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Magnetic liquids for heat exchange
A. Kuzubov, O. Ivanova
To cite this version:
A. Kuzubov, O. Ivanova. Magnetic liquids for heat exchange. Journal de Physique III, EDP Sciences,
1994, 4 (1), pp.1-6. �10.1051/jp3:1994108�. �jpa-00249085�
Classification Physics Abstracts
75.50M 85.80L
Short Communication
Magnetic liquids for heat exchange
A. O. Kuzubov and O. I. Ivanova
Tarusa Department of General Physics Institute, Russian Academy of Science, 117942 Moscow Vavilov st. 38, Russia
(Received 16 july1993, revised 17 november1993, accepted 24 November 1993)
Abstract Magnetic liquids with mixed Me-Zn ferrites as dispersed phase were considered.
The dependence of magnetization of magnetic liquids on temperature was measured, pyromag-
netic coefficients were calculated from experimental data. The comparison with commonly used magnetic liquid was made.
The dependence of magnetic fluids magnetization on temperature gives the opportunity to use them as heat carrier in different types of heat exchange devices: energy-conversion systems, pumps, heat exchangers [I]. The advantage of apparatus which use magnetic liquids as heat carrier is the absence of any moving parts necessary for making liquid to flow in commonly used heat exchangers. The current of magnetic liquid is generated by temperature difference and nonuniform magnetic field which can be formed by the means of permanent magnet system.
The configuration of the latter determines the direction and type of magnetic liquid flow. Thus
thermomagnetic convection is easily directed. Moreover thermomagnetic convection is much
more intensive than gravitational one, that render the former an important advantage over the latter [2].
The intensity of thermomagnetic convection and therefore the efficiency of heat exchangers containing magnetic liquid is provided, under other equal conditions, by the value of pyro- magnetic coefficient of magnetic liquid K
=dM/dT, that is by the degree of dependence of
magnetization thereof on temperature. Langevin's formula for magnetization is appropriate for magnetic liquids:
M
=~amm(coth( I/(), (
=
pomvh/kT, (1)
where ~am is the volume concentration of magnetic phase, m is the saturation magnetization of dispersed material, V is the average volume of magnetic particle, H is the strength of magnetic field, k is Boltzmann constant, T is absolute temperature, po is magnetic permeability of
vacuum.
2 JOURNAL DE PHYSIQUE III N°1
By differentiation of magnetization with respect to temperature we get the value of pyro-
magnetic coefficient as the sum of three terms:
K
=PM + (3M/3m)(dm/dT( + (3M/3T)(, fl
=
-(I /p)dp/dT, (2)
where p is the density of magnetic liquid, fl is its thermal coefficient of expansion.
Each of these terms corresponds to concrete reason of magnetization change with temper-
ature. First of all it is thermal expansion of liquid and consequently the change of volume concentration of magnetic particles. Secondly it is change of the magnitude of magnetic mo-
ment of the particles. For the most part it is due to variation of saturation magnetization of magnetic material with temperature. The change of particle volume due to thermal expansion
is negligible because of small value of volumetric expansion of solid substances in comparison
with that of liquids. Thirdly the alteration of maglietic moment direction of concrete particle
occurs on account of disorienting thermal motion of molecules of liquid carrier.
In high enough magnetic fields, when magnetization of liquid is close to saturation, the
equation for pyromagnetic coefficient can be simplified to:
K
=M(p + p~), p~
=
-(i/m)(dm/dT), (3)
where pm can be defined as relative pyromagnetic coefficient of dispersed material.
Thereby the problem of increasing of pyromagnetic coefficient of magnetic liquids consists in the appropriate choice of such magnetic material which should provide for the corresponding liquid the maximum value of sum (pm + (dm/dT( in required temperature range (for the same values of fl and ~am, I-e- for the same liquid carrier and the same concentration of magnetic phase). Hence the choice of magnetic material depends on type of liquid carrier too. It is
evident from the last formula that for the liquids with large coefficient of volumetric expansion with temperature the value of magnetization of dispersed material is of great significance. For the liquids with small value of this coefficient the magnitude of (dm/dT( is more important.
In low magnetic fields, when the linear law of magnetization may be assumed, pyromagnetic coefficient is expressed as follows:
K
=M(I IT + fl + 2flm) (4)
Thereby the share of dispersed material in pyromagnetic coefficient becomes more significant.
The most commonly used magnetic material used as the basis of magnetic liquids is mag- netite Fe304. Although magnetite saturation magnetization is rather high (Ms Cf 500 kA/m) pyromagnetic coefficient thereof is low enough since Curie point of magnetite Tc
"858 K is much higher than temperature range of existence of most liquids.
Since the pyromagnetic coefficient of magnetic liquid is of primary consideration in context of this work the task was to choose magnetic material with rather low Curie temperature so
that pyromagnetic coefficient of corresponding magnetic liquid should be significant at room
temperature. Depending on the particular application it is possible to obtain oxides, nitrides
or ferromagnetic metal alloys with appropriate Curie points. Mixed ferrites MezZni-zFe204 where Me is Mn, Ni, Co were employed for preparation of particular ferrofluids in this work [3].
Ferrites are oxides and have the structure of inverse spinel similar to that of magnetite. Great
advantage of these ferrites is that varying the ratio of initial components we can vary ferrite compositions thereby obtain magnetic liquids with different Curie temperatures and different
pyromagnetic coefficients.
For the purpose of choice of particular magnetic fluids most suitable for heat exchangers 20
samples of different magnetic liquid compositions were synthesized. Ferrites MezZni-zFe204
were prepared by chemical precipitation of proper salts mixture with sodium hydroxide. The precipitate was boiled for some hours, whereat magnetic particles were covered with dispersing agent (oleic acid) and dispersed in hydrocarbon (dodecane). The properties of six samples
were investigated in details. Details of individual magnetic liquids are represented in table I.
Densities of magnetic liquids were measured by the method of hydrostatic weighing at temper-
ature of 20 °C. The error of density measurements was no more than 0.I %. Measurements of
magnetization were carried out by the means of vibration magnetometer in the magnetic field of 0.175 T in the temperature range from 20 °C up to 150 °C. The accuracy of magnetization
measurements was about 4 % for standart magnetite sample at 20
°C. The main source of the
error arises from the noise in the detection coils. Table I also comprise values of pm calculated
from available literature data on temperature dependence of saturation magnetization of cor-
responding ferrites [4,5]. Figure I shows variation of magnetization of magnetic liquids with temperature.
Table I. Density, magnetization and relative pyromagnetic coejJicients of magnetic liquids and disperse materials at 20 °C.
Composition of Pi
~
flM.103, M, flm.10~,
disperse phase kg/m K~~ kA/m K~~
l120 15.2 6.5 6.9
1080 5.0 9.9 4.1
1070 8.2 7.8 2.9
7Zno.3Fe204 l150 3.5 16.2 1.6
Coo_5Zno_5Fe204 1080 llA 8.0 5A
Coo_7Zno_3Fe204 1220 4.9 23.4 4.7
l140 1.2 26.1 0.55
As mentioned above relative pyromagnetic coefficient falls into range which limits depend
on that weather magnetic liquid attains its saturation magnetization (3) or its magnetization corresponds to the linear part of magnetization curve (4). Thereby the value of pyromagnetic coefficient enable us to draw conclusion about degree of magnetization of magnetic liquid in given magnetic field. The point to be noted is the fact that the measurements of magnetization by this method does not take into account variation of magnetization with temperature due to
thermal expansion of liquid. To consider this fact one must multiply the value of magnetization (Fig, I) by additional coefficient (I fl(t 20) where t denotes temperature in degrees Celsius.
Thus while comparing relative pyromagnetic coefficient of magnetic liquid PM
=KIM with its limits (3, 4) one must either omit the value of fl from equations (3, 4) or add the values of pm from the table to the magnitude of fl.
Tabulated results demonstrate that the only liqpid comprising ferrite Coo_7Zno.3Fe204 as the basis attains the saturation magnetization in given magnetic field. Pyromagnetic coefficients of
other liquids are intermediate. If magnetic liquid achieves saturation magnetization it is easy to determine the concentration of magnetic phase if saturation magnetization m thereof is known.
Having determined the concentration from the magnetizations of liquid and corresponding
ferrite at definite temperature we can gain the dependence m(T)
=
M(T) /~am from established
dependence M(T) and compare it with literature data [4]. Figure 2 depict good agreement in
considered temperature range.
4 JOURNAL DE PHYSIQUE III N°1
M/M2°
1 ~q
o
~
a0.8 $
a a
0.6 °~ o
o
°
~ +
°'
o
S
6 iy
o o
6
o_~
0 20 40 60 80 100 120 140
t, ~C a)
M/M20
1-1
1j ~~&jf&
~
q
~ & a~°~
a ~ ~ " " ~ & aaa a
o~ a
0.8
°~
o~
a~ a
o
~ +
0.5 ~ "
o
0 20 40 60 80 100 120 140
t, °C b)
Fig. 1. -Relative magnetization of magnetic liquid M/M(t
=
20 °C) versus temperature: a)
Meo.5Zno.5Fe204, Me (+) Mn, (U) Ni, (Q) Co; b) (li) Fe304> Meo.7Zno.3Fe204, Me:
(+) MD, (U) Ni, (Q) Co.
For those magnetic liquids which have not attained saturation magnetization one can em-
ploy the equation (2) and measured value PM to calculate Langevin's parameter ( as value PM depends only on this parameter. Hence it is possible to evaluate magnetic diameter of
the particle dm and then using formula (1) estimate saturation magnetization of magnetic liq-
uid and concentration of magnetic phase. Table II demonstrate calculated hereby the values
of concentration of magnetic phase, particle sizes as well as concentrations of solid phase ~a
m,kA/m
550 v~ b
500 ~
ir
450 «w
400
~~ v
o w
300
~
~o
250
"280 300 320 340 360 380 400
T, K
Fig. 2. Comparison of magnetization of ferrite Coo. 7Zno.3Fe204 obtained from the measured mag- netization of magnetic liquid (V) with data of Okamura Xc Kojima [4] (Q).
Table II. Volume concentration of magnetic and solid phase, magnetic size of the particle
and the thickness of nonmagnetic layer of the particle calculated from experimental data on
magnetization of magnetic liquids.
Compositionof dm, ~am ~a h,
phase ~fll ~m
Mno_5Zno.5Fe204 6.0 0.058 0A
Mno.7Zno.3Fe204 10.5 0.029 1.9
5.0 0.054 0.2
7.5 0.062 0.5
Coo.5Zno.5Fe204 6.0 0.039 0.7
Coo.7Zno.3Fe204 0.047
8.5 0.063 0.5
calculated from data on densities of magnetic liquids p and density of liquid carrier p~
~a
=(P Po)/(Pf Pa), (5)
where pi is the density of solid phase. The values of concentrations of solid phase and magnetic phase make it possible to estimate the thickness of nonmagnetic layer of the particle:
h
=0.5(d dm)
=0.5 dm
((~a/~am)~/~ l)
,
