Solve all four of the following problems to receive full credit.
Remember:
- collect fluid and material properties (Appendix A of Textbook)
- understand the configuration
- select the proper correlations and equations
- configure the equations to yield what is asked for
- don't overthink, problems don't require temperature iterations (constant, or negligible change)
- however, check the validity ranges of all correlations and equations you use
- it is advisable that you set the solutions up in Matlab or equivalent
Problem 1:
The insulation on a chilled water pipe segment of internal diameter d=0.3 m, wall thickness δ = 0.005m and length L=30 m was temporarily removed for inspection and then "forgotten about". The segment is made from run-of-the-mill AISI 1010 carbon steel. The chilled water has a volume flow rate of Q = 1,000 gall min and enters the segment at one end at temperature Tm = 280K and exits at the other end at unknown temperature Tma. In mid-summer, when the need for chilled water is greatest, the segment is now directly exposed to external cross flow of air at u∞ =5 m/s and T∞ = 300K. Ignoring solar irradiation, how much chilled water cooling capacity is lost along the exposed segment? How does this compare to the total chilled water cooling capacity, for which the design chilled water temperature difference is ΔTm = 6K? You may assume fully developed flow where necessary.
Problem 2:
A fluid is to be heated with the help of an aligned tube bank. Each tube has diameter D= 0.01m , length L=0.5 m and is electrically heated with electrical power P=100 W. All of the electrical power to a tube is available as thermal power to the fluid. The number of tubes in the transverse direction is NT = 20. The transverse and longitudinal pitches are ST = 0.02 m and SL = 0.02m , respectively. The fluid enters the tube bank at velocity u=2 m/s and temperature Ti =280 K. How many tubes in the longitudinal direction NL are required to heat the fluid to To = 320K and what will the surface temperature Ts of each tube be? Note that the fluid has constant properties, including mass density Ρ = 1 kglm3, heat capacity cp = 1000 J/kgK, dynamic viscosity μ = 2.10-5 kg/sm and thermal conductivity k = 2.10-2W/Km
Problem 3:
A produce company thought they had found an ingeneous way to keep cost down in moving their produce from farm to market. They would purchase decommissioned UPS delivery trucks and equip their cargo areas with three (3) low-cost "through-the-wall" air conditioners of Q = 3.5 kW cooling capacity each. Their approach, so they thought, would keep their produce at T <18°C for the drive from farm to market. They even proved this by running a test on a protoype parked in their farm's lot in mid-summer, when the air was at T∞ = 35°C , the heat transfer coefficient from air to exterior cargo area wall was its = 5 W/Km2 and the sun heated (only) the roof of the cargo area with an intensity of q''∞ =1,000 win?.
Unfortunately, after driving the many miles from farm to market at u∞, =100 km/ - right after the protoype test - the produce arrived in less fresh condition than they had anticipated. Can you help them figure out what the temperature in the cargo area was during the drive?
The cargo area measures L= 6 m , W = 2m and H =2 m , and its roof absorbs α= 50 % of the solar irradiation. The front of the cargo area faces the driver's cabin and may be considered adiabatic, the back and bottom of the cargo area see no change in air flow, whether the truck is stationary or mobile. The primary resistance to heat transfer into the cargo area is that of external convection. You may assume constant air properties of mass density Ρ =1.1 kg/m3, heat capacity cp =1,008 .J/kgK, dynamic visosity u = 190.10-2 kg/ sm and thermal conductivity k = 0.028 W/Km , and for simplicity, you may assume that the produce has the same properties as the air.
Problem 4:
A cyclist carries a water bottle, which may be approximated as a cylinder of diameter D=0.075 m and length L =0.2 m. Though generally attached to the bicycle's frame, for this problem, you may assume it is exposed to full cross flow from the air at T, =35° C , as the cyclist progresses at a speed of u, = 6.5 m/s . The bottle came from a refrigerator, so that the water contained in it is initially at T,=7.5°C . Ignoring radiation, ignoring the thermal effects of the end caps of the cylinder, and ignoring the thermal effects of the bottle's "mantle" material, how much time does the cyclist have before the water reaches a temperature of Ter-20°C and therefore becomes too warm to be refreshing? Can you speak to the accuracy of the approach you have (likely) taken? Use the same properties for air as those in Problem 1) above.