The diameter and surface emissivity of an electrically heated plate are D = 300 mm and B = 0.80, respectively.

(a) Estimate the power needed to maintain a surface temperature of 200°C in a room for which the air and the walls are at 25°C. The coefficient characterizing heat transfer by natural convection depends on the surface temperature and, in units of W/m² ∙ K, may be approximated by an expression of the form h = 0.80(T_s - T_∞) ^1/3.

(b) Assess the effect of surface temperature on the power requirement, as well as on the relative contributions of convection and radiation to heat transfer from the surface.