Chapter 5, Problem 5.38P

A long. highly polished aluminum rod of diameter $D=35\text{mm}$ is hung horizontally in a large room. The initial rod temperature is $T_i=90°\text{C,}$ and the room air is $T_{\infty }=20°\text{C}\text{.}$ At time $t_1=1250\text{s,}$ the rod temperature is $T_1=65°\text{C,}$ and, at time $t_2=6700\text{s,}$ the rod temperature is $T_2=30°\text{C}\text{.}$ Determine the values of the constants C and n that appear in Equation 5.26. Plot the rod temperature versus time for $0\le t\le 10,000\text{s}\text{.}$ 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 $\bar{T}=\left(T_i+T_{\infty }\right)/2.$