Chapter 5, Problem 5.61P

A long cylinder of 30-mm diameter, initially at a uniform temperature of 1000 K, is suddenly quenched in a large, constant-temperature oil bath at 350 K. The cylinder properties are $k=1.7\text{W/m}\cdot \text{K,}c=1600\text{J/kg}\cdot \text{K,}$ and $\rho =400{\text{kg/m}}^{\text{3}},$ while the convection coefficient is $50{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Calculate the time required for the surface of the cylinder to reach 500 K.
2. Compute and plot the surface temperature history for $0\le t\le 300\text{s}.$ If the oil were agitated. providing a convection coefficient of $250{\text{W/m}}^{\text{2}}\cdot \text{K,}$ how would the temperature history change?