m−2⋅K−1\alpha = 12\,\mathrm{W\cdot m^{-2}\cdot K^{-1}} and the thermal conductivity coefficient is λ=50 W⋅m−1⋅K−1\lambda = 50\,\mathrm{W\cdot m^{-1}\cdot K^{-1}}. The metal rod is very long. Where closest to the heated end can gnomes grab the rod with their bare hands if the temperature on the spot they touch is not to exceed T2=40 ∘\mathupCT_2 = 40\,\mathrm{^\circ\mskip-2mu\mathup{C}}? Neglect the flow of air and heat radiation.

Related theory

Browse the problem library