A thick casting with a thermal diffusivity of 5 x 10-6 m2/s is initially at a uniform temperature of 150oC. One surface of the casting is suddenly exposed to a high-speed water jet at 20oC, resulting in a very large convective heat transfer coefficient (Hint: assume imposed surface temperature). The thermal conductivity of the casting is 20 W/m-K. Determine the temperature 20 mm in from the surface after 40 seconds. Check your answer using an alternative technique. Your final answer should be about 101.3 oC.

Explanation:

Given that;

Thermal diffusivity

Thermal conductivity

Heat transfer coefficient h = ( we are to assume the imposed surface temperature ) = 20 W/m².K

Initial temperature = 150 ° C = (150+273) K = 423 K

Then coolant temperature with which the casting is exposed to = 20° C = (20+273)K = 293 K

Time = 40 seconds

Length = 20mm = 0.02 m

The objective is to determine the  temperature at the surface  at a depth of 20 mm after 40 seconds.

Bi == 0.02

For a wall at 0.2 Bi

Therefore;

i mean i gues

explanation:

do you have any options?