Problem on convection coefficient

Question

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) Determine the contributions of convective and radiation heat fluxes to steel casting?

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

c) Supposing similar convection coefficient as the value coputed in part a), what would be the temperatures measured by the thermocouples?

d) Assume that the steel casting were well insulated from each and evry side 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∞ = Tsurr = 200^oC?
ii) The experiment is executed in non-insulated duct at T∞ = 100^oC and Tsurr = 20^oC?