Unformatted text preview: Homework 7 – due Wednesday, October 13th 1. Consider a 100 mm long, 5 mm diameter 2024 aluminum pin that is inserted through a wall separating two fluids. The purpose is to segment heat transfer. The pin is inserted to a depth of 50 mm in air with a temperature of 10o C and velocity of 10 m/s. Fluid 2 is also air, but with a temperature of 40o C and velocity of 3 m/s. a) What is the rate of heat transfer from the warm air to the cool air through the pin? b) Plot the variation of heat transfer rate with the insertion distance, d. Is there an optimal insertion distance? 2. In an industrial facility, air is to be preheated before entering a furnace by geothermal water at 120o C flowing through the tubes of a tube bank located in a duct. Air enters the duct at 20o C and 1 atm with a mean velocity of 4.5 m/s and flows over the tubes in normal direction. The outer diameter of the tubes is 1.5 cm and the tubes are arranged in‐line with longitudinal and transverse pitches of SL = ST = 5 cm. There are 6 rows in the flow direction with 10 tubes in each row. Determine the rate of heat transfer per unit length of the tubes, and the pressure drop across the tube bank. 3. It is proposed to cool a square hot molded plastic plate 0.5 m to a side having a surface temperature of 140o C by using an array of slotted nozzles with width and pitch of 4 mm and 56 mm respectively, and a nozzle‐to‐plate separation of 40 mm. The air exits the nozzle at a temperature of 15o C and a velocity of 10 m/s. a) What is the improvement in cooling rate using the slotted nozzle arrangement rather than parallel flow of air over the plate? b) What would happen to the cooling in both cases if the air velocities were doubled? 4. Copper spheres of 20 mm diameter are dropped into a tank of water that is at 280 K. The spheres reach terminal velocity on impact and drop freely through the water. a) Do a force balance to determine the terminal velocity. b) How high would the tank have to be in order to cool the spheres from an initial temperature of 360 K to a centerline temperature of 320 K? Do not use lumped capacitance. ...
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- Heat Transfer, heat transfer rate, mm diameter, slotted nozzle arrangement, optimal insertion distance, hot molded plastic