Chapter 5, Problem 5.47P

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

1. 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.
2. 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).
3. 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.