Chapter 7, Problem 7.32P

A steel strip emerges from the hot roll section of a steel mill at a speed of 20 m/s and a temperature of 1200 K. Its length and thickness are $L=100\text{m}$ and $\delta =0.003\text{m,}$ respectively, and its density and specific heat are $7900{\text{kg/m}}^{\text{3}}$ and $640\text{J/kg}\cdot \text{K,}$ respectively.

Accounting for heat transfer from the top and bottom surfaces and neglecting radiation and strip conduction effects, determine the time rate of change of the strip temperature at a distance of 1 m from the leading edge and at the trailing edge. Determine the distance from the leading edge at which the minimum cooling rate is achieved.