Three long, \(20-\mathrm{mm}\)-diameter cylindrical bars are to be heat-treated in an oven. The bars are initially at a temperature of \(300 \mathrm{~K}\), while the oven walls are charcoated and at \(450 \mathrm{~K}\). The bar and oven wall emissivities are 0.85 and 1 , respectively. Determine the initial radiation heat rate per unit bar length to each of the three bars if they are all placed in parallel on a horizontal, thin-wire rack within the oven. Consider surfaceto-surface separation distances of \(s=0,10\), and \(50 \mathrm{~mm}\). At what separation distance and for which \(\operatorname{bar}(\mathrm{s})\) is the radiation heat rate maximized? At what separation distance and for which \(\operatorname{bar}(\mathrm{s})\) is radiation heating minimized? Plot the initial heat rate per unit length to the middle bar and to an exterior bar for separation distances \(0 \leq s \leq 1 \mathrm{~m}\).