MEN 310 Exam 2, Fall 2015

MEN310 - Dr. Charbel Habchi 1/8 Faculty of Engineering Department of Mechanical Engineering Fall 2015 MEN310 - Heat Transfer Instructors: Dr. Charbel Habchi Exam #2 - 10% 75 minutes (December 10, 2015 – 8:00-9:15) Student Name: ____________________________ Student ID: _______________ Section: ____ There are 2 questions in the booklet each has several parts, please answer all parts of these questions to the best of your ability. Marking Scheme Questions Weight Mark Question 1 30 points Question 2 70 points Total 100 points 1. Open book examination. Only original books are allowed. 2. Do not take the staple out. The exam booklet must remain intact. 3. Cheating penalty will be an “F” grade on the exam. 4. Mobile phones/devices are to be turned off and stowed away. 5. If something is not understood write your assumptions and solve the problem without asking questions. Good luck MEN310 - Dr. Charbel Habchi 2/8 QUESTION 1: Lumped Capacitance Method During the annealing process, steel ball bearings leaving the oven at a uniform temperature of 900oC are exposed to cold air at h = 125 W/m2.K and a temperature of 30oC for a while before they are dropped into the water for quenching. The diameter of each ball is 12 mm. The properties of the steel balls are 𝜌 = 8000 kg/m3 , 𝑘 = 15.1 W/m. K and 𝐶𝑝 = 480 J/kg. K. Assume uniform temperature distribution for the steel balls. a) Calculate the time that the balls can stand in the air before their temperature falls below 850oC. b) Calculate the rate of heat loss from the balls during this process if we have 120 balls moving per minute. MEN310 - Dr. Charbel Habchi 4/8 QUESTION 2: Transient Conduction and External Convection Consider the steady-state convection heat transfer between an air flow, with 𝑇∞ = 10℃, and a flat plate with an obstacle having both a surface temperature 𝑇𝑠 = 44℃ as shown in the figure. The obstacle, inserted at 𝑥0 = 25 cm, is called vortex generator because it generates vortices to enhance the heat transfer process. Experiments show that for 𝑢∞ = 1 𝑚/𝑠 , the local heat transfer coefficient can be expressed by:                 0 2 0 1 for 1800 1000 for 0 1000 1000 x x x x h x x x h x where x is in m and h in W/m2.K. The plate is 1 m width into the plane of the paper and it is made of iron steel 1% with: Δ𝑥 = 25 𝑐𝑚; 𝛥𝑦 = 12.5 cm. a) Sketch   h1 x and h2  x on the same graph showing the main features. b) Determine the average Nusselt number for the entire plate. c) Now let’s consider the unsteady conduction heat transfer process in the plate. The bottom surface and sides of the plate are considered heat sinks which means that nodes 1, 3, 4, 5 and 6 are maintained at constant temperature of 70℃. Assume that the air properties and convection coefficients are unchanged and that the heat transfer coefficient for each node is equal to the heat transfer coefficient averaged on the corresponding control volume. Calculate the temperature at node 2 after 600 seconds if its initial temperature was 70oC. d) Calculate the instantaneous heat loss from the upper surface of the plate for t = 300 s.