Reconsider Prob. 20€“47. To reduce the heating cost of the pipe, it is proposed to insulate it with sufficiently thick fiberglass insulation (k = 0.035 W/m·K) wrapped with aluminum foil (ε = 0.1) to cut down the heat losses by 85 percent. Assuming the pipe temperature to remain constant at 25°C, determine the thickness of the insulation that needs to be used. How much money will the insulation save during this 15-h period? Evaluate air properties at a film temperature of 5°C and 1 atm pressure. Is this a good assumption?

Reconsider Prob. 20€“47.

Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such a fluid through a 100-m-long pipe of outer diameter 30 cm in calm ambient air at 0°C. The pipe is heated electrically, and a thermostat keeps the outer surface temperature of the pipe constant at 25°C. The emissivity of the outer surface of the pipe is 0.8, and the effective sky temperature is 230°C. Determine the power rating of the electric resistance heater, in kW, that needs to be used. Also, determine the cost of electricity associated with heating the pipe during a 10-h period under the above conditions if the price of electricity is $0.09/kWh.

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Tsky = -30°C 0°C 30 cm Ts = 25°C E = 0.8 Asphalt Resistance heater