Athick steel slab (rho= 7800 kg/m3 , cp= 480 j/kg k, k= 50 w/m k) is initially at 300 °c and is cooled by water jets impinging on one of its surfaces. the temperature of the water is 25 °c, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to reach 50 °c at a distance of 25 mm from the surface?

A3-mm-thick panel of aluminum alloy (k 177 w/m-k, c 875 j/kg-k and ? = 2770 kg/m) is finished on both sides with an epoxy coating that must be cured at or above t,-150°c for at least 5 min. the production line for the curing operation involves two steps: (1) heating in a large oven with air at ts,0-175°c and a convection coefficient of h, 40 w/m2. k, and (2) cooling in a large chamber with air at 25°c and a con- vection coefficient of he 10 w/m2.k. the heating portion of the process is conducted over a time interval te which exceeds the ime required to reach 150°c by 5 min (h = r + 300 s). the coating has an emissivity of ? = 0.8, and the temperatures of the oven and chamber walls are 175 and 25°c, respectively. if the panel is placed in the oven at an initial temperature of 25°c and removed from the chamber at a safe-to-touch tempera ture of 37°c, what is the total elapsed time for the two-step curing operation?