Review Topical Sections

A comprehensive study on structure, properties, synthesis and characterization of ferrites

  • The research on ferrites is fast moving owing to their exponentially growing usage in magnetic shielding, magnetic biosensors, magnetic recording devices, information storage, mobile communication, electronic devices, gyromagnetic device, medical devices, transformers, pollution control, catalysis, and pigments. This review comprises the present state of the art on hexagonal ferrites (HFs) and spinel ferrites (SFs). The article covers the background, properties, classification schemes, synthesis and characterization of ferrites. It focuses on a comparative understanding of four synthesis routes, magnetic properties and characterization of the ferrites. The article emphases X-ray diffraction, scanning electron microscopy, transmission electron microscopy, vibrating sample magnetometer, spectroscopy, thermal analysis and vector network analyser results. The present work is meant for the faster understanding of this research area.

    Citation: Ajitanshu Vedrtnam, Kishor Kalauni, Sunil Dubey, Aman Kumar. A comprehensive study on structure, properties, synthesis and characterization of ferrites[J]. AIMS Materials Science, 2020, 7(6): 800-835. doi: 10.3934/matersci.2020.6.800

    Related Papers:

    [1] Chii-Dong Ho, Jr-Wei Tu, Hsuan Chang, Li-Pang Lin, Thiam Leng Chew . Optimizing thermal efficiencies of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes. Mathematical Biosciences and Engineering, 2022, 19(9): 8648-8670. doi: 10.3934/mbe.2022401
    [2] Yi Ren, Guolei Zhang, Longbin Yang, Yanwei Hu, Xiaojing Nie, Zhibin Jiang, Dawei Wang, Zhifan Wu . Study on seafloor hydrothermal systems circulation flow and heat transfer characteristics. Mathematical Biosciences and Engineering, 2022, 19(6): 6186-6203. doi: 10.3934/mbe.2022289
    [3] Weirui Lei, Jiwen Hu, Yatao Liu, Wenyi Liu, Xuekun Chen . Numerical evaluation of high-intensity focused ultrasound- induced thermal lesions in atherosclerotic plaques. Mathematical Biosciences and Engineering, 2021, 18(2): 1154-1168. doi: 10.3934/mbe.2021062
    [4] K. Maqbool, S. Shaheen, A. M. Siddiqui . Effect of nano-particles on MHD flow of tangent hyperbolic fluid in a ciliated tube: an application to fallopian tube. Mathematical Biosciences and Engineering, 2019, 16(4): 2927-2941. doi: 10.3934/mbe.2019144
    [5] EYK Ng, Leonard Jun Cong Looi . Numerical analysis of biothermal-fluids and cardiac thermal pulse of abdominal aortic aneurysm. Mathematical Biosciences and Engineering, 2022, 19(10): 10213-10251. doi: 10.3934/mbe.2022479
    [6] Rebeccah E. Marsh, Jack A. Tuszyński, Michael Sawyer, Kenneth J. E. Vos . A model of competing saturable kinetic processes with application to the pharmacokinetics of the anticancer drug paclitaxel. Mathematical Biosciences and Engineering, 2011, 8(2): 325-354. doi: 10.3934/mbe.2011.8.325
    [7] Nattawan Chuchalerm, Wannika Sawangtong, Benchawan Wiwatanapataphee, Thanongchai Siriapisith . Study of Non-Newtonian blood flow - heat transfer characteristics in the human coronary system with an external magnetic field. Mathematical Biosciences and Engineering, 2022, 19(9): 9550-9570. doi: 10.3934/mbe.2022444
    [8] Colette Calmelet, John Hotchkiss, Philip Crooke . A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Mathematical Biosciences and Engineering, 2014, 11(6): 1449-1464. doi: 10.3934/mbe.2014.11.1449
    [9] Peng Zheng, Jingwei Gao . Damping force and energy recovery analysis of regenerative hydraulic electric suspension system under road excitation: modelling and numerical simulation. Mathematical Biosciences and Engineering, 2019, 16(6): 6298-6318. doi: 10.3934/mbe.2019314
    [10] Daniel Cervantes, Miguel angel Moreles, Joaquin Peña, Alonso Ramirez-Manzanares . A computational method for the covariance matrix associated with extracellular diffusivity on disordered models of cylindrical brain axons. Mathematical Biosciences and Engineering, 2021, 18(5): 4961-4970. doi: 10.3934/mbe.2021252
  • The research on ferrites is fast moving owing to their exponentially growing usage in magnetic shielding, magnetic biosensors, magnetic recording devices, information storage, mobile communication, electronic devices, gyromagnetic device, medical devices, transformers, pollution control, catalysis, and pigments. This review comprises the present state of the art on hexagonal ferrites (HFs) and spinel ferrites (SFs). The article covers the background, properties, classification schemes, synthesis and characterization of ferrites. It focuses on a comparative understanding of four synthesis routes, magnetic properties and characterization of the ferrites. The article emphases X-ray diffraction, scanning electron microscopy, transmission electron microscopy, vibrating sample magnetometer, spectroscopy, thermal analysis and vector network analyser results. The present work is meant for the faster understanding of this research area.


    A wide variety of heat-transfer problems applied to Newtonian fluids flow in bounded conduits of cylindrical or parallel-plate geometries with negligible axial conduction has been successfully reduced and known as the Graetz problem [1,2]. Multi-stream or multiphase systems, however, are fundamentally different since conjugated boundary conditions must be coupled at the boundaries, referred to as conjugated Graetz problems [3,4], which were solved analytically by means of an orthogonal expansion technique [5,6] with the eigenfunction expansion in terms of the extended power series. Extension to markedly increased applications of practical processes with recycle-effect concept is possible. It's been widely used in separation, fermentation, and polymerization such as distillation [7], extraction [8], loop reactors [9], air-lift reactor [10], draft-tube bubble column [11], mass exchanger [12], and thermal diffusion column [13].

    Many materials of food, polymeric systems, biological process, pulp and paper suspensions [14] with high molecular weight in processing industries exhibit a range of non-Newtonian fluid behavioral features and display shear-thinning and/or shear thickening behavior [15,16]. Those non-Newtonian fluids can be treated as the laminar flow conditions with negligible viscoelastic effects based on their high viscosity levels in the appropriate shear rate range [17]. Therefore, the analytical solution could be analogously obtained under the similar mathematical treatment when dealing with Newtonian fluids. A considerable body of literature has shown the practical feasibility of solving the power-law model of non-Newtonian flows by LBM (Lattice Boltzmann Method). It is also devoted to studying the non-Newtonian behavior with shear-thinning and shear-thickening liquids on sedimentation [18,19] and flows over a heated cylinder [20], an inclined square [21], cylinder [22] and various shapes [23]. Furthermore, the heat-transfer responses to the distributions of the conduit wall and fluid temperature are two major concerns in investigating the heat-transfer efficiency improvement under different kinds of boundary conditions which can be detected at the conduit wall. Two cases of the uniform wall temperature (Dirichlet problem) [24,25] and uniform heat flux (Neumann problem) [26,27] were processed in the application of engineering field, in general. Recently, a non-trivial amount of research use metal foams of PCMs (phase change materials) and nanoparticles of NEPCMs (nano-encapsulated phase change materials) to enhance heat transfer properties in some applications regarding constant heat load, transient, or cyclic loads. Thermal and energy storage managements of crucial importance of systems were investigated within the thermal performance given variable heat loads [28] and non-uniform magnetic sources [29], as well as thermal benefit of NEPCMs nanoparticles in microchannels that considers forced convection [30] and natural convection flow [31,32]. However, the well-known case of sinusoidal wall heat flux distribution [33] of non-uniform heating was the simplest model of period heating within the convective heat-transfer problems in the periodic [34] and circumferentially [35] heating systems. It's been investigated by many researchers to design the cooling tubes in nuclear reactors [36].

    The present study is an extension of our previous work [37] to apply the system of non-Newtonian fluids for the conjugated Graetz problem where the power-law index of the shearing-thinning aqueous polymer solutions were given. Though the phenomenon of heat transfer in the present study could be drawn parallel comparison, in similar sense, with that of heat-transfer mechanism in our previous work [37], the manners of non-Newtonian fluids with the convective heat transfer are somehow different. It's actually affected by the velocity profile of shear-thinning fluid. A power-law fluid flowing through a double-pass laminar countercurrent-flow concentric-tube heat exchanger that implemented an impermeable sheet with sinusoidal wall fluxes was investigated for the purpose of examining the heat transfer efficiency and temperature distributions under external recycling, which was solve analytically through the resultant conjugated partial differential equations by the superposition technique. The recycle ratio and impermeable-sheet position are two parameters treated as essential and should be suitably adjusted to an improved design of heat transfer equipment. The comparison of heat-transfer efficiency improvement and Nusselt numbers in both operations (single- and double-pass device) is also discussed.

    A double-pass concentric circular heat exchanger was made by inserting an impermeable sheet into a circular tube of inside diameter 2R and length L, as shown in Figure 1. The thickness of the inner (subchannel a) and annular tube (subchannel b) are 2κR and 2(1-κ)R, respectively. Comparing with the radius of outer circular tube R and outer circular tube R1, the thickness of the impermeable barrier δ is negligible (δ << R). Two flow patterns, flow pattern A and flow pattern B, are proposed by and used in this study. An inlet fluid with volumetric flow rate V and temperature T1 will enter the subchannel a and then flows reversely into the subchannel b with the aid of a convectional pump at the end of the conduit like flow pattern A, as shown in Figure 1(a). On the other hand, the flow pattern B is that the fluid feeds into subchannel b and exits from the subchannel a, as shown in Figure 1(b). The fluid is heated by the outer wall with sinusoidal heat fluxes, qw(z)=q0[1+sin(βz)] in both flow patterns.

    Figure 1.  Schematic diagram of a double-pass concentric circular heat exchanger.

    The problem of laminar heat transfer at steady state with negligible axial conduction was known as the Graetz problem, and the convective velocity in radial direction is neglected by applying the Navier-stokes relations to obtain the hydro-dynamical equation for laminar flow. The energy balance equations of fluid flowing in the subchannel a and subchannel b in dimensional form with specified velocities are:

    ρCpva(r)Ta(r,z)z=krr(rTa(r,z)r)+k2Taz2 (1)
    ρCpvb(r)Tb(r,z)z=krr(rTb(r,z)r)+k2Tbz2 (2)

    The theoretical analysis of double-pass heat exchangers is developed based on the following assumptions: (a) constant physical properties of fluid; (b) fully-developed laminar flow with power law index ω (τ=c˙γω) in each subchannel; (c) neglecting the entrance length and the end effects; (d) ignoring the longitudinal heat conduction and the thermal resistance of the impermeable sheet; (e) well mixed at both inlet and outlet. With these assumptions, the dimensionless energy balance equations and the velocity distributions of a double-pass heat exchanger with sinusoidal heat fluxes were formulated by neglecting the second terms on the right-hand side of Eq. (1) and Eq. (2). The descriptions of two or more contiguous streams of multi-stream (or phases of multi-phase) problems with coupling mutual boundary conditions [38,39] becomes

    (va(η)R2αGzL)φa(η,ξ)ξ=1ηη(ηφa(η,ξ)η) (3)
    (vb(η)R2αGzL)φb(η,ξ)ξ=1ηη(ηφb(η,ξ)η) (4)

    where va and vb are the velocity distributions in subchannels a and b, respectively, as follows in flow pattern A:

    va=(3ω+1ω+1)Vπ(κR)2(1(ηκ)ω+1ω)=G(1(ηκ)ω+1ω),0ηκ (5)
    vb=(3+1/ω)VπR2[(1β2)1+1ωκ11ω(β2κ2)1+1ω]ηκ(β21ηη)1ωdη=Hηκ(β21ηη)1ωdη,κηβ (6)
    vb=(3+1/ω)VπR2[(1β2)1+1ωκ11ω(β2κ2)1+1ω]1η(ηβ21η)1ωdη=H1η(ηβ21η)1ωdη,βη1 (7)

    and in flow pattern B:

    va=(3ω+1ω+1)Vπ(κR)2(1(ηκ)ω+1ω)=G(1(ηκ)ω+1ω),0ηκ (8)
    vb=(3+1/ω)VπR2[(1β2)1+1ωκ11ω(β2κ2)1+1ω]ηκ(β21ηη)1ωdη=Hηκ(β21ηη)1ωdη,κηβ (9)
    vb=(3+1/ω)VπR2[(1β2)1+1ωκ11ω(β2κ2)1+1ω]1η(ηβ21η)1ωdη=H1η(ηβ21η)1ωdη,βη1 (10)

    The values of β (vb(β)=vb,max) in Eq. (6) and Eq. (7) for flow pattern A, and Eq. (9) and Eq. (10) for flow pattern B, were obtained via the given ω and κ, as shown in Table 1 [40]. The terms with the power law index ω on the right-hand side of Eq. (5) and Eq. (6) and (7) for flow pattern A (Eq. (9) and (10) for flow pattern B), respectively, were approximated using the polynomials fitted at the selected points for the acceptable tolerance as follows:

    (1(ηaκ)ω+1ω)=U1+U2η+U3η2+U4η3+U5η4 (11)
    ηκ(β21ηη)1ωdη+1η(ηβ21η)1ωdη=Z1+Z2η+Z3η2+Z4η3+Z5η4 (12)
    Table 1.  The values of β in Eqs. (4) and (5) (or Eqs. (7) and (8)) for various ω and κ.
    0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
    0.1 0.3442 0.4687 0.5632 0.6431 0.7140 0.7788 0.8389 0.8954 0.9489
    0.2 0.3682 0.4856 0.5749 0.6509 0.7191 0.7818 0.8404 0.896 0.9491
    0.3 0.3884 0.4991 0.584 0.657 0.7229 0.784 0.8416 0.8965 0.9492
    0.4 0.4052 0.5100 0.5912 0.6617 0.7259 0.7858 0.8426 0.8969 0.9493
    0.5 0.4193 0.5189 0.597 0.6655 0.7283 0.7872 0.8433 0.8972 0.9493
    0.6 0.4312 0.5262 0.6018 0.6686 0.7303 0.7884 0.8439 0.8975 0.9494
    0.7 0.4412 0.5324 0.6059 0.6713 0.7319 0.7893 0.8444 0.8977 0.9495
    0.8 0.4498 0.5377 0.6093 0.6735 0.7333 0.7902 0.8449 0.8979 0.9495
    0.9 0.4872 0.5422 0.6122 0.6754 0.7345 0.7909 0.8452 0.898 0.9495
    1.0 0.4637 0.5461 0.6147 0.6770 0.7355 0.7915 0.8455 0.8981 0.9496

     | Show Table
    DownLoad: CSV

    The coefficients were obtained with the given power law index ω=0.6 as an illustration, shown in Table 2.

    Table 2.  The coefficients in Eqs. (3) and (4) (or Eqs. (7) and (8)) for various κ.
    coefficients ω=0.6
    κ 0.3 0.5 0.7 κ 0.3 0.5 0.7
    U1 0.4898 0.8694 0.9467 Z1 -2.4715 -4.3986 -8.5530
    U2 3.2650 0.8362 0.3409 Z2 17.0332 23.4914 39.6461
    U3 -12.2439 -3.1356 -1.2783 Z3 -39.9047 -46.0023 -68.7476
    U4 -16.3251 -4.1808 -1.7045 Z4 39.5577 39.5465 52.9275
    U5 1.0203 0.2613 0.1065 Z5 -14.2148 -12.6369 -15.2730

     | Show Table
    DownLoad: CSV

    The corresponding boundary conditions are:

    φa(0,ξ)η=0 (13)
    φb(1,ξ)η=1+sin(Bξ) (14)
    φa(κ,ξ)η=φb(κ,ξ)η (15)
    φa(κ,ξ)=φb(κ,ξ) (16)

    in which

    η=rR,κ=R1R,ξ=zLGz,φa=k(TaTi)q0R,φb=k(TbTi)q0R,B=βGzL=2πGz,Gz=4VαπL (17)

    The general form of dimensionless temperature distributions of the laminar double-pass countercurrent-flow concentric tube heat exchangers with sinusoidal wall fluxes can be expressed as follows [41]:

    φa(η,ξ)=θ0aξ+θ1a(η)+θ2a(η)sin(Bξ)+θ3a(η)cos(Bξ) (18)
    φb(η,ξ)=θ0b(1Gzξ)+θ1b(η)+θ2b(η)sin(Bξ)+θ3b(η)cos(Bξ) (19)

    in which the θ0a and θ0b are the constants yet to be determined, and the θ1a(η),θ2a(η),θ3a(η),θ1b(η),θ2b(η) and θ3b(η) are the functions of η to be determined.

    Substituting Eqs. (18) and (19) into the governing equations, Eqs. (3) and (4), and the boundary conditions, Eqs. (13)–(16), yields

    ddη(ηdθ1a(η)dη)va(η)R2ηGzLαθ0a+[ddη(ηdθ2a(η)dη)+va(η)BR2ηGzLαθ3a(η)]sin(Bξ)+[ddη(ηdθ3a(η)dη)va(η)BR2ηGzLαθ2a(η)]cos(Bξ)=0 (20)
    ddη(ηdθ1b(η)dη)+vb(η)R2ηGzLαθ0b+[ddη(ηdθ2b(η)dη)+vb(η)BR2ηGzLαθ3b(η)]sin(Bξ)+[ddη(ηdθ3b(η)dη)vb(η)BR2ηGzLαθ2b(η)]cos(Bξ)=0 (21)
    dθ1a(0)dη+dθ2a(0)dηsin(Bξ)+dθ3a(0)dηcos(Bξ)=0 (22)
    (dθ1b(1)dη1)+(dθ2b(1)dη1)sin(Bξ)+[dθ3b(1)dη]cos(Bξ)=0 (23)
    (dθ1a(κ)dηdθ1b(κ)dη)+(dθ2a(κ)dηdθ2b(κ)dη)sin(Bξ)+(dθ3a(κ)dηdθ3b(κ)dη)cos(Bξ)=0 (24)
    θ0aξ+θ1a(κ)+θ2a(κ)sin(Bξ)+θ3a(κ)cos(Bξ)=θ0b(1Gzξ)+θ1b(κ)+θ2b(κ)sin(Bξ)+θ3b(κ)cos(Bξ) (25)

    Multiplying Eqs. (20)–(25) by sin(Bξ) and integrating with respect to ζ in the interval [0, 2π/B] gives:

    ddη(ηdθ2a(η)dη)+va(η)BR2ηαGzLθ3a(η)=0 (26)
    ddη(ηdθ2b(η)dη)+vb(η)BR2ηαGzLθ3b(η)=0 (27)
    dθ2a(0)dη=0 (28)
    dθ2b(1)dη=1 (29)
    dθ2a(κ)dη=dθ2b(κ)dη (30)
    θ2a(κ)=θ2b(κ) (31)

    Similarly, multiplying Eqs. (20)–(25) by cos(Bξ) and integrating with respect to ζ in the interval [0, 2π//B], one can obtain:

    ddη(ηdθ3a(η)dη)va(η)BR2ηαGzLθ2a(η)=0 (32)
    ddη(ηdθ3b(η)dη)vb(η)BR2ηαGzLθ2b(η)=0 (33)
    dθ3a(0)dη=0 (34)
    dθ3b(1)dη=0 (35)
    dθ3a(κ)dη=dθ3b(κ)dη (36)
    θ3a(κ)=θ3b(κ) (37)

    The complex functions ψa(η)=θ2a(η)+θ3a(η)i and ψb(η)=θ2b(η)+θ3b(η)i were introduced to combine Eqs. (26)–(31) and Eqs. (32)–(37) into a unique one-dimensional boundary value problem according to the prior mathematical treatment [41] as follows:

    ddη(ηψa(η)η)va(η)BR2ηGzLαψa(η)i=0 (38)
    ddη(ηψb(η)η)vb(η)BR2ηGzLαψb(η)i=0 (39)
    dψa(0)dη=0 (40)
    dψb(1)dη=1 (41)
    dψa(κ)dη=dψb(κ)dη (42)
    ψa(κ)=ψb(κ) (43)

    We can apply the method of Frobenius which enables one to create a power series solution to solve differential equations. Assuming ψa(η) and ψb(η) have the forms of power series multiplied by unknown powers of η, respectively, leads to:

    ψa(η)=n=0anηn+ra,n0 (44)
    ψb(η)=n=0bnηn+rb,n0 (45)

    One can find the constants of ra and rb are proved to be zero in this system equations. The coefficients an and bn are determined by solving Eqs. (38) and (39) and incorporating the boundary conditions of Eqs. (40) to (43), and then comparing with the real and imaginary parts of the complex functions ψa(η)=θ2a(η)+θ3a(η)i and ψb(η)=θ2b(η)+θ3b(η)i, and thus the recursive relations were obtained for flow pattern A, respectively, as follows:

    a0,a1=0,an=BGn2(U1an2+U2an3+U3an4+U4an5+U5an6),n2 (46)

    and

    b0,b1=0,bn=BHn2(Z1bn2+Z2bn3+Z3bn4+Z4bn5+Z5bn6),n2 (47)

    Similarly, the recursive relations of the coefficients an and bn for flow pattern B are

    a0,a1=0,an=BGn2(U1an2+U2an3+U3an4+U4an5+U5an6),n2 (48)

    and

    b0,b1=0,bn=BHn2(Z1bn2+Z2bn3+Z3bn4+Z4bn5+Z5bn6),n2 (49)

    Integrations of Eqs. (20) to (25) with respect to ξ in the interval [0, 2π/B], one can obtain

    ddη(ηdθ1a(η)dη)va(η)R2ηGzLαθ0a=0 (50)
    ddη(ηdθ1b(η)dη)+vb(η)R2ηGzLαθ0b=0 (51)
    dθ1a(0)dη=0 (52)
    dθ1b(1)dη=1 (53)
    dθ1a(κ)dη=dθ1b(κ)dη (54)
    θ0a=θ0b (55)
    θ1a(κ)=θ0bGz+θ1b(κ) (56)

    Furthermore, integrating Eqs. (50) and (51) twice with respect to η for θ1a(η) and θ1b(η), respectively, yields

    θ1a=Gθ0a(14U1η2+19U2η3+116U3η4+125U4η5+136U5η6)+γ1alnη+γ2a (57)

    and

    θ1b=Hθ0b(14Z1η2+19Z2η3+116Z3η4+125Z4η5+136Z5η6)+γ1blnη+γ2b (58)

    where γ1a,γ2a,γ1b and γ2b are the integrating constants in Eqs. (57) and (58). Since there are six constants (θ0a,θ0b,γ1a,γ2a,γ1b and γ2b) to be determined given five equations (Eqs. (52) to (56)), it needs one extra equation. The additional one equation of the overall energy balance is required as follows:

    ρCpV(TFTi)=L0q(z)2πRdz (59)

    Eq. (59) can be rewritten as

    φF=1Gz08[1+sin(Bξ)]dξ=8[1Gz1B(cos(BGz)1)] (60)

    where the φF is the average outlet temperature and it is defined as

    φF=1V1κvb2πR2ηφb(η,0)dη (61)

    in flow pattern A, and

    φF=1Vκ0va2πR2ηφa(η,0)dη (62)

    in flow pattern B. Further, Eqs. (61) and (62) should be solved by using Eqs. (6), (7) and (19) and Eqs. (8) and (18) at ξ=0, respectively. Therefore, the complete solutions of dimensionless temperature distributions in a double-pass concentric circular heat exchanger were obtained by substituting the functions of θ1a,θ1b,θ2a,θ2b,θ3a and θ3b, and constants of θ0a and θ0b into the φa and φb (say Eqs. (18) and (19)).

    The local Nusselt number is usually used to measure the convection heat transfer occurring at the wall surface of double-pass concentric circular heat exchangers in forced convection heat-transfer problems and defined as

    Nu(ξ)=hDek (63)

    where k is the heat conductivity coefficient of the fluid, De is the equivalent diameter of the conduit, De=2R, and h is the heat transfer coefficient. The heat-transfer coefficient h is defined as

    qw(z)=h(Tj(R,z)Ti),j=a, b (64)

    or, in the dimensionless form

    h=kRqw(ξ)q0φj(1,ξ)=kR1+sin(Bξ)φj(1,ξ),j=a, b (65)

    Substituting Eq. (65) into Eq. (63) yields

    Nu(ξ)=2[1+sin(Bξ)]φj(1,ξ),j=a, b (66)

    Similarly, the local Nusselt number of single-pass heat exchangers is defined as

    Nu0(ξ)=2[1+sin(Bξ)]φ0(1,ξ) (67)

    where the wall temperature distribution, φ0(1,ξ), of single-pass heat exchangers can be determined, according to the reference [41].

    Moreover, the average Nusselt numbers of single- and double-pass concentric circular heat exchangers, respectively, were determined by

    ¯Nu=Gz1/Gz0Nu(ξ)dξ=Gz1/Gz02[1+sin(Bξ)]φj(1,ξ)dξ,j=a, b (68)

    and

    ¯Nu0=Gz1/Gz0Nu0(ξ)dξ=Gz1/Gz02[1+sin(Bξ)]φ0(1,ξ)dξ (69)

    The heat-transfer efficiency enhancement was illustrated by calculating the percentage increase in the device by employing a double-pass operation, based on single-pass device with the same working dimensions and operating parameters

    Ih=¯Nu¯Nu0¯Nu0(%) (70)

    The power consumption increment is unavoidable due to inserting an impermeable sheet into a single-pass device to conduct double-pass operations. The power consumption only incurring the friction losses to walls in double-pass operation were significant. And relations to joint, diversion or bending of conduit are neglected for simplicity. It may be obtained by using generalized Bernoulli equation [42] with following assumptions: (a) incompressible fluid; (b) no change in average velocity; (c) no change in elevation; (d) no work performed. Hence, the power consumption may determine using Fanning friction factor fF [43]:

    wf,j=2fF,jˉv2jLDej,j=a,b (71)
    P=Vρwf,a+Vρwf,b,P0=Vρwf,0 (72)

    The relative extents IPof power consumption increment was illustrated by calculating the percentage increment in the double-pass operation, based on the single-pass device as

    IP=PdoublePsinglePsingle×100% (73)

    The applications of Frobenius method to solve for differential equations are expanded in terms of an extended power series, say Eqs. (38) and (39). To illustrate, comparison is made to such a power series with terms truncated after n=70 and n=75 with κ=0.5 and ω=0.8. The accuracy of those comparisons is analyzed and some results are presented in Table 3 for an extended power series for flow pattern A. It can be observed from Table 3 that the power series agree reasonably well with the term of n=70, and hence those power series with n=70 are employed in the calculation procedure.

    Table 3.  The convergence of power series in Eqs. (44) and (45) with n=70 and n=75 for flow pattern A as an illustration.
    Gz n θ2a(0.3) θ3a(0.3) θ2b(0.7) θ3b(0.7) ¯Nu
    1 70 -0.092 0.135 0.136 -1.124 0.07
    75 -0.092 0.135 0.136 -1.124 0.07
    10 70 5.2×1024 9.2×1023 1.71×1013 6.5×1015 1.87
    75 6.7×1025 2.6×1024 2.7×1014 1.0×1015 1.87
    50 70 1.4×1023 7.7×1024 1.8×1013 7.2×1015 6.31
    75 4.4×1025 2.4×1025 2.8×1014 1.1×1015 6.31
    100 70 5.1×1024 1.7×1024 1.8×1013 7.3×1015 7.92
    75 1.6×1025 5.2×1026 2.8×1014 1.1×1015 7.92
    1000 70 1.3×1038 2.3×1038 1.9×1013 6.3×1015 10.06
    75 4.5×1040 4.9×1040 3.0×1014 1.0×1015 10.06

     | Show Table
    DownLoad: CSV

    The dimensionless temperature distributions of power-law fluids in double-pass concentric circular heat exchanger with sinusoidal wall flux are obtained through solving the energy balance equations with the aid of the linear superposition method. Obtaining the wall temperature distributions in advance of the design of the heat exchanger equipment is important for an engineer to select the appropriate materials and to carefully consider both technical and economic feasibility. It can be observed in Figure 2 for the flow pattern A that the wall temperature is getting lower at the downstream in subchannel b. The wall temperature at the whole part of subchannel b could reach an extremely low value, especially for remarkably high flow rate, say Gz = 100. On the contrary, the wall temperature is getting higher at the downstream in subchannel b for the flow pattern B. The wall temperature profiles are growing up toward the end downstream, as shown in Figure 3 for the flow pattern B. The wall temperatures are found to be close to the inlet temperature at the flow entrance irrespective of the Gz values. The wall temperature becomes a little bit lower for smaller ω (more apparently shear-thinning), regardless of the flow pattern. It is noteworthy that the wall temperatures are monotonically increasing or decreasing along the heat-exchanger device even with the sinusoidal wall heat flux. Regarding the device performance, the simulated Nusselt number Nu is demonstrated in Figure 4, and both flow patterns of the double-pass concentric circular heat exchanger show much more effective energy transfer than that from the single-pass device. The performance of device is further improved along with the increasing Gz. The device with the flow pattern B is shown to be more effective than that of the flow pattern A and single-pass operations under the same ω condtion. For both flow patterns, the Nu is getting lower with the smaller ω.

    Figure 2.  Dimensionless wall temperature distribution with and as parameters (flow pattern A).
    Figure 3.  Dimensionless wall temperature distribution with and as parameters (flow pattern B).
    Figure 4.  Average Nusselt number vs. Gz with ω as a parameter for κ = 0.5.

    The dimensionless wall temperatures are demonstrated in Figures 5 and 6 for the flow patterns A and B, respectively, to illustrate the influence of κvalue (impermeable-sheet position). The wall temperature shows monotonically decreasing tendency for flow pattern A and increasing tendency for flow pattern B. On the other hand, the wall temperature presented longitudinal fluctuations in accordance with the sinusoidal wall flux. It is also found that the wall temperature increases with small κ (relative larger thickness of subchannel b) and decrease with a higher Gz for both flow patterns.

    Figure 5.  Dimensionless wall temperature vs. Gzξ with κ for various Gz (flow pattern A).
    Figure 6.  Dimensionless wall temperature vs. Gzξ with κ for various Gz (flow pattern B).

    In Figure 7, it is found that the Nusselt number Nu of the current double-pass heat exchanger is sensitive to the κ values. The Nusselt number Nu increases with the κ values which indicated the double-pass device with a narrower subchannel b could accomplish better heat-transfer efficiency. It is also found the device of flow pattern B could have better device performance improvement than that of flow pattern A.

    Figure 7.  The average Nusselt number vs. Gz with κ as a parameter as a parameter.

    When simultaneously considering the heat-transfer improvement enhancement Ih and the power consumption increment Ip, its ratio Ih/Ip is plotted versus Graetz number Gz with the κ value as a parameter in Figure 8 and Tables 4 and 5. The ratio of Ih/Ip rapidly increases with Gz and quickly flatten out. It also rises with the increase in κ. The double-pass device of flow pattern B demonstrated to be more beneficial in economic sense than that of flow pattern A.

    Figure 8.  The ratio of Ih/Ip vs. Gz with κ as a parameter.
    Table 4.  The ratio of Ih/Ip with ω, Gz and κ as parameters for flow pattern A.
    ω = 0.4 ω = 0.6 ω = 0.8 ω = 1.0
    Impermeable-sheet position (κ)
    0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7
    1 -5.88 -13.68 -11.02 -2.98 -9.34 -7.57 -1.38 -6.38 -5.22 -0.71 -4.31 -3.63
    10 -1.36 -3.29 -2.43 -0.60 -2.00 -1.55 -0.25 -1.16 -0.86 -0.1 -0.63 -0.47
    100 3.15 13.48 20.48 1.65 9.77 14.74 0.84 6.97 10.58 0.42 4.9 7.55
    1000 4.56 19.63 31.99 2.36 14.04 22.98 1.19 9.97 16.29 0.59 6.91 11.56

     | Show Table
    DownLoad: CSV
    Table 5.  The ratio of Ih/Ip with ω, Gzand κ as parameters for flow pattern B.
    ω = 0.4 ω = 0.6 ω = 0.8 ω = 1.0
    Impermeable-sheet position (κ)
    0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7 0.3 0.5 0.7
    1 -0.57 -1.29 -1.02 -2.26 -7.08 -5.65 -1.43 -6.43 -5.27 -0.49 -3.01 -2.45
    10 4.71 13.58 13.63 2.59 9.43 9.21 1.24 6.6 6.58 0.62 4.71 4.76
    100 4.35 18.59 28.29 2.4 13.34 20.15 1.18 9.37 14.28 0.58 6.52 10.12
    1000 4.7 20.29 33.16 2.45 14.51 23.79 1.23 10.12 16.84 0.61 7.12 11.94

     | Show Table
    DownLoad: CSV

    A mathematical formulation for a concentric circular double-pass heat exchanger of power-law fluids with sinusoidal wall flux has been formulated, and the analytical solution is obtained using orthogonal expansion technique. The double-pass flow patterns can be achieved by inserting an impermeable sheet into a cylindrical heat exchanger to examine the heat transfer behavior. The double-pass device performance can be significantly enhanced when compared to that of the single-pass one, especially for a narrower annular flow channel (subchannel b). The average Nusselt number of the device of flow pattern B (annular flow in, core flow out) is larger than that of flow pattern A (core flow in, annular flow out). The longitudinal wall temperature profile is able to be more smoothing despite the sinusoidal wall flux. The wall temperature is decreasing in longitudinal direction for flow pattern A and increasing for flow pattern B, and the variations are much more moderate for high flow rates, for example at Gz = 100. A comparison is also made for the heat-transfer improvement enhancement Ih and the power consumption increment Ip in the form of Ih/Ip. One could find that the flow pattern B always performs better than that of flow pattern A when assessing the economic feasibility of both the flow patterns A and B by ratio Ih/Ip.

    The authors wish to thank the Ministry of Science and Technology (MOST) of the Republic of China for its financial support.

    The authors have no conflict of interest.

    Nomenclature

    an [-] constants
    B [m] constant B=βGzL
    bn [-] constants
    De [m] hydraulic diameter
    fF [-] Fanning friction factor
    gc [-] gravity factor
    G [-] constant
    Gz [-] Graetz number
    H [-] constant
    h [kW/mK] heat transfer coefficient
    Ih [-] heat-transfer improvement enhancement
    Ip [-] power consumption increment
    k [kW/mK] thermal conductivity of the fluid
    L [m] conduit length
    wf [kJ/kg] friction loss in conduit
    ¯Nu [-] the average Nusselt number
    P [(Nm)/s] power consumption
    q [kW] wall heat flux
    r [m] radius coordinate
    R [m] outer tube radius
    R1 [m] inter tube radius
    T [K] temperature of fluid in conduit
    Ui [-] constants, i=1,2,3,4,5
    V [m3/s] inlet volumetric flow rate
    v [m/s] velocity distribution of fluid
    Zi [-] constant, i=1,2,3,4,5
    z [m] longitudinal coordinate
    α [m2/s] thermal diffusivity of fluid
    β [1/m] constant
    ˙γ [1/s] shear rate
    γ1a,γ2a [-] integration constants
    γ1b,γ2b [-] integration constants
    δ [m] impermeable sheet thickness
    θ [-] coefficients
    η [-] dimensionless radius coordinate, = r/R
    κ [-] constant = R1/R
    λ [-] constant
    ξ [-] dimensionless longitudinal coordinate = z/GzL
    ρ [kg/m3] density of the fluid
    τ [Pa] shear stress
    φ [-] dimensionless temperature k(TTi)/q0R
    ω [-] power-law index
    ψ [-] complex functions of dimensionless temperature

     | Show Table
    DownLoad: CSV

    Subscripts

    0 [-] = at the inlet or for the single-pass device
    a [-] = the inner flow channel
    b [-] = the outer flow channel
    F [-] = at the outlet of a double-pass device
    i [-] = at the inlet of a double-pass device
    L [-] = at the end of the channel=
    w [-] = at the wall surface

     | Show Table
    DownLoad: CSV


    [1] Adam JD, Davis LE, Dionne GF, et al. (2002) Ferrite devices and materials. IEEE T Microw Theory 50: 721-737.
    [2] Pullar RC (2012) Hexagonal ferrites: A review of the synthesis, properties and applications of hexaferrite ceramics. Prog Mater Sci 57: 1191-1334.
    [3] Dairy ARA, Al-Hmoud LA, Khatatbeh HA (2019) Magnetic and structural properties of barium hexaferrite nanoparticles doped with titanium. Symmetry 11: 732.
    [4] Snelling EC (1988) Soft Ferrites, Properties and Applications, Butterworth-Heinemann Ltd.
    [5] Smit J, Wijn HPJ (1959) Ferrites, Eindhoven: Philips Technical Library, 150.
    [6] Issa B, Obaidat I, Albiss B, et al. (2013) Magnetic nanoparticles: Surface effects and properties related to biomedicine applications. Int J Mol Sci 14: 21266-21305.
    [7] Ammar S, Helfen A, Jouini N, et al. (2001) Magnetic properties of ultrafine cobalt ferrite particles synthesized by hydrolysis in a polyol medium. J Mater Chem 11: 186-192.
    [8] Šutka A, Gross KA (2016) Spinel ferrite oxide semiconductor gas sensors. Sensor Actuat B-Chem 222: 95-105.
    [9] Veena M, Somashekarappa A, Shankaramurthy GJ, et al. (2016) Effect of 60Co gamma irradiation on dielectric and complex impedance properties of Dy3+ substituted Ni-Zn nanoferrites. J Magn Magn Mater 419: 375-385.
    [10] Krishnan V, Selvan RK, Augustin CO, et al. (2007) EXAFS and XANES investigations of CuFe2O4 Nanoparticles and CuFe2O4-MO2 (M = Sn, Ce) Nanocomposites. J Phys Chem C 111: 16724-16733.
    [11] Vaidyanathan G, Sendhilnathan S (2008) Characterization of Co1-xZnxFe2O4 nanoparticles synthesized by co-precipitation method. Physica B 403: 2157-2167.
    [12] Valenzuela R (2012) Novel applications of ferrites. Phys Res Int 2012: 591839.
    [13] Kaur M, Kaur N, Verma V (2016) Ferrites: synthesis and applications for environmental remediation, Ferrites and Ferrates: Chemistry and Applications in Sustainable Energy and Environmental Remediation, American Chemical Society, 1238: 113-136.
    [14] Haspers JM (1962) Ferrites: Their properties and applications, In: Hausner HH, Modern Materials, Elsevier, 3: 259-341.
    [15] Shaikh PA, Kambale RC, Rao AV, et al. (2010) Structural, magnetic and electrical properties of Co-Ni-Mn ferrites synthesized by co-precipitation method. J Alloy Compd 492: 590-596.
    [16] Jaswal L, Singh B (2014) Ferrite materials: A chronological review. J Int Sci Technol 2: 69-71.
    [17] Saville P (2005) Review of radar absorbing materials. Defence Research and Development Atlantic Dartmouth (Canada). Available from: https://www.researchgate.net/publication/235178242_Review_of_Radar_Absorbing_Materials.
    [18] Meng F, Wang H, Huang F, et al. (2018) Graphene-based microwave absorbing composites: A review and prospective. Compos Part B-Eng 137: 260-277.
    [19] Abu-Dief AM, Abdel-Fatah SM (2018) Development and functionalization of magnetic nanoparticles as powerful and green catalysts for organic synthesis. BJBAS 7: 55-67.
    [20] Kharisov BI, Dias HR, Kharissova OV (2019) Mini-review: Ferrite nanoparticles in the catalysis. Arab J Chem 12: 1234-1246.
    [21] Kefeni KK, Mamba BB, Msagati TAM (2017) Application of spinel ferrite nanoparticles in water and wastewater treatment: A review. Sep Purif Technol 188: 399-422.
    [22] Kumar M, Dosanjh HS, Singh J, et al. (2020) Review on magnetic nanoferrites and their composites as alternatives in waste water treatment: synthesis, modifications and applications. Environ Sci-Water Res 6: 491-514.
    [23] Reddy DHK, Yun YS (2016) Spinel ferrite magnetic adsorbents: Alternative future materials for water purification. Coordin Chem Rev 315: 90-111.
    [24] Stephen ZR, Kievit FM, Zhang M (2011) Magnetite nanoparticles for medical MR imaging. Mater Today 14: 330-338.
    [25] Shokrollahi H, Khorramdin A, Isapour G (2014) Magnetic resonance imaging by using nano-magnetic particles. J Magn Magn Mater 369: 176-183.
    [26] Pegoretti VCB, Couceiro PRC, Gonçalves CM, et al. (2010) Preparation and characterization of tin-doped spinel ferrite. J Alloy Compd 505: 125-129.
    [27] Shokrollahi H, Avazpour L (2016) Influence of intrinsic parameters on the particle size of magnetic spinel nanoparticles synthesized by wet chemical methods. Particuology 26: 32-39.
    [28] Ramimoghadam D, Bagheri S, Hamid SBA (2014) Progress in electrochemical synthesis of magnetic iron oxide nanoparticles. J Magn Magn Mate 368: 207-229.
    [29] Sechovsky V (2001) Magnetism in solids: General introduction, In: Jürgen Buschow KH, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Elsevier, 5018-5032.
    [30] Gregersen E (2011) The Britannica Guide to Electricity and Magnetism, New York: Britannica Educational Publishing and Rosen Educational Services.
    [31] Ferrimagnetism, Engineering LibreTexts (2020) Avaliable from: https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Magnetic_Properties/Ferrimagnetism.
    [32] Cullity BD, Graham CD (2008) Introduction to Magnetic Materials, 2 Eds., Wiley-IEEE Press.
    [33] Hench LL, West JK (1990) Principles of Electronic Ceramics, Wiley.
    [34] Biagioni C, Pasero M (2014) The systematics of the spinel-type minerals: An overview. Am Mineral 99: 1254-1264.
    [35] Spinel: mineral, Encyclopedia Britannica (2020) Available from: https://www.britannica.com/science/spinel.
    [36] Mineral gallery—The spinel group. Avaliable from: http://www.galleries.com/spinel_group.
    [37] Biagioni C, Pasero M (2014) The systematics of the spinel-type mineralas: An overview. Am Mineral 99: 1254-1264.
    [38] About: cuprospinel. Avaliable from: http://dbpedia.org/page/Cuprospinel.
    [39] Nickel EH (1973) The new mineral cuprospinel (CuFe2O4) and other spinels from an oxidized ore dump at Baie Verte, Newfoundland. Can Mineral 11: 1003-1007.
    [40] Pekov IV, Sandalov FD, Koshlyakova NN, et al. (2018) Copper in natural oxide spinels: The new mineral thermaerogenite CuAl2O4, cuprospinel and Cu-enriched varieties of other spinel-group members from fumaroles of the Tolbachik Volcano, Kamchatka, Russia. Minerals 8: 498.
    [41] Fleischer M, Mandarino JA (1974) New mineral names. Am Mineral 59: 381-384.
    [42] Manju BG, Raji P (2018) Synthesis and magnetic properties of nano-sized Cu0.5Ni0.5Fe2O4 via citrate and aloe vera: A comparative study. Ceram Int 44: 7329-7333.
    [43] Liu Y, Wu Y, Zhang W, et al. (2017) Natural CuFe2O4 mineral for solid oxide fuel cells. Int J Hydrogen Energ 42: 17514-17521.
    [44] Estrella M, Barrio L, Zhou G, et al. (2009) In situ characterization of CuFe2O4 and Cu/Fe3O4 water-gas shift catalysts. J Phys Chem C 113: 14411-14417.
    [45] The mineral Franklinite. Avaliable from: http://www.galleries.com/Franklinite.
    [46] Abdulaziz A, Wael HA, Kirk S, et al. (2020) Novel franklinite-like synthetic zinc-ferrite redox nanomaterial: synthesis, and evaluation for degradation of diclofenac in water. Appl Catal B-Environ 275: 119098.
    [47] Lucchesi S, Russo U, Giusta AD (1999) Cation distribution in natural Zn-spinels: franklinite. Eur J Mineral 11: 501-512.
    [48] Palache C (1935) The Minerals of Franklin and Sterling Hill, Sussex County, New Jersey, US Government Printing Office.
    [49] Jacobsite. Avaliable from: https://www.mindat.org/min-2061.html.
    [50] Deraz NM, Alarifi A (2012) Novel preparation and properties of magnesioferrite nanoparticles. J Anal Appl Pyrol 97: 55-61.
    [51] Magnesioferrite. Avaliable from: https://www.mindat.org/min-2501.html.
    [52] Banerjee SK, Moskowitz BM (1985) Ferrimagnetic properties of magnetite, In: Kirschvink JL, Jones DS, MacFadden BJ, Magnetite Biomineralization and Magnetoreception in Organisms: A New Biomagnetism, Boston: Springer, 17-41.
    [53] Wasilewski P, Kletetschka G (1999) Lodestone: Natures only permanent magnet-What it is and how it gets charged. Geophys Res Lett 26: 2275-2278.
    [54] Blaney L (2007) Magnetite (Fe3O4): Properties, synthesis, and applications. Lehigh Rev 15: 33-81.
    [55] O'Driscoll B, Clay P, Cawthorn R, et al. (2014) Trevorite: Ni-rich spinel formed by metasomatism and desulfurization processes at Bon Accord, South Africa? Mineral Mag 78: 145-163.
    [56] About: Trevorite. Avaliable from: http://dbpedia.org/page/Trevorite.
    [57] de Paiva JAC, Graça MPF, Monteiro J, et al. (2009) Spectroscopy studies of NiFe2O4 nanosized powders obtained using coconut water. J Alloy Compd 485: 637-641.
    [58] Mogensen F (1946) A ferro-ortho-titanate ore from Södra Ulvön. Geol Fören Stockh Förh 68: 578-587.
    [59] Ulvöspinel. Avaliable from: https://www.mindat.org/min-4089.html.
    [60] Rossiter MJ, Clarke PT (1965) Cation distribution in Ulvöspinel Fe2TiO4. Nature 207: 402-402.
    [61] Mineralienatlas —Fossilienatlas. Avaliable from: https://www.mineralienatlas.de/lexikon/index.php/MineralData?lang = de & mineral = Cuprospinel.
    [62] Magnetite. Avaliable from: https://www.mindat.org/min-2538.html.
    [63] Trevorite. Avaliable from: https://www.mindat.org/min-4012.html.
    [64] Bromho TK, Ibrahim K, Kabir H, et al. (2018) Understanding the impacts of Al+3-substitutions on the enhancement of magnetic, dielectric and electrical behaviors of ceramic processed nickel-zinc mixed ferrites: FTIR assisted studies. Mater Res Bull 97: 444-451.
    [65] Burdett JK, Price GD, Price SL (1982) Role of the crystal-field theory in determining the structures of spinels. J Am Chem Soc 104: 92-95.
    [66] Verwey EJW, Heilmann EL (1947) Physical properties and cation arrangement of oxides with spinel structures I. cation arrangement in spinels. J Chem Phys 15: 174-180.
    [67] Greenberg E, Rozenberg GK, Xu W, et al. (2009) On the compressibility of ferrite spinels: a high-pressure X-ray diffraction study of MFe2O4 (M = Mg, Co, Zn). High Pressure Res 29: 764-779.
    [68] Yadav RS, Havlica J, Hnatko M, et al. (2015) Magnetic properties of Co1-xZnxFe2O4 spinel ferrite nanoparticles synthesized by starch-assisted sol-gel autocombustion method and its ball milling. J Magn Magn Mater 378: 190-199.
    [69] Paramesh D, Kumar KV, Reddy PV (2016) Influence of nickel addition on structural and magnetic properties of aluminium substituted Ni-Zn ferrite nanoparticles. Process Appl Ceram 10: 161-167.
    [70] Antao SM, Hassan I, Parise JB (2005) Cation ordering in magnesioferrite, MgFe2O4, to 982 ℃ using in situ synchrotron X-ray powder diffraction. Am Mineral 90: 219-228.
    [71] O'neill H, St C (1992) Temperature dependence of the cation distribution in zinc ferrite (ZnFe2O4) from powder XRD structural refinements. Eur J Mineral 571-580.
    [72] Singh S, Ralhan NK, Kotnala RK, et al. (2012) Nanosize dependent electrical and magnetic properties of NiFe2O4 ferrite. IJPAP 50: 739-743.
    [73] Nejati K, Zabihi R (2012) Preparation and magnetic properties of nano size nickel ferrite particles using hydrothermal method. Chem Cent J 6: 23.
    [74] Melagiriyappa E, Jayanna HS (2009) Structural and magnetic susceptibility studies of samarium substituted magnesium-zinc ferrites. J Alloy Compd 482: 147-150.
    [75] Morán E, Blesa MC, Medina ME, et al. (2002) Nonstoichiometric spinel ferrites obtained from α-NaFeO2 via molten media reactions. Inorg Chem 41: 5961-5967.
    [76] Lazarević ZŽ, Jovalekić Č, Sekulić D, et al. (2012) Characterization of nanostructured spinel NiFe2O4 obtained by soft mechanochemical synthesis. Sci Sinter 44: 331-339.
    [77] Sáez-Puche R, Fernández MJ, Blanco-gutiérrez V, et al. (2008) Ferrites nanoparticles MFe2O4 (M = Ni and Zn): Hydrothermal synthesis and magnetic properties. Bol Soc Esp Cerámica Vidr 47: 133-137.
    [78] Gözüak F, Köseoğlu Y, Baykal A, et al. (2009) Synthesis and characterization of CoxZn1−xFe2O4 magnetic nanoparticles via a PEG-assisted route. J Magn Magn Mater 321: 2170-2177.
    [79] Souriou D, Mattei JL, Chevalier A, et al. (2010) Influential parameters on electromagnetic properties of nickel-zinc ferrites for antenna miniaturization. J Appl Phys 107: 09A518.
    [80] Went JJ, Rathenau GW, Gorter EW, et al. (1952) Hexagonal iron-oxide compounds as permanent-magnet materials. Phys Rev 86: 424-425.
    [81] Belrhazi H, Hafidi MYE, Hafidi ME (2019) Permanent magnets elaboration from BaFe12O19 hexaferrite material: Simulation and prototype. Res Dev Mater Sci 11: 1-5.
    [82] Stergiou CA, Litsardakis G (2016) Y-type hexagonal ferrites for microwave absorber and antenna applications. J Magn Magn Mater 405: 54-61.
    [83] Jotania R (2014) Crystal structure, magnetic properties and advances in hexaferrites: A brief review. AIP Conf Proc 1621: 596-599.
    [84] Mahmood SH, Al-Shiab Q, Bsoul I, et al. (2018) Structural and magnetic properties of (Mg, Co)2W hexaferrites. Curr Appl Phys 18: 590-598.
    [85] Izadkhah H, Zare S, Somu S, et al. (2017) Utilizing alternate target deposition to increase the magnetoelectric effect at room temperature in a single phase M-type hexaferrite. MRS Commun 7: 97-101.
    [86] Kitagawa Y, Hiraoka Y, Honda T, et al. (2010) Low-field magnetoelectric effect at room temperature. Nat Mater 9: 797-802.
    [87] Muleta G (2018) The study of optical, electrical and dielectric properties of cadmium and zinc substituted copper ferrite nanoparticles. Ethiopia: Arba Minch University.
    [88] Albanese G (1977) Recent advances in hexagonal ferrites by the use of nuclear spectroscopic methods. J Phys Colloq 38: C1-85.
    [89] Maswadeh Y, Mahmood S, Awadallah A, et al. (2015) Synthesis and structural characterization of non-stoichiometric barium hexaferrite materials with Fe:Ba ratio of 11.5-16.16. IOP Conf Ser Mater Sci Eng 92: 23.
    [90] Kruželák J, Hudec I, Dosoudil R, et al. (2015) Investigation of strontium ferrite activity in different rubber matrices. J Elastom Plast 47: 277-290.
    [91] Wartewig P, Krause MK, Esquinazi P, et al. (1999) Magnetic properties of Zn- and Ti-substituted barium hexaferrite. J Magn Magn Mater 192: 83-99.
    [92] Kanagesan S, Jesurani S, Velmurugan R, et al. (2012) Structural and magnetic properties of conventional and microwave treated Ni-Zr doped barium strontium hexaferrite. Mater Res Bull 47: 188-192.
    [93] Xia A, Zuo C, Chen L, et al. (2013) Hexagonal SrFe12O19 ferrites: Hydrothermal synthesis and their sintering properties. J Magn Magn Mater 332: 186-191.
    [94] Ghahfarokhi SM, Ranjbar F, Shoushtari MZ (2014) A study of the properties of SrFe12-xCoxO19 nanoparticles. J Magn Magn Mater 349: 80-87.
    [95] Nga TTV, Duong NP, Hien TD (2009) Synthesis of ultrafine SrLaxFe12-xO19 particles with high coercivity and magnetization by sol-gel method. J Alloy Compd 475: 55-59.
    [96] Zhang Z, Liu X, Wang X, et al. (2012) Electromagnetic and microwave absorption properties of Fe-Sr0.8La0.2Fe11.8Co0.2O19 shell-core composites. J Magn Magn Mater 324: 2177-2182.
    [97] Zhang Z, Liu X, Wang X, et al. (2012) Effect of Nd-Co substitution on magnetic and microwave absorption properties of SrFe12O19 hexaferrites. J Alloy Compd 525: 114-119.
    [98] Chen N, Yang K, Gu M (2010) Microwave absorption properties of La-substituted M-type strontium ferrites. J Alloy Compd 490: 609-612.
    [99] Šepelák V, Myndyk M, Witte R, et al. (2014) The mechanically induced structural disorder in barium hexaferrite, BaFe12O19, and its impact on magnetism. Faraday Discuss 170: 121-135.
    [100] Yuan CL, Tuo YS (2013) Microwave adsorption of Sr(MnTi)xFe12-2xO19 particles. J Magn Magn Mater 342: 47-53.
    [101] Handoko E, Iwan S, Budi S, et al. (2018) Magnetic and microwave absorbing properties of BaFe12-2xCoxZnxO19 (x = 0.0; 0.2; 0.4; 0.6) nanocrystalline. Mater Res Express 5: 064003.
    [102] Mallick KK, Shepherd P, Green RJ (2007) Magnetic properties of cobalt substituted M-type barium hexaferrite prepared by co-precipitation. J Magn Magn Mater 312: 418-429.
    [103] Liu Q, Liu Y, Wu C (2017) Investigation on Zn-Sn co-substituted M-type hexaferrite for microwave applications. J Magn Magn Mater 444: 421-425.
    [104] Tyagi S, Baskey HB, Agarwala RC, et al. (2011) Synthesis and characterization of microwave absorbing SrFe12O19/ZnFe2O4 nanocomposite. Trans Indian Inst Met 64: 607-614.
    [105] Tyagi S, Verma P, Baskey HB, et al. (2012) Microwave absorption study of carbon nano tubes dispersed hard/soft ferrite nanocomposite. Ceram Int 38: 4561-4571.
    [106] Sharbati A, Khani JMV, Amiri GR (2012) Microwave absorption studies of nanocrystalline SrMnx/2(TiSn)x/4Fe12-xO19 prepared by the citrate sol-gel method. Solid State Commun 152: 199-203.
    [107] Reddy NK, Mulay VN (2002) Magnetic properties of W-type ferrites. Mater Chem Phys 76: 75-77.
    [108] Ahmed MA, Okasha N, Kershi RM (2010) Dramatic effect of rare earth ion on the electrical and magnetic properties of W-type barium hexaferrites. Phys B Condens Matter 405: 3223-3233.
    [109] Ul-ain B, Zafar A, Ahmed S (2015) To explore a new class of material (X-type hexaferrites) for N2O decomposition. Catal Sci Technol 5: 1076-1083.
    [110] Ueda H, Shakudo H, Santo H, et al. (2018) Magnetocrystalline anisotropy of single crystals of M-, X-, and W-type strontium hexaferrites. J Phys Soc Jpn 87: 104706.
    [111] Mohebbi M, Vittoria C (2013) Growth of Y-type hexaferrite thin films by alternating target laser ablation deposition. J Magn Mag. Mater 344: 158-161.
    [112] Rama KK, Vijaya KK, Dachepalli R (2012) Structural and electrical conductivity studies in nickel-zinc ferrite. Adv Mater Phys Chem 2012: 23241.
    [113] M. Ben Ali et al. Effect of zinc concentration on the structural and magnetic properties of mixed Co-Zn ferrites nanoparticles synthesized by sol/gel method. J Magn Magn Mater 398: 20-25.
    [114] Raut AV, Barkule RS, Shengule DR, et al. (2014) Synthesis, structural investigation and magnetic properties of Zn2+ substituted cobalt ferrite nanoparticles prepared by the sol-gel auto-combustion technique. J Magn Magn Mater 358-359: 87-92.
    [115] Mu G, Chen N, Pan X, et al. (2008) Preparation and microwave absorption properties of barium ferrite nanorods. Mater Lett 62: 840-842.
    [116] Li Y, Huang Y, Qi S, et al. (2012) Preparation, magnetic and electromagnetic properties of polyaniline/strontium ferrite/multiwalled carbon nanotubes composite. Appl Surf Sci 258: 3659-3666.
    [117] Chen N, Mu G, Pan X, et al. (2007) Microwave absorption properties of SrFe12O19/ZnFe2O4 composite powders. Mater Sci Eng B 139: 256-260.
    [118] Chang S, Kangning S, Pengfei C (2012) Microwave absorption properties of Ce-substituted M-type barium ferrite. J Magn Magn Mater 324: 802-805.
    [119] Rane AV, Kanny K, Abitha VK, et al. (2018) Methods for synthesis of nanoparticles and sabrication of nanocomposites, In: Bhagyaraj MS, Oluwafemi OS, Kalarikkal N, et al., Synthesis of Inorganic Nanomaterials, Woodhead Publishing, 121-139.
    [120] Gu Y, Sang S, Huang K, et al. (2000) Synthesis of MnZn ferrite nanoscale particles by hydrothermal method. J Cent South Univ Technol 7: 37-39.
    [121] Xia A, Liu S, Jin C, et al. (2013) Hydrothermal Mg1-xZnxFe2O4 spinel ferrites: Phase formation and mechanism of saturation magnetization. Mater Lett 105: 199-201.
    [122] He HY (2011) Magnetic properties of Co0.5Zn0.5Fe2O4 nanoparticles synthesized by a template-assisted hydrothermal method. J Nanotechnol 2011: 182543.
    [123] Mostafa NY, Zaki ZI, Heiba ZK (2013) Structural and magnetic properties of cadmium substituted manganese ferrites prepared by hydrothermal route. J Magn Magn Mater 329: 71-76.
    [124] Köseoğlu Y, Alan F, Tan M, et al. (2012) Low temperature hydrothermal synthesis and characterization of Mn doped cobalt ferrite nanoparticles. Ceram Int 38: 3625-3634.
    [125] Mostafa NY, Hessien MM, Shaltout AA (2012) Hydrothermal synthesis and characterizations of Ti substituted Mn-ferrites. J Alloy Compd 529: 29-33.
    [126] Rashad MM, Mohamed RM, Ibrahim MA, et al. (2012) Magnetic and catalytic properties of cubic copper ferrite nanopowders synthesized from secondary resources. Adv Powder Technol 23: 315-323.
    [127] Tyagi S, Agarwala RC, Agarwala V (2011) Reaction kinetic, magnetic and microwave absorption studies of SrFe11.2N0.8O19 hexaferrite nanoparticle. J Mater Sci-Mater El 22: 1085-1094.
    [128] Mattei JL, Huitema L, Queffelec P, et al. (2011) Suitability of Ni-Zn ferrites ceramics with controlled porosity as granular substrates for mobile handset miniaturized antennas. IEEE T Magn 47: 3720-3723.
    [129] Moscoso-Londoñ o O, Tancredi PABLO, Muraca D, et al. (2017) Different approaches to analyze the dipolar interaction effects on diluted and concentrated granular superparamagnetic systems. J Magn Magn Mater 428: 105-118.
    [130] Harzali H, et al. (2016) Structural and magnetic properties of nano-sized NiCuZn ferrites synthesized by co-precipitation method with ultrasound irradiation. J Magn Magn Mater 419: 50-56.
    [131] Iqbal MJ, Ashiq MN, Hernandez-Gomez P, et al. (2007) Magnetic, physical and electrical properties of Zr-Ni-substituted co-precipitated strontium hexaferrite nanoparticles. Scr Mater 57: 1093-1096.
    [132] Thanh NK, Loan TT, Anh LN, et al. (2016) Cation distribution in CuFe2O4 nanoparticles: Effects of Ni doping on magnetic properties. J Appl Phys 120: 142115.
    [133] Gomes JA, Sousa MH, Da Silva GJ, et al. (2006) Cation distribution in copper ferrite nanoparticles of ferrofluids: A synchrotron XRD and EXAFS investigation. J Magn Magn Mater 300: e213-e216.
    [134] Arulmurugan R, Vaidyanathan G, Sendhilnathan S, et al. (2006) Thermomagnetic properties of Co1-xZnxFe2O4 (x = 0.1-0.5) nanoparticles. J Magn Magn Mater 303: 131-137.
    [135] Arulmurugan R, Jeyadevan B, Vaidyanathan G, et al. (2005) Effect of zinc substitution on Co-Zn and Mn-Zn ferrite nanoparticles prepared by co-precipitation. J Magn Magn Mater 288: 470-477.
    [136] Gordani GR, Ghasemi A, Saidi A (2014) Enhanced magnetic properties of substituted Sr-hexaferrite nanoparticles synthesized by co-precipitation method. Ceram Int 40: 4945-4952.
    [137] Baniasadi A, Ghasemi A, Nemati A, et al. (2014) Effect of Ti-Zn substitution on structural, magnetic and microwave absorption characteristics of strontium hexaferrite. J Alloy Compd 583: 325-328.
    [138] Modi KB, Shah SJ, Pujara NB, et al. (2013) Infrared spectral evolution, elastic, optical and thermodynamic properties study on mechanically milled Ni0.5Zn0.5Fe2O4 spinel ferrite. J Mol Struct 1049: 250-262.
    [139] Tehrani MK, Ghasemi A, Moradi M, et al. (2011) Wideband electromagnetic wave absorber using doped barium hexaferrite in Ku-band. J Alloy Compd 509: 8398-8400.
    [140] Ohnishi H, Teranishi T (1961) Crystal distortion in copper ferrite-chromite series. J Phys Soc Jpn 16: 35-43.
    [141] Tachibana T, Nakagawa T, Takada Y, et al. (2003) X-ray and neutron diffraction studies on iron-substituted Z-type hexagonal barium ferrite: Ba3Co2-xFe24+xO41 (x = 0-0.6). J Magn Magn Mater 262: 248-257.
    [142] Sözeri H, Deligöz H, Kavas H, et al. (2014) Magnetic, dielectric and microwave properties of M-Ti substituted barium hexaferrites (M = Mn2+, Co2+, Cu2+, Ni2+, Zn2+). Ceram Int 40: 8645-8657.
    [143] González-Angeles A, Mendoza-Suarez G, Grusková A, et al. (2005) Magnetic studies of Zn-Ti-substituted barium hexaferrites prepared by mechanical milling. Mater Lett 59: 26-31.
    [144] Zou H, Li S, Zhang L, et al. (2011) Determining factors for high performance silicone rubber microwave absorbing materials. J Magn Magn Mater 323: 1643-1651.
    [145] Lixi W, Qiang W, Lei M, et al. (2007) Influence of Sm3+ substitution on microwave magnetic performance of barium hexaferrites. J Rare Earth 25: 216-219.
    [146] Ghasemi A, Hossienpour A, Morisako A, et al. (2008) Investigation of the microwave absorptive behavior of doped barium ferrites. Mater Design 29: 112-117.
    [147] Choopani S, Keyhan N, Ghasemi A, et al. (2009) Static and dynamic magnetic characteristics of BaCo0.5Mn0.5Ti1.0Fe10O19. J Magn Magn Mater 321: 1996-2000.
    [148] Pradhan AK, Saha S, Nath TK (2017) AC and DC electrical conductivity, dielectric and magnetic properties of Co0.65Zn0.35Fe2-xMoxO4 (x  =   0.0, 0.1 and 0.2) ferrites. Appl Phys A-Mater 123: 715.
    [149] Silva LG, Solis-Pomar F, Gutiérrez-Lazos CD, et al. (2014) Synthesis of Fe nanoparticles functionalized with oleic acid synthesized by inert gas condensation. J Nanomater 2014: 643967.
    [150] Zheng X, Yu SH, Sun R, et al. (2012) Microstructure and properties of ferrite/organic nanocomposite prepared with microemulsion method. Maters Sci Forum 722: 31-38.
    [151] Košak A, Makovec D, Žnidaršič A, et al. (2004) Preparation of MnZn-ferrite with microemulsion technique. J Eur Ceram Soc 24: 959-962.
    [152] Malik MA, Wani MY, Hashim MA (2012) Microemulsion method: A novel route to synthesize organic and inorganic nanomaterials: 1st Nano Update. Arab J Chem 5: 397-417.
    [153] Mazario E, Herrasti P, Morales MP, et al. (2012) Synthesis and characterization of CoFe2O4 ferrite nanoparticles obtained by an electrochemical method. Nanotechnology 23: 355708.
    [154] Rivero M, del Campo A, Mayoral A, et al. (2016) Synthesis and structural characterization of ZnxFe3-xO4 ferrite nanoparticles obtained by an electrochemical method. RSC Adv 6: 40067-40076.
    [155] Saba A, Elsayed E, Moharam M, et al. (2012) Electrochemical synthesis of nanocrystalline Ni0.5Zn0.5Fe2O4 thin film from aqueous sulfate bath. ISRN 2012: 532168.
    [156] Bremer M, Fischer ST, Langbein H, et al. (1992) Investigation on the formation of manganese-zinc ferrites by thermal decomposition of solid solution oxalates. Thermochim Acta 209: 323-330.
    [157] Angermann A, Töpfer J, Silva K, et al. (2010) Nanocrystalline Mn-Zn ferrites from mixed oxalates: Synthesis, stability and magnetic properties. J Alloy Compd 508: 433-439.
    [158] Li D, Herricks T, Xia Y (2003) Magnetic nanofibers of nickel ferrite prepared by electrospinning. Appl Phys Lett 83: 4586-4588.
    [159] Na KH, Kim WT, Park DC, et al. (2018) Fabrication and characterization of the magnetic ferrite nanofibers by electrospinning process. Thin Solid Films 660: 358-364.
    [160] Nam JH, Joo YH, Lee JH, et al. (2009) Preparation of NiZn-ferrite nanofibers by electrospinning for DNA separation. J Magn Magn Mater 321: 1389-1392.
    [161] Phulé PP, Wood TE (2001) Ceramics and glasses, sol-gel synthesis of, In: Buschow KHJ, Cahn RW, Flemings MC, et al., 2 Eds., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 1090-1095.
    [162] Peterson DS (2013) Sol-gel technique, In: Li D, Encyclopedia of Microfluidics and Nanofluidics, New York: Springer Science + Business Media, 1-7.
    [163] Muresan LM (2015) Corrosion protective coatings for Ti and Ti alloys used for biomedical implants, In: Tiwari A, Rawlins J, Hihara LH, Intelligent Coatings for Corrosion Control, Boston: Butterworth-Heinemann, 585-602.
    [164] Xu P (2001) Polymer-ceramic nanocomposites: ceramic phases, In: Buschow KHJ, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 7565-7570.
    [165] Allaedini G, Tasirin SM, Aminayi P (2015) Magnetic properties of cobalt ferrite synthesized by hydrothermal method. Int Nano Lett 5: 183-186.
    [166] Gan YX, Jayatissa AH, Yu Z, et al. (2020) Hydrothermal synthesis of nanomaterials. J Nanomater 2020: 8917013.
    [167] O'Hare D (2001) Hydrothermal synthesis, In: Buschow KHJ, Cahn RW, Flemings MC, et al., Encyclopedia of Materials: Science and Technology, Oxford: Elsevier, 3989-3992.
    [168] Kumar A, Nanda D (2019) Methods and fabrication techniques of superhydrophobic surfaces, In: Samal SK, Mohanty S, Nayak SK, Superhydrophobic Polymer Coatings, Elsevier, 43-75.
    [169] Liu S, Ma C, Ma MG, et al. (2019) Magnetic nanocomposite adsorbents, In: Kyzas GZ, Mitropoulos AC, Composite Nanoadsorbents, Elsevier, 295-316.
    [170] Šepelák V, Bergmann I, Feldhoff A, et al. (2007) Nanocrystalline nickel ferrite, NiFe2O4:  Mechanosynthesis, nonequilibrium cation distribution, canted spin arrangement, and magnetic behaviour. J Phys Chem C 111: 5026-5033.
    [171] Rao CNR, Biswas K (2015) Ceramic methods, Essentials of Inorganic Materials Synthesis, John Wiley & Sons, 17-21.
    [172] Chatterjee AK (2001) X-ray diffraction, In: Ramachandran VS, Beaudoin JJ, Handbook of Analytical Techniques in Concrete Science and Technology: Principles, Techniques and Applications, Norwich, New York: William Andrew Publishing, 275-332.
    [173] Sudha D, Dhanapandian S, Manoharan C, et al. (2016) Structural, morphological and electrical properties of pulsed electrodeposited CdIn2Se4 thin films. Results Phys 6: 599-605.
    [174] Kumar A, Agarwala V, Singh D (2013) Effect of particle size of BaFe12O19 on the microwave absorption characteristics in X-band. Prog Electromagn Res 29: 223-236.
    [175] Kambale RC, Adhate NR, Chougule BK, et al. (2010) Magnetic and dielectric properties of mixed spinel Ni-Zn ferrites synthesized by citrate-nitrate combustion method. J Alloy Compd 491: 372-377.
    [176] Singhal S, Singh J, Barthwal SK, et al. (2005) Preparation and characterization of nanosize nickel-substituted cobalt ferrites (Co1-xNixFe2O4). J Solid State Chem 178: 3183-3189.
    [177] Tyagi S, Baskey HB, Agarwala RC, et al. (2011) Reaction kinetic, magnetic and microwave absorption studies of SrFe12O19/CoFe2O4 ferrite nanocrystals. Trans Indian Inst Met 64: 271-277.
    [178] Swamy PP, Basavaraja S, Lagashetty A, et al. (2011) Synthesis and characterization of zinc ferrite nanoparticles obtained by self-propagating low-temperature combustion method. Bull Mater Sci 34: 1325-1330.
    [179] Sharma R, Agarwala RC, Agarwala V (2008) Development of radar absorbing nano crystals by microwave irradiation. Mater Lett 62: 2233-2236.
    [180] Thakur A, Singh RR, Barman PB (2013) Structural and magnetic properties of La3+ substituted strontium hexaferrite nanoparticles prepared by citrate precursor method. J Magn Magn Mater 326: 35-40.
    [181] Tang X, Yang Y, Hu K (2009) Structure and electromagnetic behavior of BaFe12-2x(Ni0.8Ti0.7)xO19-0.8x in the 2-12 GHz frequency range. J Alloy Compd 477: 488-492.
    [182] Sigh P, Andola HC, Rawat MSM, et al. (2011) Fourier transform infrared (FT-IR) spectroscopy in an-overview. Res J Med Plants 5: 127-135.
  • This article has been cited by:

    1. Chii-Dong Ho, Jr-Wei Tu, Hsuan Chang, Li-Pang Lin, Thiam Leng Chew, Optimizing thermal efficiencies of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes, 2022, 19, 1551-0018, 8648, 10.3934/mbe.2022401
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(27907) PDF downloads(2662) Cited by(87)

Figures and Tables

Figures(16)  /  Tables(12)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog