This preview shows pages 1–2. Sign up to view the full content.
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 nondimensional 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 nondimensional 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 loglog 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 loglog plot to determine
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
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.
 Spring '08
 Blah

Click to edit the document details