Consider an opaque horizontal plate that is well insulated on the edges and the
ID: 1857400 • Letter: C
Question
Consider an opaque horizontal plate that is well insulated on the edges and the lower surface. The plate is uniformly irradiated from above while air at T= 300 K flows over the surface providing a uniform convection heat transfer coefficuent of 40 W/m^2 K. Under steady state conditions the surface has a radiosity of 4000 W/m^2, and the plate temperature is maintained uniformly at 350 K. If the total absorptivity of the plate is 0.40. determine (a) the irradioate on the plate (b) the total reflectivity (c) the emissive power of the plate and (d) the total emissivity of the plate.
Explanation / Answer
Perform an energy balance on the plate.
E_in = E_out.
Thus we have G, the irradiation as the E_in and J, the radiosity = 4000 and the convection heat transfer.
The final equation looks like E_in = 40 *(350-300)+4000 = 6000 W/m^2. For
(b), there is an equation for blackbodies that have been idealized and are perfect absorbers, (lpha+ ho=1) ,
thus solving for ( ho) we get 0.6.
For part (c), emissive power can be found by J-(1-alpha)G=E.
Plug the numbers in and you should get 400 W/m^2 F