A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/mK, = 7900

A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/m·K, ρ = 7900 kg/m³, c_p = 477 J/kg·K, and α = 3.95 × 10^-6 m²/s) comes out of an oven at a uniform temperature of 400°C. The shaft is then allowed to cool slowly in a chamber at 150°C with an average convection heat transfer coefficient of h = 60 W/m²·K. Determine the temperature at the center of the shaft 20 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period. Solve this problem using analytical one-term approximation method (not the Heisler charts).