HW3_sol - Thermal & Fluids Engineering I. Spring 2006....

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Thermal & Fluids Engineering I. Spring 2006. Homework #3 Solution. WebCT post date: 02/09/2006 3-1 An arctic explorer builds a temporary shelter from wind-pack snow. The shelter is roughly hemispherical with an inside radius of 1.5 meters. After completing the shelter, the explorer crawls inside and closes off the entrance with a block of snow. Assume the shelter is now air tight and loses negligible heat by conduction through the walls. If the air temperature when the explorer completes the shelter is -10 o C, how long will it take before the air temperature inside reaches 10 o C? Assume the explorer does not freeze to death or suffocate, but sits patiently waiting for the temperature to rise. The explorer generates body heat at a rate of 300 kJ/h. Approach: Use the first law to find the change in temperature. Assumptions: 1. The air behaves like an ideal gas under these conditions. 2. The shelter is perfectly insulated and air-tight. 3. The specific heat of the air is constant. Solution: Let the system be the air inside the shelter. From the first law v Q U mc T = Δ = Δ The mass of air can be determined from the ideal gas law ( ) ( ) ( ) ( )( ) 3 3 1 4 101kPa π 1.5 m 28.97kg kmol 2 3 9.46kg 8.314kJ kmol K 10 + 273 K PVM m RT    = = = - The only heat added to the air is body heat. The walls are assumed to be thick and highly insulating. The rate of heat transfer is related to the total heat transferred by v Q Q t mc T = Δ = Δ d Solving for elapsed time ( ) ( ) ( ) ( ) ( ) 2 1 9.46kg 0.717kJ kg K 10 10 K 300kJ h v mc T T t Q t - Δ = - - Δ = d where c v may be found in Table A-8. Evaluating 0.45h 27min t Δ = = Answer Comments: In actuality, there must be some air entering and leaving the shelter or the explorer would be unable to breathe; therefore, the rise in temperature may not be as rapid as calculated.
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Thermal & Fluids Engineering I. Spring 2006. Homework #3 Solution. Page 2 3-11 On a cold winter day, the interior walls of a room are at 55 o F. A man standing in the room loses heat to the walls by thermal radiation. The man’s surface area in 16 ft 2 , his clothing has an emissivity of 0.93 and his surface temperature is 70 o F. He generates 300 Btu/h of body heat. What percentage of the man’s body heat is transferred by radiation to the walls? Approach: Use ( ) 4 4 s surr Q A T T ε σ = - d to determine radiation heat transfer from the man and compare this to his body heat. Assumptions:
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HW3_sol - Thermal & Fluids Engineering I. Spring 2006....

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