Work Problem 5.47 for the case of a sphere of radius r_o.

Data From Problem 5.47

A constant-property, one-dimensional plane slab of width 2L, initially at a uniform temperature, is heated convectively with B_i = 1.

(a) At a dimensionless time of Fo1, heating is suddenly stopped, and the slab of material is quickly covered with insulation. Sketch the dimensionless surface and midplane temperatures of the slab as a function of dimensionless time over the range 0 < Fo < ∞. By changing the duration of heating to Fo₂, the steady-state midplane temperature can be set equal to the midplane temperature at Fo₁. Is the value of Fo₂ equal to, greater than, or less than Fo₁?
(b) Letting Fo₂ Fo₁ + ΔFo, derive an analytical expression for ΔFo, and evaluate ΔFo for the conditions of part (a).
(c) Evaluate ΔFo for Bi = 0.01, 0.1, 10, 100, and ∞ when Fo₁ and Fo₂ are both greater than 0.2.