An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves insertion of thermocouples in the casting at distances of 10 mm and 20 mm from the surface.  When the experiment was performed in a well insulated air duct so that the temperature of the walls surrounding the steel surface was the same as the air temperature, the thermocouples measured the temperatures of 50°C and 40°C in the steel, respectively, when the air and the surrounding wall temperatures were 200^oC.

a)    If the steel has a thermal conductivity of 15 W/m²K and surface emissivity of 0.95, what is the convection coefficient between the steel and hot air?

b)     What are the contributions of the convective and radiation heat fluxes to the steel casting?

In the repeated experiments the duct insulation was removed and even though the hot air temperature was the same as before, i.e., 200^oC, the surrounding walls temperature dropped to 20^oC. As a result the steady state heat flux to the steel casting dropped by 13.3% compared to the first experiment.

c)   Assuming the same convection coefficient as the value calculated in part a), what would be the temperatures measured by the thermocouples?

d)    Suppose that the steel casting were well insulated from all sides except for the surface from which the distance to thermocouples is measured. Assuming the same convection coefficient as the value calculated in part a), what would be the temperatures of the thermocouples when:

i)  The experiment is performed in the well insulated duct at T_∞ = T_surr = 200^oC?

ii)  The experiment is performed in non-insulated duct at T_∞ = 100^oC and T_surr = 20^oC?