A thick casting initially at a uniform temperature of 150 C has properties of ? = 2790 kg/m3, k = 1.6 W/m-K and Cp = 956 J/kg-K. The surface of the casting is suddenly exposed to turbulent water at 20 C, giving a very large convective heat transfer coefficient.

a) Using an explicit finite-difference scheme with ?x = 6mm, determine the length of time required for the temperature 18 mm beneath the surface to change from its initial value.

b) Based on the results of your finite-difference solution, determine an approximate value for the heat (q??) being convected from the surface after 2 minutes.

c) Sketch a plot of surface heat flux, q”, as a function of time.

d) Using the time obtained in part a of part a for the temperature 18 mm from the surface to change from its initial value, check the temperature at that location (x = 18 mm) using a different method.