Square channels of dimension \(L_{c}=\sqrt{2} \cdot 10 \mathrm{~mm}=\) \(14.14 \mathrm{~mm}\) are evenly spaced at \(S=25 \mathrm{~mm}\) along the centerline of a plate of thickness \(L_{p}=40 \mathrm{~mm}\). Hot and cold fluids flow through the channels in an alternating pattern as shown. Determine the maximum and minimum temperatures within the solid plate and the heat transfer rate per unit plate length. There are \(N=50\) total channels with \(T_{\infty, h}=120^{\circ} \mathrm{C}, T_{\infty, c}=20^{\circ} \mathrm{C}, h=40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), and \(k=14 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Use \(\Delta x=\Delta y=5 \mathrm{~mm}\) and the computational domain identified in the sketch.

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L Lp Th Th Computational domain