A long, highly polished aluminum rod of diameter D = 35 mm is hung horizontally in a large room. The initial rod temperature is T_i = 90°C, and the room air is T_∞ = 20°C. At time t₁ = 1250 s, the rod temperature is T₁ = 65°C, and, at time t₂ = 6700s, the rod temperature is T₂ = 30°C. Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for 0 ≤ t ≤ 10,000 s. On the same graph, plot the rod temperature versus time for a constant value of the convection heat transfer coefficient, evaluated at a rod temperature of T = (T_i + T_∞)/2. For all cases, evaluate properties T = (T_i  + T_∞)/2.

h = C(T – T∞)ⁿ