Consider .9 except now the combined vol-ume of the oil

Chapter 5, Problem 5.111

(choose chapter or problem)

Consider 5.9 except now the combined vol-ume of the oil bath and the sphere is Vtot?1m3. Theoil bath is well mixed and well insulated.(a) Assuming the quenching liquids properties arethat of engine oil at 380 K, determine the steady-state temperature of the sphere.(b) Derive explicit finite difference expressions forthe sphere and oil bath temperatures as a func-tion of time using a single node each for thesphere and oil bath. Determine any stabilityrequirements that might limit the size of the timestep ?t.(c) Evaluate the sphere and oil bath temperaturesafter one time step using the explicit expressionsof part (b) and time steps of 1000, 10,000, and20,000 s.(d) Using an implicit formulation with ?t?100 s,determine the time needed for the coated sphere toreach 140C. Compare your answer to the timeassociated with a large, well-insulated oil bath.Plot the sphere and oil temperatures as a functionof time over the interval 0 h?t?15 h. Hint:SeeComment 3 of Example 5.2.