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QUESTION 9 [10 MARKS] A vessel with spherical shape is used in an industry facility to store fluids at constant temperature of 100 °C. The vessel with thermal conductivity of 1.5 W/m-K is designed for inner radius of 40 cm and outer radius of 41 cm. In order to maintain the temperature of the fluids inside the vessel, 800 W heater is wrapped at the outer surface of the vessel and covered with an insulation to prevent the heat loss. However, 10% from the heat generated is lost to the surrounding through the insulation. The remaining heat is transferred into the vessel and maintained the inner surface temperature at 120 °C. a) Express the differential equation and the boundary conditions for steady one-dimensional heat conduction [2 marks] b) Obtain a relation for the variation of temperature in the vessel [5 Marks] c) Evaluate the outer surface temperature of the vessel [2 marks] d) Estimate the amount of fluids per hour can be supplied into the vessel if the fluids enters at 20 °C. [1 Marks]