Chapter 3, Problem 3.130P

Consider the thick slab of copper in Example 5.12, which is initially at a uniform temperature of 20°C and is suddenly exposed to a net radiant flux of $3\times {10}^{5}W/m^2$. Use the Finite-Difference Equations/One-Dimensional/Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the interior nodes. In your analysis, use a space increment of $\Delta x=37.5mm$ with a total of 17 nodes $\left(00-16\right)$, and a time increment of $\Delta t=1.2s$. For the surface node 00, use the finite-difference equation derived in Section 2 of the Example.

(a) Calculate the 00 and 04 nodal temperatures at $t=120s$, that is, $T\left(0,120s\right)$ and $T\left(0.15m,120s\right)$, and compare the results with those given in Comment 1 for the exact solution. Will a time increment of 0.1 2 s provide more accurate results?

(b) Plot temperature histories for $x=0$, 150, and 600 mm, and explain key features of your results.