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 I bigh

S Uiwoverall heat transfer coefficient of 300 W/m2 K. Based on experience, it is anticipated that the fouling factors on the inner and outer surfaces will increase linearly with time as R", = a,t and R10-" m? · K/W -s and a, = 1.0 x 10- m2 ·the inner and outer tube surfaces, respectively. If the%3D= a,t where a, = 2.5 x%3DK/W •s for 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.