Chapter 3, Problem 3.57P

A long, highly polished aluminum rod of diameter $D=35mm$ is hung horizontally in a large room. The initial rod temperature is $T_i=90°C$, and the room air is $T_{\infty }=20°C$. At time $t_1=1250s$, the rod temperature is $t_1=65°C$, and, at time $t_2=6700s$, the rod temperature is $T_2=30°C$. Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for $0\le t\le 10,000s$. 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 $\bar{T}=\left(T_i+T_{\infty }\right)/2$. For all cases, evaluate properties at $\bar{T}=\left(T_i+T_{\infty }\right)/2$.