w— '5—_.._

 

QNVESTIGATION OF THE HEAT
CDNDUOTIVITY OF THE BOUNDARY
FILM SURROUNDING HOT BODIES

THESIS FOB THE DEGREE OF M. S.

William G. Keck
1933

N-_--* ‘--‘m

Ilfiajfiigfljflijmifiifliflwn'ml

 

8767

. . .v ,‘
‘1. \. # 15,1; .

:41“? 56543.5 aimr- .: '

' #3394991;

‘ —_:~"

‘0‘

-....'.-. .

I” ‘V '. A..“..' 'C‘.
_ , “gm”? 5 '

       

 

r ~¥ : -‘
2‘;qu: L‘Ur) {/1 a; 3‘2 ‘

#5,;
'2'V' ' '

LIBRARY

Michigan State
University

 

PLACE IN REI‘URN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

DATE DUE DATE DUE DATE DUE

 

 

INVESTIGATION
OF THE
HEAT CONDUCTIVITY OF THE BOUNDARY FILM

SURROUNDING HOT BODIES.

Thalia for Degree 6‘ I; S.
V

J
Iillium G?’ Keck

1933

I with to expren my appreciation to
Dr. 0. U. Chamberlain as director of my problem,
to Prof. C. I. Chapman for hie invaluable co-
Operation in obtaining equipment, and to George L.
Chapman for his help in the tedious task of building

apparatus .

10.3.8" ‘13

CONTENTS

Introduction

Previous Investigatione.
'l'he Hot lire Anenometer.
Apparatue and Procedure .
Data and Computatione.

Interpretation of Reeulte .

1.

3.

8.

11.

16.

28.

INTRODUCTION

The behavior of the region immediately surrounding a
solid, bathed. in a fluid, has long been a subject of conjecture for
both the physicist and the chemist. The physicist's interest is
two-fold. Be wishes to learn what effect this region say have upon
kinetic considerations for the Iain body of the fluid, and also why
it so stubbornly resists conduction of heat. The chemist desires
to know what effect this boundary has upon the speed of chemical
reactions between pass and solids, gases and liquids, or liquids

and solids.

the difficulty encountered in studying these interfaces
lies in the fact that their thickness is of an order app-oriental;
that of intermolecular distances. As a result of this not all

investigators are in couplets accord concerning their physical

properties.

The investigation to be discussed in this article has to
do with an attempt to learn something about the properties of the
region surrounding a platinum wire bathed in air as the fluid. It is
evident that we have represented in this research the two extremes in
which matter is known to exist. On the one extremity, platinm
represents the solid state with very high density. 0n the other is

air, which under conditions of standard temperature and pressure comes

-1-

very close to behaving as a perfect gas. In general we should, with

the help of previous investigation, be able to substantiate one of

the following suppositions: (l) l'hat at the surface of the solid

a discontinuity in density occurs, so that on the one side of this

plane the density is uniformly that of the gas, on the other it is
uniformly that of the solid. (2) l'hat there are no density discontinuities;
that is, we suppose that in the neidiborhood of the solid the density of
the gas begins to increase until it attains some of the properties of a
solid right at the interface, and that beyond this plane the density is
uniformly that of the solid. 0r (3) we should also be able to form
an opinion as to whether a combination of these two suppositions

actually is the correct one.

PREVIOUS INVESTIGATIONS.

Any discussion of previous investigations must begin with
experiments performed to determine the limiting thickness of a
liquid film shieh can support itself. Though this does not serve as
a direct measurement upon the physical properties of the boundary
region, still it investigates the behavior of molecules taken as
individuals rather than in the agregate. Obviously, if the thickness
of the boundary region is comparable to intermolecular distances,
then the forces acting will be in a large part determined by

individual molecular behavior.

As early as 1861, Plateau? held that a liquid film could
not possibly exist if its thickness were not twice the distance thru
which a molecule could effectively attract another. Quincke°° and
Johonott°°' were of the same opinion. For convenience, this distance
thru.which one molecule can attract another, beyond which it has
no attraction, will be designated by the symbol (R). Bakker,°°°°
however, held that there was a gradual transition from the licuid to
the vapor phase, and that a film must consist of a layer of liquid
as a capillary, plus two transition layers, one on either side, each

having a thickness (R). Thus the value of (B) would be one-third

e
'Plateau. Recherches experimentales etc., 5 ser., Mom d. Brux., 1861

.cquian.e Pogg. Me, Bde 137, p 403s 1869s
°°°Johonott. Phil. mag. (5) 47, p 501. June 1899.

0000M°r. Phil. Mag. (6’ 17, p 337s Mh lagge

.3-

the thickness of the limiting liquid film.

many attempts were made to experhmentally detenmine the
Ineiting film thickness during this period, but the work of Lord
Rayleigh°, and Johnnctt” is outstanding. Rayleigh found that a
csmpher particle exerted no influence on water, if the water surface
were covered by an oil film.which was greater than 8 x 10"7 cm. in
thickness. That a film thinner than this value might rest upon the
water surface seems without doubt. Johonctt, by measuring’the
difference in light path produced by introducing a large number of
films of water between one set of’mirrors of’an interferometer, found
that the thinnest film he could produce was 6 x 10-7 cm. in thickness.
Of these experiments, Lord Rayleigh's would seem to be a direct
measurement of the value (R), while Johonott's is a measurement of the
limiting film thickness. If we accept Bakkers theory as true, then

there is excellent agreement between.these two results.

In 1910, Chamberlain°‘° undertook an experiment which
constituted a direct measurement of’the value of (R) as well as a check
on Johcnctt's value of the thinnest possible film. In this research,
use was made of the fact that a water surface meets silver at an angle

of 90' and therefore does not "wot” a silver surface, while it does

°Lord Rayleigh. Proc. Roy. Soc. 47, p 364 1899-90.
“’Johonctt. Phil. mag. (5) 47, p 622, June 1899. (6) 11, p 149 June 1906.

'°‘chamberlain, Physical Review. Vol. 51 p 170 1910.

“wot” a glass surface. If a thin wedge of silver be interposed between
glass and water in,a thin capillary plane, wherever the wedge of silver
is so thick that the glass molecules cannot reach thru.the silver and
attract the water molecules, a water surface will not rise in the
capillary. lhsn however the wedge has a thickness less than (R) the
water surface will begin to rise, attaining its maximum height above the
free surface when it makes direct contact to glass. The thickness of the
silver at the point where the glass and water molecules begin to interact
is obviously the value of (RI. To measure this thickness a special
instrument, now known as the compound interferometer had to be developed.
The result obtained by Chamberlain an. the value of (a) as 1.5 x 10‘7 cm.
The newly developed compound interferometer was then employed to check

Johonott's work and it was found that he had made no detectable error.

Further investigations seem to have taken the direction of
either making a direct observation of films adhering to solids and
liquids, or of a study of the effect upon chemical reactions caused by

the interface between two phases of matter.

Davis and Crandall' make the following statement: "It is now
becoming generally recognised that whenever a liquid and a gas come
in contact,there exists on the gas side of the interface a layer of
gas in which motion by convection is slight compared to that in the
main body of the gas, and that similarly on the liquid side there

is a surface of liquid practically free from mixture by convection.

‘navis and Grandall. Am. Ghent soc. J. O. 1930

We assune them stationary films of gas and liquid. There is good
evidence that a similar stationary liquid film exists at a liquid-
solid interface. The thickness of the liquid film is several thousand

times the diameter of the water molecule.”

In light of the present investigation the experiments per-
formed by latson and Kibler‘? have especial interest. These investigators
were making a visual observation on the behavior of smoke particles
entering a liquid surface in which they were being absorbed. They
make the statement that fine smoke particles ”played" for long intervals

in the space Just above the liquid, before entering and being absorbed.

Under the direction of Bolt” the lational Physical Laboratories
made observations upon the effect of the boundary film around accurate
guage surfaces. In their experiment the thickness of wringing films
for Pitter guage blocks was investigated. Sixteen new one—eighth inch
blocks were accurately measured with an interferometer and then wrung
together with various oils, water, and finally air as the wringing media.
'hen wrung together, the combined length of the blocks was measured by
interference methods. It was found that they now measured more than
two inches, but the surprising result was that in all cases the excess
was the same regardless of the wringing film. This would indicate that
even air, near a solid, behaves somewhat as a liquid film. These

experiments indicated that adhering to each surface of the guages

0Watson an! Kibler. Phy. Chem. J1. '31.

”Bolt. Guages and Pine Measurements. By P. 11. Bolt.

was a film whose thickness is 1.8 x 10’7dm. This result, which is in

fair agreement with the value of’(B) as obtained by Chamberlain, would
indicate to us that a solid is able to bind the molecules of air to
itself, out to a distance (R) asay from.the solid, and that this layer

exhibits all the properties of’a liquid.

These experiments, along with the easily observed phenomena
of welding together of glass optical surfaces, and the necessity of
raising'metals to a high temperature in order to effect welding, ferces
us to the conclusion that all solids immersed in gases are surrounded
by a film of the same gas which behases very much like a liquid.

Indeed that whenever a transition in phase of matter occurs there is
always evident an effect which can only be attributed to the presence

of some sort of fihn.

-7-

THE HOT WIRE ANEMOHETER.

Since the research being discussed makes use-vof the principle
of the hot wire anemometer, it will be worth while to study this
instrument briefly.

It is well known that a body, heated above the temperature of
the surrounding fluid, will dissipate heat more rapidly when the fluid
streams past it than it does if the fluid remains stationary. Since it
is so easy to heat a body electrically, the anemometers built on this
principle are all of the electrical type. The input to a wire, which
serves as the hot body, is very easily measured, as is also the
temperature of the wire, by a knowledge of the resistance of the wire
and the current passing thru it. Imediately two possibilities present
themselves. a wire may be heated so as to maintain a constant temperature
above that of the fluid, and the input to maintain this temperature
difference used as a measure of the fluid velocity, or a constant input
may be maintained and the resulting temperature used as a measure of the

fluid velocity.

The first possibility has been admirably treated by King‘, both
from a theoretical and an experimental standpoint. King used platinum
as the hot wire. This wire was mounted on a whirling table whose speed
of rotation could be very easily controlled. The air was assumed to be
still with the wire moving thru it, which, when a correction for swirl of

the rotating arm was made, gave him a very close approximation to a

‘King. Phil. Trans. Roy. Soc. vol. 214, 1914. p 273

~8-

stationary wire with air streaming past it. King showed that the
relation between the heat lost (I!) per second, per unit length of

a cylinder of diameter (d) maintained at a temperature (T) above that

of the fluid in which it is imersed and the velocity of the fluid

(V), could be represented very nearly by the equation:

(1) n-m. (ZKBad)! ,l,

where K is the thermal conductivity of the fluid, 3 its specific heat
at constant volume, and (a) its density. This expression my be written
in the font

(a) a - s vL . c

The actual values of the constants (B) and (O) as obtained experimentally
by King were in fairly good agremsent with the theoretical values as

given by equation (1).

R. Ower’ describes an instrmsent operating on the principle
that the current be kept constant and the temperature measurement be
an indication of the air velocity past the wire. In this case (I!) will
be given by Her), where (r) is the resistance of the wire and I is the
current thru it. Since (r) itself is a function of (T) this prohibits
converting equation (1) into anything which will be very helpful in
determining the calibration of any one wire. For this reason this type
of instrument is to be calibrated experimentally. It has however, the
advantage that it is more sensitive for determination of low air velocities

than the constant temperature difference instrument. Then too, the fact

’3. Ower. Instruments Vol 4. i 12 p 670 December 1931.

.9-

that the current may be maintained a constant allows one to use a
potentiometric method of measurement for both current and potential
of the hot wire. Ihen one considers the fact that a type K, Leeds and
northrup potentiometer will measure potentials to the microvolt, this

becomes an unbelievably sensitive instrument.

~10-

APPARATUS AND PROCEDURE

It was while attempting to calibrate an anemometer, suitable
for measuring very low air velocities, that periodic variations in
the calibration curve were noticed. Since no theoretical treatment
had as yet been advanced which could account for such variations, it

was considered important that a study of this phenomena be made.

For this purpose the constant current type of snemometer was
chosen as being most suitable. In describing this part of the apparatus
reference will be made to Plate 1. ‘

(I) is the hot wire and consists of a # 44 platinum wire, mounted
diametrically, in a bakelite collar whose inner dimension is 3.6 cm.
The wire is mounted between brass springs which maintain it always taut
and vertical. The reason for mounting vertically is to minimise the
effect of natural convection currents due to heating of the wire above
room temperature.

(R) is a variable resistance in series with the hot wire (I) and
a standard resistance (R.). Its purpose is to permit adjustment of
the current to the constant value to be used in the experiment.

(Ra) is a standard one ohm resistance with a very low temperature
coefficient of resistivity. It is capable of being water cooled to
further reduce resistance variation with respect to temperature change.
Its purpose is to permit measurement of current in microamperes thru-
out a wide range by a measurement of the potential drop across itself,

using a potentiometer.

-11-

(PL, are two potential leads, of*# 44 platinum wire, electrically
welded to the hot wire. They take only a small part of the total
drop across the hot wire, right at the center. The reason this is done
is so that the measurement will be effective at the portion of the
hot wire which has a fairly uniform velocity of air flowing around
it. It also minimizes the effect of cooling at the ends of the hot
wire.

(8) is a reversing switch by means of which the potential drop
across the potential leads, or the drop across the standard resistance,
may be taken at will.

(80) and (G) are a standard cell and galvanometer respectively.
These instruments were suitable for use with the Type I Leeds and

lorthrup»pctentiomster, which.was used as a means of measuring potential.

numerous attempts were made to produce an air stream whose
velocity could be determined with sufficient accuracy to be used as
a means of calibrating the above anemometer. In all cases, with the
possible exception of the final one, the result was that the electrical
method was capable of detecting differences in air velocity which
could be measured in no other way. A few of these attempts will be
described by way of showing the sensitivity which may be attained with

this type of anemometer.

rhe first method employed was that used by King in which a
whirling table moved the anemoneter on the end of‘a rotating'arm thru

still air. It was found that a sufficiently accurate correction for

-12-

the swirl of the rotating arm could not be made, and also that
vibration of the wire, caused by the moving parts of the whirling

machine, produced spurious cooling effects.

In the second attempt, air was forced out thru a tube by
means of water displacement in a fairly large reservoir. The quantity
of water flowing into the reservoir per second could be measured,
and from this, as will be described later, the velocity of the air
at the center of the tube could be calculated. The source of water was
the college water system, and it was soon discovered that pressure.

fluctuations were so large that no consistent results could be obtained.

A third attempt made use of the same tube for mounting of the
anemometer element, but differed from the second in that water was
discharged from the reservoir under its own head. The actual velocity
of the air was then calculated on the assumption that the orifice
coefficient of discharge would be a constant, regardless of the slight
change in head of discharge, for the water. It was found that the
orifice coefficient did not remain constant fer all heads, and no
method of determining its change with changing head was discovered.
However, in using this method a very interesting observation was made.
As the velocity of the air stream gradually decreased with falling
head of discharge, it was found that the anemometer reading would
abruptly change at certain values of the velocity. Due to the un-

satisfactory apparatus, these values of velocity could not be determined

-13-

with great accuracy and so no actual data could be taken.

The final apparatus for measurement of actual air velocities
will be described by reference to Plate 2.

(A) is the hot wire anemometer mounted in the bakelite collar
whose inside dimension is exactly that of the aluminum tube shown
in the diagram.

(6) is a reservoir containing calcium chloride used to dry the
air thoroughly before passing it thru the aluminum tube. This reservoir
contained about 25 pounds of calcium chloride.

(B) is a reservoir from which air is displaced by water flowing
from the reservoir (8').

(V) is a valve by means of which the flow of water to (B) may be
controlled by very small increments.

(V)' is a valve admitting water from the college mains to the
reservoir (3'). This valve was manually controlled so that the
difference in level of water in (R) and (R') was maintained a constant
while the reservoir (R) was filling. In this way a constant flow of
water was maintained to within an error of one fourth of one percent.
The water guages (G) and (G') were equipped with graduations which
allowed adjustment of the water level in (R) and (R') to a constant

difference in level of 100 cm.

The following procedure was observed in taking readings. The
levels of the water in (B) and (B') were adjusted and a given valve setting

of 7 made. When the water had attained a steady rate of flow, the

-14-

time required for a certain quantity of water to enter (R) was measured

by means of a stop-watch. This measurement gave the average rate of
displacement of air from the reservoir (B). Meanwhile readings had been
made with the electrical anemometer. These readings consisted of an
adjustment of the current thru.the anemometer wire to .200 amperes

with an accuracy of 10'5 amperes. With this current flowing the drop
across the wire was measured and recorded. These readings were constantly
being taken as the water rose in the reservoir. Their average values

were uwed in.computing the loss in resistance due to the cooling action

of the air stream, as will be shown later.

The above procedure was followed for velocities which ranged

from 0 to 32 cm/sec. at approximately 1/2 em/soc. intervals.

-15-

DATA AND COMPUTATIONS.

The data obtained directly from experiment consists of
readings on the quantity of air forced out thru the anemometer tube
in cc./ sec. and the corresponding electrical readings which give
the resistance of the anemometer wire when at room.temperature and
when heated by a current of .20000 amperes. In order to keep the
data tabulations within bounds where they will not be burdensome to
the reader, only the final form from which the curves are plotted

will be given.

The computations required in order to obtain the velocity
of the air stream in cm./sec. from.the data which gives the quantity
of air, in cc./sec. , flowing thru the anemometer tube will be
considered first. Leigh Page’ gives the expression for the flow of

viscous fluid through a circular pipe as:

v. (21-221 (az-r") (1)

4 u.L
there I is the velocity of the fluid at a radius (r) from the center
of the pipe, (Pléle is the pressure difference across length (L)
of the pipe, (u) is the coefficient of viscosity of the fluid, and
(a) is the radius of the pipe. Page also shows that t

4
Q-vre (P-P) (2)
8 u.L 1 a

lhere Q is the volume of fluid / unit of time passing thru the pipe

and other quantities are as in equation (1}.

’Leigh.rages "Introduction to Theoretical Physics" pp. 279.

If we combine these two equations we get an expression:

V . 2 Q C a2 - r3) (3)
77“

If (r) be taken equal to 0 in this expression we obtain the velocity
at the center of the pipe:

Yo - 2 Q (4)
Via!

If (r) be taken equal to (a) we get the velocity at the walls of the
pipe to be equal to 0, which is what we should expect. Furthermore,
upon inspection of (3), we note that with V and (r) as the variables,
we have the equation of a parabola with its axis coincident with the
axis of the pipe. And if we take the derivative of V with respect to
(r), we get:

%- -;;_%r (5)
which shows that when (r) is small, the rate of change of V with
respect to (r) is also small, and therefore we should expect that the
velocity will be essentially constant for small distances from.the
center of the pipe. It is for this reason that the potential leads
take only a small portion of the total drop across the hot wire, right

at the center of the anemometer tube.

Making use of equation.(4) the values of the velocity at the
center of the anemometer tube were computed making use of the observed
displacement of air thru the tube in cc./sec. This data is plotted
as the independent variable in curve # 1. It is also tabulated under

the column I on pages 19 and 20.

The most convenient treatment of the electrical readings would
seem.to be the fellowingx It will be remembered from previous discussion
that the resistance of the anemometer wire, for any given velocity of
air stream, was always measured under two conditions. Under the first
condition the resistance is measured with a very small current flow so
that there is negligible heating; Since the resistance of any wire is
a function of flhe temperature we may denote the value of resistance
obtained in this manner (3‘). It may be further noted that this value
of the resistance would be the same regardless of the velocity of the
air stream, since it only measures the temperature of the air stream.

In the second case the resistance ef’the anemometer wire is measured
with a current of .20000 amperes flowing. This of course caused a rise
in temperature of the i 44 platinum wire, with a consequent rise in
resistance of’ths wire. low since the temperature of the wire depends

to a great extent upon the velocity of the air stream it will be well
to designate this value of resistance by (3'). Since not all the readings
are taken with exactly the same temperature of air stream the quantity
we are interested in as a measure of the velocity is not (3,), but the
difference between (RV) and (3‘). we may denote this quantity by the
symbol (6') or the gain in resistance due to 200 milliamperes when a
velocity V of the air stream exists. We might decide to plot this value
against V as the independent variable, but we should find that the curve
is displaced above the origin of our coordinate axis. For convenience
we may take the value of the gain.in resistance in still air, (6b) as

the reference, and plot values of (Go-6') against Y. Ihen we do this

DATA TABUIATION FOR CURVE # 1.
In the following tabulation:
F - velocity of air stream past the anemometer wire. ( em./sec.)
R‘u Resistance of wire at the temperature of the air stream. ( ohms )
B'- Resistance of wire carrying current I- 200 ma. in air at velocity V.
Ry‘na' Gain in resistance of wire due to passage of 200 ma.
Go-G'- Gain.in resistance of wire when velocity of air is 0 compared

to the gain in resistance when the velocity of the air is V.

V 3 3‘ z B, : Rvfln‘ : 00-0
8 8 8 8
0 8 04176 8 05001 8 00825 8 0
2.48 8 04175 8 0‘92? 8 00753 8 00073
3.33 a .4179 x .4898 a .0719 s .0106
4.07 8 .4179 8 .4881 8 .0702 8 .0123
4.91 z .4179 a .4863 t .0684 : .0l4l
5 033 8 04177 8 04850 8 00673 8 00158
5.06 8 .4179 8 .4860 8 .0681 8 .0144
5.06 8 .4181 8 .4862 8 .0681 8 .0144
4 0 19 8 04182 8 0‘88: 8 00701 8 00124
4 059 8 04184 8 0487‘ 8 00690 8 00135
4.80 s .4184 8 .4871 : .0687 x .0138
6.62 3 .4188 8 .4866 8 .0670 a .0155
5 0 79 8 04188 8 04850 8 0 0652 8 00165
6.47 8 .4189 8 .4837 8 .0648 8 .0177
6.97 8 .4191 8 .4827 8 .0636 8 .0189
70 59 8 04190 8 04816 8 00626 8 00199
8 041 8 04193 8 04803 8 00510 8 00210
8.85 8 .4194 8 .4796 8 .0602 8 .0223
9.29 8 .4197 8 .4789 8 .0592 8 .0233
9.70 8 .4195 8 .4782 8 .0587 8 .0238
9 096 8 04198 8 04778 8 00580 8 .0245
9.75 8 .4196 8 .4782 8 .0586 8 .0239
10.59 8 .4197 8 .4768 8 .0571 8 .0254
11 007 8 04195 8 04752 8 00567 - 8 00358
11.46 8 .4198 8 .4759 8 .0561 8 .0264
11 091 8 04198 8 04751 8 00553 8 00272
14.16 3 .4199 : .4726 x .0527 s .0298

-19-

14.62
15.10
15.49
15.92
16.44
17.14
17.58
17.99
18.36
17.50
19.91
20.42
20.84
21.33
21.73
21.68
22.44
22.86
23.28
21.18
23.88
24.27
25.12
25.76
26.67
27.60
26.16
26.39
26.83
27.94
28.39
29.67
29.88
30.64
31.42

”00.0.0.0”...OOO”~”””””"--“~”“0000......”OOOOuu

.4198
.4197
.4197
.4198
.4194
.4196
.4198
.4199
.4197
.4200
.4200
.4199
.4199
.4199
.4199
.4199
.4199
.4197
.4200
.4209
.4209
.4209
.4207
.4207
.4208
.4208
.4208
.4207
.4208
.4206
.4205
.4203
.4202
.4203
.4203

”N00000000“unnunuunnweeuueeeeueeun”00000000000000”

.4718
.4713
.4708
.4704
.4699
.4694
.4690
.4687
.4683
.4692
.4676
.4673
.4670
.4666
.4665
.4663
.4661
.4658
.4657
.4685
.4669
.4664
.4658
.4655
.4650
.4642
.4650
.4649
.4646
.4641
.4639
.4632
.4630
.4625
.4622

00.000.000.00...00”....00.0....”OO”””””””OOOOOO”~OOOOOONOO

.0520
.0516
.0511
.0506
.0505
.0498
.0492
.0488
.0486
.0492
.0476
.0474
.0471
.0467
.0466
.0464
.0462
.0461
.0457
.0468
.0452
.0447
.0443
.0440
.0434
.0426
.0434
.0434
.0430
.0427
.0426
.0421
.0420
.0414
.0411

00000000900090”00000000000000.0000000000000”00000000000000.000000000

.0305
.0309
.0314
.0319
.0320
.0327
.0333
.0337
.0339
.0333
O 0549
.0351
.0354
.0358
.0359
.0361
.0363
.0364
.0368
.0357
.0373
.0378
.0382
.0385
.0391
.0399
.0391
.0391
.0395
.0398
.0399
.0404
.0405
.0411
.0414

we find that our curve passes thru the origin and becomes asymptotic

to the value (60) for infinite values of V. This of course means that

it woudd require infinite velocity of air flowing by a wire to cool it

to the temperature of the air stream, it the wire carried current.

The experimental values of R“, EV, Gv-Rv-B‘, and Go-Gv are also tabulated
on pages 19 and 20, and the values of Go'Gv are plotted as the

dependent variable in Curve # 1.

Upon examination of Curve # 1, it is noticed that there are
small variations from its general trend. These variations are not very
large, being just barely noticeable above experimental error. The
fact that upon closer inspection we notice that there is periodicity
to these variations, lends to the argument that they really are existent.
It was considered worth.while to see if it might not be conclusively
shown that these variations exist separate from experimental error, and

that they have definite periodicity.

To do this the fellowing general method is proposed. It a
curve may be obtained which is an average of curve # 1, that is one
which does not show variations, then we might plot the deviation of the
experimental curve frmm the average curve against velocity. If the
variations are real and periodic, then these deviations will plot

much as a sine save against velocity as the independent variable.

To obtaine this average curve it was assumed that the

3
expression: T - a V + b V2, e c 7 + d

.21-

would hold over the limits fer which data has been taken. In

this equation T has replaced (Go-6V). The constants a, b, c, and

d must now be evaluated. Since (d) represents the point where the
curve crosses the T axis, it can very readily be obtained from.a large
scale drawing of the curve. It represents a loss in resistance due

to cooling of the wire by natural convection currents. It may be well
to point out at this place that (d) is exceedingly small, indicating
that natural convection currents have been reduced to a minimum. This
could be done on account of the high sensitivity of the electrical
apparatus. King has shown that the sensitivity is increased if the
temperature of the wire above that of the air stream is increased.
But large temperatures of the wire mean that natural convection currents
will also be large. These currents introduce uncontrolled, erratic
variations which can become larger than the periodic variations which
this experiment is attempting to prove. In Kings work temperature
differences of from 200 to 1000 degrees 0 were obtained. The maximum
temperature difference obtained in this experiment was 53°C, the
minimum difference was only 26°C. This accounts for the negligille

effects of convection currents.

The values of the constants a, b, and c were evaluated in
the following manner. Three points on the experimental curve were
chosen and three simultaneous equations in Y and T set up. From these
equations the values of a, b, and c could be determined. It was
recognised that these three points would not necessarily give the

average curve and so the operation was repeated as many times as possible

using different points for each solution. The average of the values
thus obtained were taken for the final form of the equation which

became: 3 2
T - .00000175 7 — .0001264 V + .003628 V - .00100

The computed values of T - Go—Gv for all values of Y observed
experimentally are tabulated on sheet # 24 and # 25. The observed
values of Go'Gv were now compared to the computed values and their
differences also tabulated on sheets 24 and 25. These differences
were then plotted as the dependent variable against velocity on curve
# 2. This curve partially fulfills our predictions that a sinusoidal
curve would be obtained. However the effect of experimental error
still overshadows the actual variation and it is difficult to determine

at what interval the curve repeats itself.

It is possible however, to mathematically show that these
variations actually exist, and to determine what the interval of
periodicity actually is. As a method of illustration, assume a
curve, y - sin ZWx . This curve is of course definitely periodic,
repeating itself at x - l, 2, 3 etc., and if we examine points which
are separated on the x axis by a distance x . l we will find that
there is no difference in the y values for such points. If however
points are chosen which are either larger or smaller than x - l in
separation, we obtain differences in the y values for such points. If
we were to average the y differences for a large number of applications

of a given x separation, regardless of sign, and then plot these averages

-23-

DATA TABULATIOH FOR CURE! ‘# 2.

In the following tabulation:

 

7 - Velocity of air stream past the anemmeter wire. ( ssh/sec.)
(Go-G')° - Computed values of (Go-6') using the equation
3 2 .4
(Go-6') I a V e b V + 0 V e 6 (ohms x 10 )
(Go-8') - Observed values of gain in resistance of anemometer
wire when 7 - 0 compared to the gain when velocity
of the air is 7.
D - Difference between observed and computed values of ( Go' 6')
7 : (Go-c')° : (Go-6') x D
x z a
0 a 0 8 0 z
2048 8 720‘ 8 73 8 4 05
3052 8 10:00 8 106 8 + 300
‘00? 8 11801 8 123 8 4 409
4.91 a 139.7 s 141 z 4 1.3
5033 8 1500‘ 8 153 8 4 105
5006 8 14305 8 144 8 4 05
‘019 8 12102 8 12‘ 8 4 208
4.59 a 131.7 x 135 x + 3.3
4.80 x 137.4 : 138 z e .6
5052 8 15705 8 155 8 i 305
5.79 8 161.3 x 163 z + .7
50‘? 8 17607 8 177 8 O 03
6097 8 1850‘ 8 189 8 4 306
7059 8 2000: 8 199 8 - 103
8.41 x 216.3 8 210 z - 6.1
8085 8 82405 8 223 8 - 105
9029 8 23202 8 233 8 4 08
9070 8 23908 8 258 8 - 102
9095 8 3‘50: 8 2‘5 8 + 107
9.75 a 240.0 x 239 a - 1.0
10059 8 2530‘ 8 254 8 + 06
11007 8 2500‘ 8 258 8 - 20‘
11046 8 26603 8 264 8 ~2.3
11.91 s 272.6 : 272 z - .6
14.16 x 300.2 x 298 x - 2.2
14.62 x 305.2 3 305 : - .2
15010 8 30909 8 309 8 ‘ 09

-24-

15.49
15.92
16.44
17.14
17.58
17.99
18.36
17.50
19.91
20.42
20.84
21.33
21.73
21.68
22.44
22.86
23.28
21.18
23.88
24.27
25.12
25.76
26.67
27.60
26.61
26.39
28.39
29.67
27.94
26.83
29.88
30.64
31.42
32.12

.0”00”..”09””””””””~”00”””””””00”09””””””

313.9
318.1
322.8
328.9
332.5
335.7
338.6
332.0
349.6
353.0
355.5
357.5
361.3
361.0
365.6
368.4
370.6
358.0
374.1
376.4
381.3
385.2
390.7
396.6
388.9
387.5
402.7
409.2
399.5
393.2
410.7
417.2
423.0
430.0

09..””00””"00”H"”~””””~””””N””N””00”....”

-25-

314
319
320
327
333
337
339

349
351
354
358
359
361
363

368'

357
373
378
382
385
391
399
391
391
399

398
395
405
411
414
416

”OO”O0.0””OO”N”NOO

””N”N””"””“”NNNOONOO””OO

I + I I l + + + + I | + +

I I I I 4 I I I + 0 + + I * + I I I I I

.1
.9
2.8
1.9
.5
1.3
.4
1.0
.6
2.0
1.5
.5
2.3

2.6
4.4
2.6
1.0
1.1
1.6
_ .7
.2
.3
2.4
2.9
3.5
3.7
5.2
1.5
1.8
5.7
6.2
9.0

14.0

against separations of x we should find that x . 0 the y values would
be 0, as x was increased the y values would increase coming to a
maximum and decreasing again to 0 when the x separation became 1. In
this way the value of the period would be very sharply defined.

How we may consider the case in which we have only random distribution
of points about an axis due to experimental error. If the same analysis
is made we would obtain a curve for which the y averages would be 0
when x - 0 separation. As the x separation increased the y averages would
rapidly increase and become asymptotic to a value of the y averages
which would represent the average experimental error. It is evident
that no increase of the x separation could ever reduce the y values to
0. If we should have a combination of these two situations, as we
suspect we have, in Curve # 2, analysis by the above method should

show that for x separation - 0 the y average will also be 0. As the

1 separation is increased the y averages will also increase, come to

a maximum and decrease to a minimum at a value of x separation equal to
the period. ve should not expect that this minimum be 0 however, but
rather the value which would be obtained for the average experimental
error. On page 27 are tabulated the results of such an analysis

of Curve # 2. On Curve sheet i 3 these results have been plotted and
show exactly what has been predicted. The minimum occurs at a value
of 2.9 cm/ sec. separation. This can now be taken as the average
period of the variations in curves # l, and f 2. With the help of

this result we may now draw the sinusoidal curve shown for curve 3 2.

~26-

DATA TABULATION FOR CURVE £ 3.
In the following tabulation the left hand column gives velocity
intervals in ass. per second. The right hand column gives the average
difference between computed values of (Go-8') and the observed values

of the same quantity, for each of these velocity intervals.

.5 cm./sec. 1.28 x 10"4 ohms

.8 1.62
1.0 1.97
1.2 1.93
1.4 2.22
1.6 2.13
1.8 2.07
2.0 2.17
2.2 2.00
2.4 1.95
2.5 1.87
2.8 1.78
2.9 1.72
3.0 1.74
3.2 1.91
3.4 2.04
3.6 2.31
3.8 2.25
4.0 2.37

-27-

INTERPRETATION OF RESULTS.

Having shown that there are variations in Curve # 1, it is
new necessary to interpret their meaning. Since Go-Gv represents a
loss in resistance due to a stream of air at velocity V, and since the
resistance is a direct function of the temperature of the platinum wire,
we really have plotted fall in temperature of a hot body against velocity
of the air stream past it. A decrease in temperature of a body'means
that an increase in the rate of heat dissipation has been effected in
some manner. Since there are only three ways in which a body may
dissipate heat, namely, by radiation, by conduction, or by convection,
it would be well to examine how each of these three factors enter into

the present problem.

We may consider radiation first. fhe characteristic form of

the equation giving the total radiation from metallic surfaces is z

e - a E
where T represents the absolute temperature,and (a) and (b) are
constants depending on the nature of the metal surface. From the ob-
servations of Bummer and Knrlbanm' it is determined that the radiation
loss for polished platinum is given in watts/cm? by:

. .- o.514 (fa/100015"2
In our particular problem it can be shown that the loss by radiation

is negligible. The highest temperature attained is 55°C above room

°anmer~a d Knrlbanm, 'Verh. Phys. Ges.,' Berlin, 17, p 106, 1898.

-28 -

temperature. With the room temperature 27°C this gives a value of
SSS‘A as the temperature of the wire. The total energy radiated to
a space at absolute 0 would then be:

0 I e514 (.3515.2 3 2.287 x 10.3

watts / sq. cm.

no. the wire used had a diameter of .0047 cm and was .56 cm. in length.
m. gives a total radiating surface of 3.09 x 10’5 cm. and we obtain
that the total energy radiated is E1 - 7.067 x 10"9 watts. However,
the wire is also picking up radiation from the surrounding space which
is at 500°A. Using the same equation it is found that the radiant
energy received by the wire is 32 . 3.002 x 10.9 watts. Upon subtracting
these, Eléiz - 4.065 x 10"9 watts, which represents the loss of
energy by radiation for the anemometer wire. The actual input to the
wire may be found very quickly by means of the Izr loss. The maximise
temperature of the wire is attained at 0 velocity of the air stream.

The value of the resistance at this temperature may be obtained from
page 19 and is r - .5001 ohms. The current used to maintain this tem-
perature was I - .200 amperes. The watts input to the wire are found
to be, I - .02 watts. It is readily seen that radiation is insignifi-

cant when compared to this value, and that no variations in the radiation

losses could possibly cause the variations observed.

When we consider the case of conduction of heat away from a
cylinder as small as the one employed in this research, it is admitted
that very little is known about the actual laws which govern such

conduction. However, a mathematical treatment of conduction and

~29-

 

convection of heat from short, hot, vertical cylinders by Khmball and
Childs' has verified the law that the heat transfer from such cylinders
is proportional to the five fourths power of the temperature excess.
This law should not be able to give us variations such as are noted,
since the heat transfer is shown to be a continuous function of the

temperature excess.

In considering the case of convection effects of the stream
of air passing the anemometer wire we must fall back on King's theoretical
equation given earlier in this paper, namely:

3 - KT + 3 VI’ T

In this equation the heat loss is again shown to be a continuous.function
of both T and V, and it could not vary periodically as our curve has done.
In general we may say that no known laws of either conduction or convection
could give us periodic variations in the heat loss of a hot body with
respect to either temperature or velocity, since they all indicate that
the heat loss should increase by a smooth curve,as both velocity and

temperature excess, or either one independently, increases.

Since no known laws can produce such variations in the curve
as have been obtained the only recourse we have is to assume that the
physical conditions of the boundary have actually changed. And since
there is definite periodicity of the variations with respect to velocity,
we are led to assume that it is an effect of the velocity of the air
stream.which is producing these changes in the structure of the boundary
region. It is with this thought as the basis that the following

explanation of these variations is advanced.

450-

As has been mentioned previously, Bolt has shown that there
is adhering to every solid, a film of gas which behaves very much like
a liquid. The thickness of this film is that of the radius of molecular
attraction (B). The reasoning we might advance for this phenomena is
that molecules of air are trapped in the strong field of attraction which
exists within the thickness (B). This causes an increase in density of
this layer. This value of density is of course less than that of the
solid, but decidedly greater than that of the main body of the air. In
fact Rolt showed that it exhibited the properties of a liquid, being

0.1 51.9.!

incompressible but having‘resistance to shear. As a film it is highly

stable, requiring very high pressures to puncture it.

It would be strange indeed if we should find that this film
could not do as the solid before it has done, namely produce another
fihm, also having thickness (R), with a density greater than that of air,
but less than that of its originator, and in general being Just a little
less stable. In fact with this one start we can visualize how a large
number of such films might exist, each one decreasing in density and
stability as its distance from the solid increases. we may next attempt
to show how this condition fits with the observed facts in our experiment.
Since these layers are more stable than a gas, we assume that there is
lhmited convection of molecules from one layer to another. With all
layers intact the only way that heat may be dissipated from the solid

cylinder is by actual conduction thru films having* very poor conductivity.

~31-

This means that the rate of heat transfer is quite low. Now if we should
allow the air stream to pick up velocity very slowly, as we should
expect, the rate of heat flow from the cylinder would also increase,
according to laws which King has derived. Then however the viscous drag
of the air stream increases to a value which equals the tensile strength
of the outermost, least stable film, that film is torn away and now heat
flow takes place more rapidly, due to the elimination of one of these
blanket films. As the velocity of the air stream is further increased,
cooling will also further increase, but with new constants which involve
the new thickness of the boundary films. As the velocity of air stream
is still further increased it is easy to imagine that the viscous drag
becomes equal to,and tears,successive films until finally, with very high
velocities, we have possibly only one remaining. This being the one Bolt
found was so hard to eliminate from the surface of guage blocks.

This explains why King's experimental data fits quite closely his
theoretical curve at high velocities, since he had sheared all the films
slay, and had only existent those conditions he was taking into account
in his theory. It also explains why King found it necessary to calibrate

low velocity anemometers by experiment rather than by his theoretical

fomul‘e

452-

BIBLIOGRAPHY.

Heat From Small Cylinders in a Stream of Fluid.
Phil. Trans. Roy. Soc. Ser A. 1914.
Prof. Louis Vessot King.

.Measurement of Air Flow.
Instruments. Vol. 4. # 12. p 670. Dec. 1931.
Be Our.

The Directional Hot tire Anmometer.
Phil. M36. D. 640. 1920.
J 0 S 0 Ge Thom, e

The Hot Wire Anemometer; Its Application to Investigation
of Velocity of Cases in Pipes.
P1111. Ms De 505s 19200
J. s. G. Thomas.

The Hot Tire Inclinometer; Its Sensitivity in Air and in
Carbon Dioxide.
Phil. Mag. 1925.
J. Se Ge Thomas.

The Physics and Chemistry of Surfaces.
Journal of Chem. Education. Nov. 1931.
Erik Ridge.

Smoke Particles on Liquid Films.
Phy. Chem. Journal. 1931.
Watson and Kibler.

Chemical Reactions at Liquid Surfaces .
M. Chem. SOC. J s 00': e 1930.
Davis and Crandall.

A Measurement of the Radius of Molecular Attraction.
Physical Review. Vol. 31. p. 170. 1910.
Ce 'e murhine

Guages and Fine Measurements. Vol. I.
F. He ROlt.

On the Conduct ion and Convection of Heat From Short,
Hot Vertical Cylinders.
Phil. Me 361'. 7e '01. 140 p 3370 1932s
I. S. Kimball and L. D. Childs.

 

 

 

1""- llll
ill“

1!..Nsimt 1 Na Yul

 

 

 

 

 

 

 

1.
.. . . H a w

.0 m3 mZoPfiNnmw

 

 

1‘

 

 

 

i r31} 3

_

 

 

 

 

 

 

 

 

I. . 1.!

 

 

 

 

\
—-

 

 

 

 

 

 

,
f‘ l
r /
3
E—

,< l /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

333-Mn33i-3- -- in 1% a - .4- a
.. _ Jam; tut 5.3 - 3aa§od>
_ A u *
_ l .
. a m r
_ . _
333- -L-.- - 51! - - - i.
A
- 34-333-333-33 -- 3 3 1.33.-.-- a--.. 3 -.
. l _ .
V333133-331-3 3.3-33 a 4:-
. _
U _ . i.
. . .x. l
_ \
\I
:1- _ 17.33--- i 33. :- . 4., --
. \-
.
W
3.3.3334. 33.3.3333 . 3 3 \3 3.- - - - H
w\Q\ees\
.\.
333-3...“- 3 3 - -
l \.\.

 

 

 

 

 

 

. eicx
ASVKQQQ \ “new

'iv‘

 

 

 

5011‘! -I

K

ka‘O

 

.113.»

 

mmhri

 

 

......

.....

. . ....

......

. . w - .

MTG -4--q§mm§\\ xaioms

 

.........

........

......

........

L... ._e L...

 

........

.....

mSU .

 

 

 

 

......

 

     
  

‘1

3333*?- --

 

 

 

 

o_ .3210

«watt \ \wukucuukfi

machete: v.

 

 

 

 

 

 

O.-90“l‘.

 

 

 

 

 

. II‘. II 3"

 

 

 

 

 

 

||||||3|||||33|||313131133133113 13313111331

 

312930168793