(Adapted from William J. Thomson, Introduction to Transport Phenomena, PrenticeHall, 2000, Problem XXXXXXXXXXA pressurized spherical storage tank contains liquid oxygen and oxygen vapor. As the oxygen...

(Adapted from William J. Thomson, Introduction to Transport Phenomena, PrenticeHall, 2000, Problem 3.18). A pressurized spherical storage tank contains liquid oxygen and oxygen vapor. As the oxygen vaporizes
it is vented off, compressed, refrigerated, and returned to the tank as liquid. Assume that the ambient temperature is T_a
and that heat is conducted into the tank from all directions equally.

 a. Derive an expression for the steady-state temperature distribution within the tank wall as a function of radius r and the boil-off rate ˙m.

b. Determine the boil-off rate if the tank is constructed of stainless steel and if the temperature of the inner shell is constant at –60 ◦C. The following data apply (see Figure P5.1):

Problem 3.18