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

For a particular wall, case 1, the temperature at x = L₁ after t₁ = 100s is T₁ (L₁, t₁) = 315°C. Another wall, case 2, has different thickness and thermal conditions as shown below. How long will it take for the second wall to reach 28.5°C at the position x = L₂? Use as the basis for analysis, the dimensionless functional dependence for the transient temperature distribution expressed in Equation 5.38.

Wall, Tx, 0) = T;, k, a -Insulation T, h T; (C) (W/m K) (C) (m/s) (W/m K) Case (m) 15 10-6 0.10 50 300 400 200 25 x 10-6 20 0.40 100 30 100