Instructions: Please write your answers on separate sheets of paper. You do not have to recopy the problem statement. The exam is open-note and open-book, however, you may not communicate with any individual other than the instructor about the exam. Submit a scan or picture of your answers through Canvas by the deadline. If you are unsure about an answer, explain your thought process for potential partial credit. For all calculations, show your work, include the units, and express your final answer with the appropriate number of significant figures.
At the top of your first page, copy the following statement and then sign your name. “I have not received nor given any unauthorized help on this exam. I will not discuss the exam until the solutions are posted.” Your exam will not be graded without this signed statement.
PROBLEM #1 (30 points)
In the production of frozen breaded fish sticks, food safety requires that the fish reach an internal temperature of 65°C before the sticks can be frozen. You have been asked to evalute the cooking time of a new techique, baking in a convection oven, to traditional deep frying (immersion in hot oil). In the oven, the sticks are set on a tray with hot air blowing over the top. The fish sticks can be treated as long rectangles with square cross sections (1.5 cm on a side). The thermal conductivity and thermal diffusivity of cod fish are 0.58 W/m·K and 1.22 x 10-7 m2/s, respectively.
(a) (10 points) Draw a diagram for the scenario showing the dimensions, known information, and the type and direction(s) of heat transfer.
(a) (10 points) Show how you would simplify the heat equation to solve for the time needed for the fish to be safely cooked before freezing (you do not have to solve the heat equation). List your assumptions.
(c) (10 points) Give two examples of boundary conditions that would be appropriate for this scenario to solve for the temperature distribution.
PROBLEM #2 (30 points)
To simplify the calculations of the fish stick cooking time for the two methods, you decide to model the sticks as long cylinders with a diameter 1.5 cm, where the sticks are rotated during baking to ensure even heating on all sides. For each scenario, determine which would be the most appropriate transient conduction method to use. Show any calculations needed to justify your answer.
(a) (10 points) The convection coefficient of frying in hot corn oil is 270 W/m2·K and you need to determine the temperature of the fish just underneath the breading layer right at the start of frying (to sear the fish).
(b) (10 points) The convection coefficient of frying in hot corn oil is 270 W/m2·K and you need to determine the center temperature of the fish near the end of the baking time.
(c) (10 points) The convection coefficient of baking is 35 W/m2·K and you need to determine the center temperature of the fish near the end of the baking time.
PROBLEM #3 (30 points)
Transporting frozen food requires a great deal of energy, in fuel for operating the truck and fuel used to run a compressor to keep the food storage compartment cold. In places like New Mexico, the intense solar radiation hitting the roof and sides of the truck adds to the challenge. Using insulation inside the roof/wall panels can help. Another solution is to install solar panels on the roof of the trailer to provide electricity to run the refrigerator’s compressor. To determine if the solar panels are sufficient, you need to calculate the heat load entering through the two sides of the trailer (neglect heat transfer through the front, bottom, and back panels).
(Photo: https://www.trucks.com/wp-content/uploads/2018/04/eNow-All-Electric-Reefer-Trailer_front-1.jpg)
A standard “reefer” trailer is 16.2 m long and 2.6 m tall. The side panels are made of a 5.0 cm thick layer of foam insulation (k = 0.026 W/m·K) sandwiched between two layers of aluminum, each 0.8 cm thick, with a thermal conductivity of 180 W/m·K and a surface emissivity of 0.6. Each side receives 900 W/m2 of irradiation, and gives off heat at the outer surface through radiation emission and convection. The temperature on the inside surface of the trailer is kept at -10°C. If the truck is driving at 110 km/hour through air at 30°C, the sides of the trailer experience a convection coefficient of 55 W/m2·K.
(a) (10 points) Draw a resistance circuit showing the heat transfer between the environment and the inside of the trailer. Label the circuit nodes, the direction of heat transfer, and the resistances. Explain any abbreviations you use.
(b) (10 points) Show how you can use an energy balance to determine the outer surface temperature for a side of the trailer. (You do not have to solve for the temperature).
(c) (10 points) If you calculated the steady state temperature for the trailer side out surfaces to be 34°C, what is the corresponding heat load (q) for the trailer?
PROBLEM #4 (10 points)
Based on the data in the graph, which fin performs better? Justify your answer.