Estimate the heated tube length necessary to raise the mean temperature of a power law liquid from 100 °F to 110 °F, when the average flow velocity through a smooth tube of 3 inches ID is 8 ft/sec. The tube wall is at 180 °F. At 105 °F, the fluid properties are: density = 75 lb/ft³, heat capacity = 0.5 Btu/lb-°F, thermal conductivity = 0.2 Btu/hr-ft-°F, and the consistency index (K) = 0.2 lb-sec^n-2/ft. The flow behavior index (n) is 0.6.