- Email: [email protected]
Effect of a magnetic field on the performance of an energy conversion system using magnetic fluid
Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
E!ect of a magnetic "eld on the performance of an energy conversion system using magnetic #uid K. Shimada *, S. Kamiyama, M. Iwabuchi Faculty of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-77, Japan Received 8 May 1998; received in revised form 10 August 1998
Abstract A magnetic #uid's thermo-hydrodynamic characteristics in an energy conversion system with parallel ducts depend strongly on the system's type of magnetic "eld distribution. These characteristics are estimated by the numerical analysis taking into account the internal angular momentum of particles in the magnetic #uid qualitatively. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic #uids; Energy conversion; Thermo-hydrodynamic characteristics; Internal angular momentum; E$ciency; Numerical analysis
1. Introduction Concerning energy conversion systems utilizing magnetic #uids, much research has been conducted using various types of #ow ducts to clarify the e!ect of applied magnetic "elds on the #ow characteristics of the system [1}4]. In these investigations, most of the theoretical analyses have been conducted by using one-dimensional #ow models or momentum equations taking into account only magnetic pressure. Theoretical analyses taking into account the e!ect of the internal angular momentum of particles have not been conducted in detail. Also, the e!ect of magnetic "elds on the system's thermo-hydrodynamic characteristics has not been well-elucidated. * Corresponding author. Fax: #81-764-45-6781. E-mail address: [email protected] (K. Shimada)
Therefore, in the present paper, we clarify experimentally the e!ect of the applied magnetic "eld on the conversion e$ciency and the thermo-hydrodynamic characteristics of a system with parallel ducts. We also conduct a theoretical analysis taking into account the e!ect of internal angular momentum of particles on the performance of the conversion system.
2. Experimental investigation The test apparatus as shown in Fig. 1 has a #ow section of two parallel ducts. The ducts have height of S"2.5 mm with constant high temperature ¹ and S "1.25 mm with constant low & temperature ¹ . The width is 50 mm in both ducts. ! We also use another #ow section with S"1.25 mm and S "2.5 mm. Several types of non-uniform
0304-8853/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 1 0 8 - 0
358
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
e$ciency of the system is obtained from the data of pressure and temperature di!erences between ¹ and ¹ , volumetric #ow rate, and the speci"c heat of the magnetic #uid solvent.
3. Theoretical analysis Numerical analysis of the basic equations of mass, momentum, and energy conservation as shown by Eqs. (1)}(5) are conducted by taking into account the internal angular momentum of the spherical particles:
) *"0, o
(1)
1 AB DyH "! pH# **H# (MH ) )HH Re C Re DtH B Gr #
;(SH!XH)! ¹He , E 2C Re Re
DSH A 1 " MH;HH! (SH!XH), D DtH D
(3)
DMH 1 1 MH " (SH;MH)! MH!HH , DtH B C HH
(4)
1 D¹H " ¹H#r H#UH, T Pe DtH
(5)
where 1 UH" ( *H#*H ) : ( *H#*H ) T E
Fig. 1. Experimental apparatus and type of magnetic "eld.
steady magnetic "elds as shown in Fig. 1 are applied to the duct by the arrangement of a few electromagnetic poles. The test #uid is a kerosenebased magnetic #uid with a 50% mass concentration of particles whose magnetization depends strongly on temperature. We measure temperatures ¹ and ¹ at both ends of the applied magnetic "eld region in the duct, ¹ at the middle portion of the duct, ¹ , ¹ , and ¹ at each point in the region of the circulating #ow loop connected to the duct as well as pressure di!erence and volumetric #ow rate in the pipe of the circulating #ow loop. The
(2)
B Bo q ! (SH!XH)#
SH : SH EC EC Re AB # (SH;HH), EC * *H" , v p p H" , ov S SH" (I/q
x t xH" , ¸"S, tH" , ¸ (¸/v ) r ¹!¹ , r H" , ¹H" c *¹v /¸ *¹ N )
, XH"q X,
M MH" , M
H HH" , H
M , MH" M
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
359
H HH" , *¹"¹ !¹ , & H
j j v " , Re" , c o¸ cg N N k M H qq I Pe"1, A" , B" , I gq jq jq oc *¹¸ o C" , D" , E" N , o " , c o¸ c o¸ gv o N N q o !o ¹ #¹
, ¹ " & , q " , b"
o (¹ !¹ ) 2 q
in which t is the time, v the velocity, x the direction, p the pressure, o the density of magnetic #uid, r the quantity of heat, c the speci"c heat, ¹ the temperN ature, S the internal angular momentum of particles, I the sum of the moment of inertia of particles per unit volume, q the relaxation time of Brownian motion, q the relaxation time of rotational motion of the #uid, X the rotation of the #uid, M the magnetization, M the equilibrium magneti zation, H the magnetic "eld, H the maximum of
the magnetic "eld, j the thermal conductivity, g the
Fig. 3. Experimental results of e$ciency variation over time.
Fig. 2. Experimental results of temperature variation over time.
viscosity in a non-magnetic "eld, Gr the Grashof number, Re the Reynolds number, Pe the Pecret number, o the density of the solvent, b the coe$ cient of volume expansion, ¹ the reference tem perature, o the value of o at ¹ and o the value of
o at ¹ .
We use the HSMAC method to calculate time variation of temperature, pressure, and velocity of
360
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
Fig. 4. Theoretical results of temperature variation over time.
Fig. 5. Theoretical results of e$ciency variation over time.
the magnetic #uid #ow including the e!ect of natural convection.
sis. However, the e$ciency estimated is smaller than the experimental data. The cause of this di!erence is that the pressure di!erence and saturated value of temperature ¹ estimated by theory are too small. The cause may be considered to be due to the e!ect of particles aggregating during the experiment, however, more investigations should be made.
4. Results and discussion Figs. 2 and 3 show the experimental results of time variation of temperature and conversion e$ciency. Figs. 4 and 5 show the calculated results of time variation of temperature and conversion e$ciency by numerical analyses taking into account internal angular momentum (Mag.) at S"2.5 mm and NS-9A under Pr"0.2985, Gr"14.15, A" 3.253;10, B"8.613;10\, C"2.472;10\, D"7.466;10\, E"5.964;10, o "1.551 and q "3.020;10\, as well as taking into account only magnetic pressure (Only Mag. Pressure). There is an e!ect of the dimensions of #ow sections of S and S on e$ciency. The e$ciency level can be changed by using a magnetic "eld with a crossed direction rather than a single direction. There are small quantitative di!erences between at Mag. and at Only Mag. Pressure in Fig. 5, in spite of appearances of almost the same values. Actually, we obtained the results that ¹ , pressure di!erence, generating #ow rate, and e$ciency except for ¹ and ¹ are larger at Mag. than at Only Mag. Pressure. These parameters become larger by the e!ect of internal angular momentum. On the other hand, the saturated value of temperature ¹ can be e!ectively predicted by theoretical analy
5. Conclusions (1) The thermo-hydrodynamic characteristics of magnetic #uid and its e$ciency in new energy conversion systems depend strongly on the type of applied magnetic "eld distribution. (2) The analytical results obtained taking into account the particles' internal angular momentum estimate thermo-hydrodynamic characteristics qualitatively. Also, the high temperature can be estimated quantitatively by the analysis. However, system e$ciency cannot be clearly estimated. References [1] E.L. Resler Jr., R.E. Rosensweig, AIAA J. 2 (1964) 1418. [2] H. Matsuki, K. Yamada, K. Murakami, IEEE Trans. Mag. 13 (1977) 1143. [3] J.A. Barclay, J. Appl. Phys. 53 (1982) 2887. [4] K. Shimada, M. Iwabuchi, K. Okui, S. Kamiyama, Appl. Mech. Eng. 1 (1996) 543.
E!ect of a magnetic "eld on the performance of an energy conversion system using magnetic #uid K. Shimada *, S. Kamiyama, M. Iwabuchi Faculty of Engineering, Toyama University, 3190 Gofuku, Toyama 930-8555, Japan Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-77, Japan Received 8 May 1998; received in revised form 10 August 1998
Abstract A magnetic #uid's thermo-hydrodynamic characteristics in an energy conversion system with parallel ducts depend strongly on the system's type of magnetic "eld distribution. These characteristics are estimated by the numerical analysis taking into account the internal angular momentum of particles in the magnetic #uid qualitatively. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic #uids; Energy conversion; Thermo-hydrodynamic characteristics; Internal angular momentum; E$ciency; Numerical analysis
1. Introduction Concerning energy conversion systems utilizing magnetic #uids, much research has been conducted using various types of #ow ducts to clarify the e!ect of applied magnetic "elds on the #ow characteristics of the system [1}4]. In these investigations, most of the theoretical analyses have been conducted by using one-dimensional #ow models or momentum equations taking into account only magnetic pressure. Theoretical analyses taking into account the e!ect of the internal angular momentum of particles have not been conducted in detail. Also, the e!ect of magnetic "elds on the system's thermo-hydrodynamic characteristics has not been well-elucidated. * Corresponding author. Fax: #81-764-45-6781. E-mail address: [email protected] (K. Shimada)
Therefore, in the present paper, we clarify experimentally the e!ect of the applied magnetic "eld on the conversion e$ciency and the thermo-hydrodynamic characteristics of a system with parallel ducts. We also conduct a theoretical analysis taking into account the e!ect of internal angular momentum of particles on the performance of the conversion system.
2. Experimental investigation The test apparatus as shown in Fig. 1 has a #ow section of two parallel ducts. The ducts have height of S"2.5 mm with constant high temperature ¹ and S "1.25 mm with constant low & temperature ¹ . The width is 50 mm in both ducts. ! We also use another #ow section with S"1.25 mm and S "2.5 mm. Several types of non-uniform
0304-8853/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 1 0 8 - 0
358
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
e$ciency of the system is obtained from the data of pressure and temperature di!erences between ¹ and ¹ , volumetric #ow rate, and the speci"c heat of the magnetic #uid solvent.
3. Theoretical analysis Numerical analysis of the basic equations of mass, momentum, and energy conservation as shown by Eqs. (1)}(5) are conducted by taking into account the internal angular momentum of the spherical particles:
) *"0, o
(1)
1 AB DyH "! pH# **H# (MH ) )HH Re C Re DtH B Gr #
;(SH!XH)! ¹He , E 2C Re Re
DSH A 1 " MH;HH! (SH!XH), D DtH D
(3)
DMH 1 1 MH " (SH;MH)! MH!HH , DtH B C HH
(4)
1 D¹H " ¹H#r H#UH, T Pe DtH
(5)
where 1 UH" ( *H#*H ) : ( *H#*H ) T E
Fig. 1. Experimental apparatus and type of magnetic "eld.
steady magnetic "elds as shown in Fig. 1 are applied to the duct by the arrangement of a few electromagnetic poles. The test #uid is a kerosenebased magnetic #uid with a 50% mass concentration of particles whose magnetization depends strongly on temperature. We measure temperatures ¹ and ¹ at both ends of the applied magnetic "eld region in the duct, ¹ at the middle portion of the duct, ¹ , ¹ , and ¹ at each point in the region of the circulating #ow loop connected to the duct as well as pressure di!erence and volumetric #ow rate in the pipe of the circulating #ow loop. The
(2)
B Bo q ! (SH!XH)#
SH : SH EC EC Re AB # (SH;HH), EC * *H" , v p p H" , ov S SH" (I/q
x t xH" , ¸"S, tH" , ¸ (¸/v ) r ¹!¹ , r H" , ¹H" c *¹v /¸ *¹ N )
, XH"q X,
M MH" , M
H HH" , H
M , MH" M
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
359
H HH" , *¹"¹ !¹ , & H
j j v " , Re" , c o¸ cg N N k M H qq I Pe"1, A" , B" , I gq jq jq oc *¹¸ o C" , D" , E" N , o " , c o¸ c o¸ gv o N N q o !o ¹ #¹
, ¹ " & , q " , b"
o (¹ !¹ ) 2 q
in which t is the time, v the velocity, x the direction, p the pressure, o the density of magnetic #uid, r the quantity of heat, c the speci"c heat, ¹ the temperN ature, S the internal angular momentum of particles, I the sum of the moment of inertia of particles per unit volume, q the relaxation time of Brownian motion, q the relaxation time of rotational motion of the #uid, X the rotation of the #uid, M the magnetization, M the equilibrium magneti zation, H the magnetic "eld, H the maximum of
the magnetic "eld, j the thermal conductivity, g the
Fig. 3. Experimental results of e$ciency variation over time.
Fig. 2. Experimental results of temperature variation over time.
viscosity in a non-magnetic "eld, Gr the Grashof number, Re the Reynolds number, Pe the Pecret number, o the density of the solvent, b the coe$ cient of volume expansion, ¹ the reference tem perature, o the value of o at ¹ and o the value of
o at ¹ .
We use the HSMAC method to calculate time variation of temperature, pressure, and velocity of
360
K. Shimada et al. / Journal of Magnetism and Magnetic Materials 201 (1999) 357}360
Fig. 4. Theoretical results of temperature variation over time.
Fig. 5. Theoretical results of e$ciency variation over time.
the magnetic #uid #ow including the e!ect of natural convection.
sis. However, the e$ciency estimated is smaller than the experimental data. The cause of this di!erence is that the pressure di!erence and saturated value of temperature ¹ estimated by theory are too small. The cause may be considered to be due to the e!ect of particles aggregating during the experiment, however, more investigations should be made.
4. Results and discussion Figs. 2 and 3 show the experimental results of time variation of temperature and conversion e$ciency. Figs. 4 and 5 show the calculated results of time variation of temperature and conversion e$ciency by numerical analyses taking into account internal angular momentum (Mag.) at S"2.5 mm and NS-9A under Pr"0.2985, Gr"14.15, A" 3.253;10, B"8.613;10\, C"2.472;10\, D"7.466;10\, E"5.964;10, o "1.551 and q "3.020;10\, as well as taking into account only magnetic pressure (Only Mag. Pressure). There is an e!ect of the dimensions of #ow sections of S and S on e$ciency. The e$ciency level can be changed by using a magnetic "eld with a crossed direction rather than a single direction. There are small quantitative di!erences between at Mag. and at Only Mag. Pressure in Fig. 5, in spite of appearances of almost the same values. Actually, we obtained the results that ¹ , pressure di!erence, generating #ow rate, and e$ciency except for ¹ and ¹ are larger at Mag. than at Only Mag. Pressure. These parameters become larger by the e!ect of internal angular momentum. On the other hand, the saturated value of temperature ¹ can be e!ectively predicted by theoretical analy
5. Conclusions (1) The thermo-hydrodynamic characteristics of magnetic #uid and its e$ciency in new energy conversion systems depend strongly on the type of applied magnetic "eld distribution. (2) The analytical results obtained taking into account the particles' internal angular momentum estimate thermo-hydrodynamic characteristics qualitatively. Also, the high temperature can be estimated quantitatively by the analysis. However, system e$ciency cannot be clearly estimated. References [1] E.L. Resler Jr., R.E. Rosensweig, AIAA J. 2 (1964) 1418. [2] H. Matsuki, K. Yamada, K. Murakami, IEEE Trans. Mag. 13 (1977) 1143. [3] J.A. Barclay, J. Appl. Phys. 53 (1982) 2887. [4] K. Shimada, M. Iwabuchi, K. Okui, S. Kamiyama, Appl. Mech. Eng. 1 (1996) 543.