An industrial boiler consists of tubes inside of which flow hot combustion gases. Water boils on the exterior of the tubes. When installed, the clean boiler has an overall heat transfer coefficient of \(300 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Based on experience, it is anticipated that the fouling factors on the inner and outer surfaces will increase linearly with time as \(R_{f, i}^{\prime \prime}=a_{i} t\) and \(R_{f, o}^{\prime \prime}=a_{o} t\) where \(a_{i}=2.5 \times 10^{-11}\) \(\mathrm{m}^{2} \cdot \mathrm{K} / \mathrm{W} \cdot \mathrm{s}\) and \(a_{o}=1.0 \times 10^{-11} \mathrm{~m}^{2} \cdot \mathrm{K} / \mathrm{W} \cdot \mathrm{s}\) for the inner and outer tube surfaces, respectively. If the boiler is to be cleaned when the overall heat transfer coefficient is reduced from its initial value by \(25 \%\), how long after installation should the first cleaning be scheduled? The boiler operates continuously between cleanings.