One-dimensional, steady-state conduction with no energy generation is occurring in a plane wall of constant thermal conductivity.

(a) Is the prescribed temperature distribution possible? Briefly explain your reasoning.

(b) With the temperature at \(x=0\) and the fluid temperature fixed at \(T(0)=0^{\circ} \mathrm{C}\) and \(T_{\infty}=20^{\circ} \mathrm{C}\), respectively, compute and plot the temperature at \(x=L\), \(T(L)\), as a function of \(h\) for \(10 \leq h \leq 100 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Briefly explain your results.

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7(C) 120 100 888 80 60 40 20 0 0.18 m - 0, k 4.5 W/m-K T = 20C h = 30 W/mK Air