Chapter 2, Problem 125P

A spherical tank is filled with ice slurry, where its inner surface is at 0°C. The tank has an inner diameter of 9 m, and its wall thickness is 20 mm. The tank wall is made of a material with a thermal conductivity given as $k(T)=k_0(1+\beta T\text{) where }{k}_0=0.33\text{ W/m}\text{.K, }\beta =0.0025{\text{K}}^{\text{-1}},andT\text{ is in K}\text{.}$ and The temperature outside the tank is 35°C, and the convection heat transfer coefficient is 70 W/m² ⋅K. Solar radiation is incident on the tank’s outer surface at a rate of 150 W/m² , where the emissivity and solar absorptivity of the outer surface are 0.75. Determine the outer surface temperature of the tank.