Chapter 3, Problem 3.67P

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

(a) At a dimensionless time of $F{o}_1$, 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 $0<Fo<\infty$. By changing the duration of heating to $F{o}_2$, the steady-state midplane temperature can be set equal to the midplane temperature at $F{o}_1$. Is the value of $F{o}_2$, equal to, greater than, or less than $F{o}_1$? Hint: Assume both $F{o}_1$ and $F{o}_2$ are greater than 0.2.

(b) Letting $F{o}_2=F{o}_1+\Delta Fo$, derive an analytical expression for $\Delta Fo$, and evaluate $\Delta Fo$ for the conditions of part (a).

(e) Evaluate $\Delta Fo$ for $Bi=0.01$, 0.1, 10, 100, and $\infty$ when $F{o}_1$, and $F{o}_2$, are both greater than 0.2.