Synthesis and Characterization of Nanofluids …
17
to be in direct relation with the electrical properties of the nanofluid, which will also
be discussed later in this chapter.
3.4 Models for Thermal Conductivity Prediction
Thermal conductivity has been of great interest in the convective heat transfer study
of nanofluids on which theoretical and experimental studies have been done. Mechanism of heat conduction has been proposed, which is found to be dependent on
the Brownian motion of nanoparticles, interfacial liquid layer of nanofluid (effect of
nanolayer), nanoparticle clustering and nature of heat transport of the nanoparticles
in the nanofluid. Many researchers have strived to derive models that can exactly
predict the thermal behaviour of the nanofluid. It was Maxwell (1881), who was the
first to develop the effective thermal conductivity model as given in Eq. (2). The
equation can predict the effective thermal conductivity of the solid–liquid suspensions (k eff ), where k p is the thermal conductivity of the dispersed particles, k l is the
thermal conductivity of the basefluid (continuous phase of liquid) and ∅ is the volume
concentration of the nanoparticles in the suspension.
k eff = k f
k p + 2k l + 2∅(k p − k l )
k p + 2k l − ∅(k p − k l )
(2)
Maxwell’s model (Maxwell 1881) assumes the thermal conductivity improvement
due to the presence of nanolayer at the surface of the solid in a solid–liquid suspension.
It has been expected that the thermal conductivity of the nanolayer on the surface of
the nanoparticle is higher than that of the basefluid. Further, this model was modified
by Maxwell (1881) so as to form a modified Maxwell model as given in Eq. (3),
where β is the ratio of thickness of nanolayer (h) to the radius of the nanoparticle
(r) and is given as β = h/r . This equation is found to be valid for dispersion of
spherical-shaped particles in the basefluid.
k eff =
k p + 2k l + 2
k p − k l
(1 + β)
3
∅
k p + 2k l −
k p − k l
(1 + β)
3
∅
k l
(3)
Further, Hamilton and Crosser (1962) introduced a model for a solid–liquid suspension as given in Eq. (4), where k p is the thermal conductivity of particles, k f is
the thermal conductivity of basefluid, ∅ is the volume fraction of particles, n is the
empirical shape factor defined as n =
3
ψ
and ψ is the sphericity which is explained
as the ratio of the surface area of a sphere having the same volume as that particle to
the surface area of that particle. It is applicable for spherical and cylindrical particles.
k eff
k f
=
k p + (n − 1)k f − (n − 1)∅
k p − k f
k p + (n − 1)k f + ∅
k p − k f
(4)
17
to be in direct relation with the electrical properties of the nanofluid, which will also
be discussed later in this chapter.
3.4 Models for Thermal Conductivity Prediction
Thermal conductivity has been of great interest in the convective heat transfer study
of nanofluids on which theoretical and experimental studies have been done. Mechanism of heat conduction has been proposed, which is found to be dependent on
the Brownian motion of nanoparticles, interfacial liquid layer of nanofluid (effect of
nanolayer), nanoparticle clustering and nature of heat transport of the nanoparticles
in the nanofluid. Many researchers have strived to derive models that can exactly
predict the thermal behaviour of the nanofluid. It was Maxwell (1881), who was the
first to develop the effective thermal conductivity model as given in Eq. (2). The
equation can predict the effective thermal conductivity of the solid–liquid suspensions (k eff ), where k p is the thermal conductivity of the dispersed particles, k l is the
thermal conductivity of the basefluid (continuous phase of liquid) and ∅ is the volume
concentration of the nanoparticles in the suspension.
k eff = k f
k p + 2k l + 2∅(k p − k l )
k p + 2k l − ∅(k p − k l )
(2)
Maxwell’s model (Maxwell 1881) assumes the thermal conductivity improvement
due to the presence of nanolayer at the surface of the solid in a solid–liquid suspension.
It has been expected that the thermal conductivity of the nanolayer on the surface of
the nanoparticle is higher than that of the basefluid. Further, this model was modified
by Maxwell (1881) so as to form a modified Maxwell model as given in Eq. (3),
where β is the ratio of thickness of nanolayer (h) to the radius of the nanoparticle
(r) and is given as β = h/r . This equation is found to be valid for dispersion of
spherical-shaped particles in the basefluid.
k eff =
k p + 2k l + 2
k p − k l
(1 + β)
3
∅
k p + 2k l −
k p − k l
(1 + β)
3
∅
k l
(3)
Further, Hamilton and Crosser (1962) introduced a model for a solid–liquid suspension as given in Eq. (4), where k p is the thermal conductivity of particles, k f is
the thermal conductivity of basefluid, ∅ is the volume fraction of particles, n is the
empirical shape factor defined as n =
3
ψ
and ψ is the sphericity which is explained
as the ratio of the surface area of a sphere having the same volume as that particle to
the surface area of that particle. It is applicable for spherical and cylindrical particles.
k eff
k f
=
k p + (n − 1)k f − (n − 1)∅
k p − k f
k p + (n − 1)k f + ∅
k p − k f
(4)