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Numerical investigation of the magnetic field effect on the heat transfer and fluid flow of ferrofluid inside helical tube

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Abstract

The effect of a magnetic field on heat and fluid flow of ferrofluid in a helical tube is studied numerically. The helical tube is under constant wall temperature boundary condition. Parametric studies are done to investigate the effects of different factors such as the magnetic field gradient value and Reynolds number on heat transfer rate and pressure drop. Results indicate that the magnetic field increases the Nusselt number by about 40%. At high magnetic gradient value, Nusselt number and friction factor rise slightly, while at low magnetic gradient value, the increment of Nusselt number is considerable. Furthermore, the growth of wall shear stress on tube wall results in lower thermal–hydraulic performance at the high magnetic gradient value. There is an optimum case for thermal–hydraulic performance which results in most top performance of helical tube in the presence of the magnetic field.

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Abbreviations

\(B\) :

Magnetic field induction (T)

\(c_{{\rm p}}\) :

Specific heat at constant pressure (J kg−1 K−1)

\(d\) :

Particle diameter (m)

\(D\) :

Tube diameter (m)

\(D_{{\rm c}}\) :

Coil diameter (mm)

De :

Dean number/\(De = Re (D D_{{\rm c}}^{ - 1} )^{1/2}\)

\(f\) :

Skin friction factor

G :

Magnetic field gradient (A m−2)

\(H\) :

Magnetic field intensity (A m−1)

\(h\) :

Heat transfer coefficient (W m−2 K−1)

\(J\) :

Electric current density (A m−2)

\(j\) :

Colburn factor

\(jf\) :

Thermal–hydraulic performance

\(k\) :

Thermal conductivity (W m−1 K−1)

\(K_{{\rm B}}\) :

Boltzmann constant (= 1.3806503 × 10−23 J K−1)

\(L\) :

Langevin function

\(m\) :

Particle magnetic moment (A m−2)

M :

Magnetization (A m−1)

\(M_{{\rm s}}\) :

Saturation magnetization (A m−1)

\(Nu\) :

Nusselt number/\(hDk^{ - 1}\)

\(p_{{\rm c}}\) :

Coil pitch (mm)

\(Pr\) :

Prandtl number

\(P\) :

Pressure (Pa)

\(q''\) :

Heat flux (W m−2)

\(Re\) :

Reynolds number

\(T\) :

Temperature (K)

\(T_{0}\) :

Inlet flow temperature (K)

\(V_{{\rm av}}\) :

Average velocity at tube cross section (m s−1)

\(V = \left( {u,v.w} \right)\) :

Velocity field (m s−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\mu_{0}\) :

The magnetic permeability of vacuum (4π × 10−7 T m A−1)

\(\mu_{{\rm B}}\) :

Bohr magneton (= 9.27 × 10−24 A m2)

\(\xi\) :

Langevin parameter

\(\rho\) :

Density (kg m−3)

\(\sigma\) :

Electrical conductivity (s m−1)

\(\phi\) :

Particles volume fraction

\({\text{f}}\) :

Base fluid

\({\text{nf}}\) :

Nanofluid

\({\text{p}}\) :

Particle

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Babol University of Technology, Babol, Iran

    S. M. Mousavi

  2. Department of Mechanical Engineering, Payame Noor University (PNU), P.O.B. 19395-3697, Tehran, Iran

    N. Jamshidi

  3. Department of Mechanical Engineering, University of Mazandaran, Babolsar, Iran

    A. A. Rabienataj-Darzi

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  1. S. M. Mousavi
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Correspondence to N. Jamshidi.

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Mousavi, S.M., Jamshidi, N. & Rabienataj-Darzi, A.A. Numerical investigation of the magnetic field effect on the heat transfer and fluid flow of ferrofluid inside helical tube. J Therm Anal Calorim 137, 1591–1601 (2019). https://doi.org/10.1007/s10973-019-08066-2

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