Consider the sphere of Example 5.5, which is initially at a uniform temperature when it is suddenly removed from the furnace and subjected to a two-step cooling process. Use the Transie1l1 Conduction, Sphere model of IHT to obtain the following solutions.

(a) For step 1, calculate the time required for the center temperature to reach T(0, t) = 335°C, while cooling in air at 20°C with a convection coefficient of 10 W/m² ∙ K. What is the Biot number for this cooling process? Do you expect radial temperature gradients to be appreciable? Compare your results to those of the example.

(b) For step 2, calculate the time required for the center temperature to reach T(0, t) = 50°C, while cooling in a water bath at 20°C with a convection coefficient of 6000 W/m² ∙ K.

(c) For the step 2 cooling process, calculate and plot the temperature histories, T(r, t), for the center and surface of the sphere. Identify and explain key features of the histories. When do you expect the temperature gradients in the sphere to be the largest?