PS2_2.006S08 - Problem Set 1 (2.006, Spring 08) Part A 1. =...

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v1 2.006F08 1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.006 Thermal Fluids II Problem Set 2 Issued: Thursday, February 14, 2008 Due: Thursday, February 21, 2008 Problem 0 Please read the course notes Chapter 10, review White Chapter 6. Problem 1 U Hot wire A hot wire (or hot film) anemometer is a device that measures the velocity of the fluid passing by it. (These devices are used to meaure the mass flow rate of the air entering an automobile engine that allow the car's computer to decide the amount of fuel that must be injected into the engine.) Its simplest embodiment, shown in the figure above, a control circuit maintains the wire at constant temperature and the electrical power dissipated in the wire is used to infer the velocity of the flow. The heat transfer coefficient h is believed to depend on the velocity of the flow U, the density of the fluid ± , the viscosity of the fluid μ , the characteristic dimension of the cylinder (the diameter D), the thermal conductivity of the fluid k f , the heat capacity of the fluid c p and the thermal conductivity of the cylinder, k s . a) Please develop a set of non-dimensional parameters that can be used to characterize the flow and heat transfer. Credit will be assessed on the work shown. Clairvoyance does not foster credit here! b) Show that your PI groups can be manipulated into a set of Pi groups that include the Biot number, the Nusselt number, Prandtl number and the Reynolds number. (See your text, Incropera and Dewitt, for the definitions of these non-dimensional numbers, if you do not already know their definitions.). c) The results of several measurements are shown in the tables below. Please plot on the same axes the heat transfer rate as a function of velocity for each case. Is there any scaling laws apparent in these plots? d) Plot the data on a graph of the Nusselt number versus Reynolds number on a log-log plot. e) Assuming that the temperature across the solid cylinders is uniform (hence the Biot number is small and its contribution to the variation of the heat transfer coefficient can be neglected), show that the data can be characterized by an equation of the form Nu = Re m Pr n where m and n are constants. Determine the values of m and n. Suggestion: Note that the Prandtl number is a function only of material properties of the fluid. Start by fitting the plots of the data in part d to determine the exponent m. (The slope of the lines will cluster around a value of m but you will need to choose a specific value for m.) Then plot and fit Nu/Re m vs. Pr on a log-log plot to determine
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This note was uploaded on 10/06/2011 for the course MECHANICAL 2.006 taught by Professor Blah during the Spring '08 term at MIT.

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PS2_2.006S08 - Problem Set 1 (2.006, Spring 08) Part A 1. =...

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