A long 35-cm-diameter cylindrical shaft made of stainless steel 304 (k = 14.9 W/m·K, r = 7900 kg/m3, cp = 477 J/kg·K, and a 5 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).

Not sure where I went wrong on this please show a drawing also

A large steel plate (1.0% carbon) 5.0 cm thick is initially at a temperature of 425 °C. It is suddenly exposed on both sides to a convective environment with h = 285 W/m² °C, and T. = 65 °C. Determine the centerline temperature and the temperature inside the body 1.25 cm from the surface after 24 minutes. k= 41 W/m-K a = 1.172 × 105 m²/s (at 20 °C)

A short brass cylinder (p = 8530 kg/m³, cp=0.389 kJ/kg-K, k=110 W/m-K, and a = 3.39×10−5 m²/s) of diameter 4 cm and height 20 cm is initially at a uniform temperature of 140°C. The cylinder is now placed in atmospheric air at 20°C, where heat transfer takes place from the cylinder 15 min after the start of the cooling by convection with a heat transfer coefficient of 40 W/m2.K. Solve this problem using the analytical one-term approximation method. Interpolate table 4-2 to obtain constants ₁ and A₁. For Biot number values less than 0.01 approximate it as 0.01 for use in Table 4-2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 20 cm Brass cylinder 4 cm TiºC Ambient air 20°C Calculate the center temperature of the top surface of the cylinder. The center temperature of the top surface of the cylinder is 61 °C.