Thermodynamics HW Solutions 170

Thermodynamics HW Solutions 170 - Chapter 3 Steady Heat...

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Chapter 3 Steady Heat Conduction 3-31 An exposed hot surface of an industrial natural gas furnace is to be insulated to reduce the heat loss through that section of the wall by 90 percent. The thickness of the insulation that needs to be used is to be determined. Also, the length of time it will take for the insulation to pay for itself from the energy it saves will be determined. Assumptions 1 Heat transfer through the wall is steady and one-dimensional. 2 Thermal conductivities are constant. 3 The furnace operates continuously. 4 The given heat transfer coefficients accounts for the radiation effects. Properties The thermal conductivity of the expanded perlite insulation is given to be k = 0.052 W/m °C. Analysis The rate of heat transfer without insulation is Insulation R o T R insulation T s L A == (2 3 m)(1.5 m) m 2 & ( ) ( . ( )(80 ) Qh A T T s =− = ° ° = 10 3 30 1500 W/m C) m C W 22 In order to reduce heat loss by 90%, the new heat transfer rate and thermal resistance must be & . & & () . Q Q T R R T Q total total = =⎯ ⎯= = −°
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