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Introduction A new process that runs 24 hours per day and 365 days per year has been added at MHT Industries which requires a continuous flow of 80°C water supplied at a rate of 26 g/s. The hot water is fed from an existing boiler that is located 50 m away through a pipe that has a 22 mm inside diameter and a 1 mm wall thickness. The pipe runs in an area that is accessible to workers so it must be insulated to prevent contact burn injuries. ASTM C1055 recommends that contact surface temperature be no higher than 60°C because this is the temperature that an average person can touch for up to five seconds without sustaining irreversible burn damage. MHT policy is to add an additional safety factor so they allow a maximum of only 50°C for all contact surfaces. You have been contracted by MHT because of your expertise in heat transfer to perform an analysis on the pipe. System Data Due to the heat loss from the pipe, water must exit the boiler at 90°C to ensure that the temperature at the delivery point 50 m away will be 80°C. The heat loss from the outer surface of the pipe will be by natural convection to the ambient air in the plant which is held constant at 21°C. The convection heat transfer coefficient (regardless of whether the pipe is insulated or not) is 5 W/m2.K and any heat loss by radiation is considered negligible. The wall temperature of the pipe will be constant along its entire length. Any change in temperature to the pipe wall or water exit temperature due to adding insulation can be neglected. The thermal resistance provided by the pipe wall can also be considered negligible. The boiler burns natural gas to provide the energy input required to raise the temperature of the water to 90°C. The cost of natural gas is $0.13 per metre cubed and 1 m of natural gas has 37 MJ of energy content. The efficiency of the boiler is 80%. The insulation that is recommended for this use has a 10 year service life and a thermal conductivity of 0.08 W/m.K. The table below lists the available sizes as well as the installation cost (time and material). Insulation thickness Installation cost 8 $40/metre of pipe Pipe OD Insulation thickness 10 $60/metre of pipe 12 $80/metre of pipe 14 $100/metre of pipe Table 1: Insulation specifications 1 Page

(1) [3 marks] What will be the annual cost of natural gas to provide the energy that is lost from the water if there is no insulation on the pipe? mene. IL