A spherical tank, with an inner diameter of D₁ = 3 m, is filled with a solution undergoing an exothermic reaction that heats the surface to a uniform temperature of 120°C. To prevent thermal burn hazards, the tank is enclosed with a concentric outer cover that provides an evacuated gap of 5 cm in the enclosure. Both spherical surfaces have the same emissivity of 0.5, and the outer surface is exposed to natural convection with a heat transfer coefficient of 5 W/m² ∙ K and radiation heat transfer with the surrounding at a temperature of 30°C. Determine whether or not the vacuumed gap is sufficient to keep the outer surface temperature below 45°C to prevent thermal burns. If not, propose a solution to keep the outer surface temperature below 45°C.

Transcribed Image Text:

Air, 30°C h = 5 W/m² K Vacuum D₂- -D₁- Chemical reaction A₁ A₂ &₁ = ₂ = 0.5