A spherical tank 1m in diameter is maintained at a temperature of $120^0C$ and exposed to a convection environment with $h= 25W/m^2-K$ and temperature of ambient air is $15^0C$. What thickness of urethane foam $(k = 20×10^{-3} W/m-K)$ should be added to ensure that the outer temperature of the insulation does not exceed $40^0C$? What percentage reduction in heat loss results from installing this insulation?

Case 1

Given,

d = 1m (Diameter of spherical tank)

t1 = 120℃ = 393K (Temperature of sphere)

t2 = 15℃ = 288K (Temperature of surrounding environment)

h = 25 W/m2K (Convective heat transfer coefficient of surrounding environment)

Find: (1) Q (Heat transfer rate)

Solution:

Heat transfer rate

Q1 = …