Consider a spherical shell satellite with outer diameter of 4 m and shell thickness of 10 mm that is reentering the atmosphere. The shell satellite is made of stainless steel with properties of ρ = 8238 kg/ m³ ,  c_p  =  468 J/kg⋅K, and k = 13.4 W/m⋅K. During the reentry, the effective atmosphere temperature surrounding the satellite is 1250°C with a convection heat transfer coefficient of 130 W/m²⋅K. If the initial temperature of the shell is 10°C, determine the shell temperature after 5 min of reentry. Assume heat transfer occurs only on the satellite shell.