Chapter 5, Problem 5.68P

In a manufacturing process, long rods of different diameters are at a uniform temperature $400°\text{C}$  of in a curing oven, from which they are removed and cooled by forced convection in air at $25°\text{C}\text{.}$ One of the line operators has observed that it takes 280 s for a 40-mm-diameter rod to cool to a safe-to-handle temperature of $60°\text{C}\text{.}$ For an equivalent convection coefficient, how long will it take for an 80-mm-diameter rod to cool to the same temperature? The thermophysical properties of the rod are $\rho =2500{\text{kg/m}}^{\text{3}},c=900\text{J/kg}\cdot \text{K,}$ and $k=15\text{W/m}\cdot \text{K}\text{.}$ Comment on your result. Did you anticipate this outcome?