Chapter 5, Problem 5.44P

Consider the one-dimensional wall shown in the sketch, which is initially at a uniform temperature T, and is suddenly subjected to the convection boundary condition with a fluid at $T_{\infty }.$

For a particular wall, case 1, the temperature at $x=L_1$ after $t_1=100\text{s}$ is $T_1\left(L_1,t_1\right)=315°\text{C}\text{.}$ Another wall, case 2, has different thickness and thermal conditions as shown.

How long will it take for the second wall to reach $28.5°\text{C}$ at the position $x=L_2?$ Use as the basis for analysis, the dimensionless functional dependence for the transient temperature distribution expressed in Equation 5.41.