Research Square (Research Square),
Journal Year:
2023,
Volume and Issue:
unknown
Published: Dec. 6, 2023
Abstract
This
investigation
aims
to
determine
the
existence
of
a
dual
solution
in
magnetohydrodynamic
(MHD)
thermal
radiative
tri-hybrid
nanofluid
flow
over
an
exponential
shrinking
surface
by
considering
mass
suction
effects
at
surface.
Furthermore,
impacts
Smoluchowski
temperature
and
Maxwell
velocity
are
taken
into
account.
The
products
on
various
fields
examined
for
three
different
types
fluid:
mono
($Fe_3O_4$/$H_2O$),
hybrid
(
$Fe_3O_4$-$Al_2O_3$/$H_2O$),
($Fe_3O_4$-$Al_2O_3$-$Cu$/$H_2O$).
Estimating
entropy
production
is
also
included
current
work.
similarity
transformation
used
translate
nonlinear
partial
differential
equations
(PDEs)
set
ordinary
(ODEs).
numerical
MATLAB
function
bvp4c
utilized
construction
governing
higher-order
ODEs.
stability
these
solutions
achieved
finding
lowest
eigenvalue
because
duality
present
solutions.
A
minimum
that
positive
denotes
upper
stable
branch,
whereas
minimal
negative
indicates
bottom
unstable
branch.
tabular
graphic
analysis
conducted
impact
emergent
factors
temperature,
skin
friction
coefficient,
Nusselt
number,
generation,
etc.
results
demonstrate
when
changes
nanofluid,
profile
improve.
It
has
been
demonstrated
fluid's
pace
which
heat
transferred
greatly
influenced
radiation
parameter.
magnetic
field
aggravates
case
solution.
accelerated
considerably
radiation.
optimization
technique
offers
new
beneficial
insight
plastic
films,
exchangers,
polymer
sheets,
crude
oil,
electronic
devices.
Therefore,
it
advised
use
create
industrial
device
setup.
Scientific Reports,
Journal Year:
2024,
Volume and Issue:
14(1)
Published: Jan. 16, 2024
Abstract
The
exclusive
behaviour
of
nanofluid
has
been
actively
emphasized
due
to
the
determination
improved
thermal
efficiency.
Hence,
aim
this
study
is
highlight
laminar
boundary
layer
axisymmetric
stagnation
point
flow
Casson
past
a
stretching
plate/cylinder
under
influence
radiation
and
suction/injection.
Nanofluid
comprises
water
Fe
3
O
4
as
nanoparticles.
In
article,
novel
casson
model
developed
studied
on
stretchable
flat
plate
or
circular
cylinder.
Adequate
rational
assumptions
(velocity
components)
are
employed
for
transformation
governing
partial-differential
equations
into
group
non-dimensional
ordinary-differential
formulas,
which
then
solved
analytically.
momentum
energy
through
complementary
error
function
method
scaling
quantities.
Using
various
figures,
effects
essential
factors
flow,
heat
transportation,
Nusselt
number,
determined
explored.
From
obtained
results,
it
observed
that
velocity
field
diminishes
owing
magnification
in
parameter
$$B$$
B
fluid
$$\Lambda$$
Λ
.
temperature
increases
by
amplifying
$$N_{r}$$
Nr
,
solid
volume
fraction
$$\phi$$
ϕ
research
applicable
developing
procedures
electric-conductive
nanomaterials,
have
potential
applications
aircraft,
smart
coating
transport
phenomena,
industry,
engineering,
other
sectors.
Case Studies in Thermal Engineering,
Journal Year:
2024,
Volume and Issue:
54, P. 103965 - 103965
Published: Jan. 23, 2024
Understanding
heat
transfer
in
slip
flow
scenarios
involving
a
stretching
or
shrinking
sheet
has
immediate
applications
numerous
fields,
including
materials
processing,
production,
and
temperature
management
systems.
This
information
supports
the
development
of
novel
methods
Therefore
present
study
focuses
on
stagnant
point
discusses
dynamics
thermal
characteristics
ternary
hybrid
nanofluids
with
application
Tiwari
Das
nanofluids.
It
is
assumed
that
are
stretching/shrinking
sheet.
The
slipping
effects
suction
boundary
conditions
implemented.
simulation
will
be
performed
using
finite
element
method
software
package
COMSOL
Multiphysics
6.0.
system
ordinary
differential
equations
(ODEs)
obtained
through
similarity
transformation
solved
numerically
to
obtain
results.
average
velocity,
profiles,
Nusselt
number
patterns
non-dimensional
parameters
also
analyzed.
These
include
parameter,
ranging
from
−1
0.5,
parameter
both
0
2.
under
investigation
consist
combination
TiO2,
Silver-Ag,
ZnO
particles
base
fluid
(water).
volume
fraction
these
tested
0.03
0.3.
was
found
when
there
no
effects,
decreases
for
case
increases
case.
concluded
effect,
profile
Case Studies in Thermal Engineering,
Journal Year:
2024,
Volume and Issue:
61, P. 104958 - 104958
Published: Aug. 9, 2024
Ternary
hybrid
nanofluids
offer
significant
advantages
in
heat
transfer
due
to
their
enhanced
thermal
conductivity
compared
traditional
fluids.
Investigating
flow
behavior
over
expanding
surfaces
can
contribute
the
development
of
more
efficient
exchangers
and
cooling
systems
electronics,
energy
production,
transportation
industries.
This
paper
presents
a
detailed
analysis
characteristics
ternary
nanofluid
(SiO2–Cu–Al2O3/H2O)
radially
stretching
surface,
utilizing
both
numerical
techniques
(Keller
Box
method)
statistical
techniques.
Furthermore,
model
includes
factors
like
convective
transport,
radiation,
internal
fluid
friction,
suction.
Similarity
transformations
transform
governing
equations
for
into
system
nonlinear
ordinary
differential
equations.
Then
are
solved
numerically
using
Keller
method
with
aid
MATLAB
software.
Additionally,
we
have
employed
such
as
correlation
analysis,
probable
error
estimation,
multivariate
regression
validate
ensure
accuracy
outcomes.
Parameter
ranges
Biot
number,
unsteadiness,
Eckert
generation
parameter
0.1
≤
Mp
0.7,
Ks
1.5,
0.2
Ps
0.8,
EN
0.4,
0.5
RN
2,
1≤
BT
2.5,
Hsc
0.7
found
significantly
impact
within
these
bounds.
study
utilizes
3D
surface
plots
visualize
influence
key
parameters
on
engineering
quantities.
R
squared
values
show
that
data
strongly
match
model.
The
findings
demonstrate
excellent
concordance
between
predicted
actual
Nusselt
number
skin
friction
measurements.
has
very
strong
transfer,
minimal
chance
error.
And
same
is
evidenced
by
matrix
multiple
analysis.
also
exhibits
negative
number.
translates
situation
where
increasing
directly
leads
decrease
rate
no
margin
Energy
demonstrates
transfer.
However,
there's
slight
possibility
error,
an
estimated
percentage
around
0.0017.
Fluids,
Journal Year:
2024,
Volume and Issue:
9(8), P. 180 - 180
Published: Aug. 10, 2024
The
main
objective
of
this
study
is
to
explore
the
inventive
conception
magnetohydrodynamic
flow
a
hybrid
nanofluid
over-porous
stretching/shrinking
sheet
with
effect
radiation
and
mass
suction/injection.
advances
both
manufactured
current
region
base
fluid.
For
investigation,
nanofluids
comprising
two
different
kinds
nanoparticles,
aluminium
oxide
ferrofluid,
contained
in
water
as
fluid,
are
considered.
A
collection
highly
nonlinear
partial
differential
equations
used
model
whole
physical
problem.
These
then
transformed
into
ordinary
using
an
appropriate
similarity
technique.
nonlinear,
thus
it
difficult
analytically
solve
considering
temperature
increases.
Then,
outcome
described
incomplete
gamma
function
form.
considered
parameters
namely,
magnetic
field,
Inverse
Darcy
number,
velocity
slip,
suction/injection,
jump
effects
on
velocity,
temperature,
skin
friction
Nusselt
number
profiles
reviewed
plots.
results
reveal
that
values
increase
momentum
boundary
layer
decreases.
Moreover,
higher
heat
sources
thermal
enhance
layer.
present
problem
has
various
applications
manufacturing
technological
devices
such
cooling
systems,
condensers,
microelectronics,
digital
cooling,
car
radiators,
nuclear
power
stations,
nano-drag
shipments,
automobile
production,
tumour
treatments.
Numerical Heat Transfer Part B Fundamentals,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 29
Published: May 10, 2024
The
present
investigation
aims
to
determine
the
existence
of
a
dual
solution
in
magnetohydrodynamic
(MHD)
mixed
convective
radiative
flow
Cu-Ag-Al2O3/H2O
tri-hybrid
nanofluid
permeable
Darcy–Forchheimer
porous
medium
over
an
exponentially
shrinking
surface
by
considering
velocity,
thermal
slips,
and
suction
effects
at
surface.
This
study
focuses
on
assessing
entropy
production
novel
coolant
applications.
To
streamline
analysis,
complex
nonlinear
partial
differential
equations
(PDEs)
are
simplified
converting
them
into
set
ordinary
(ODEs)
through
utilization
similarity
transformation
technique.
These
ODEs
then
solved
utilizing
bvp4c
numerical
MATLAB
function.
Graphical
tabular
analyses
conducted
investigate
impact
emerging
variables
generation,
as
well
temperature,
skin
friction
coefficient,
Nusselt
number.
Due
contraction
surface,
solutions
found,
but
cannot
be
found
beyond
critical
values.
values
SC
1.58928,
1.48700,
1.66058,
ξC
−1.239499,
−1.416999,
−1.130030
for
Cu/H2O
nanofluid,
Cu−Ag/H2O
hybrid
Cu−Ag−Al2O3/H2O
respectively.
A
positive
minimum
eigenvalue
γ1
signifies
upper
stable
branch,
while
negative
minimal
indicates
presence
lower
unstable
branch.
exhibits
superior
properties
compared
fluids.
Adding
nanoparticles
traditional
fluids
is
perceived
improving
their
ability
transmit
heat.
analysis
has
demonstrated
that
radiation
temperature
slip
parameters
significantly
influence
heat
transfer
rate.
Thermal
speed
up
creation
entropy.
Additionally,
case
solution,
increase
Forchheimer
number
results
deceleration
liquid
flow,
effect
which
further
amplified
magnetic
field
velocity
parameter.
International Journal of Modern Physics B,
Journal Year:
2025,
Volume and Issue:
unknown
Published: March 15, 2025
The
aim
of
this
study
is
to
find
out
the
solution
for
viscous
ternary
nanofluid
flow
over
a
semi-infinite
permeable
stretching/shrinking
medium
with
mass
transpiration,
by
taking
into
account
Navier’s
slip
or
second-order
slip.
However,
idea
water-based
nanofluids
incorporating
triple
different
forms
solid
nanoparticles
densities
and
outlines
(ternary
hybrid
nanofluids)
remains
fantastic
due
their
range
applications
in
engineering
such
as
polymer
production,
solar
energy
storage
distribution.
Silver
(Ag),
SWCNTs
Graphene
are
immersed
base
fluid
H
2
O
resulting
nanofluid.
A
number
boundary
conditions
employed
research
considered
supposition,
which
generalization
them.
physical
problem
Mathematically
modeled
partial
differential
equations.
These
regulating
equations
transformed
related
nonlinear
ordinary
choice
appropriate
set
similarity
transformations.
analytical
technique
solve
reduced
transformation.
Remarkably,
despite
nonlinearity
equation,
an
exact
momentum
derived.
insights
being
provided
means
various
phase
diagrams
also,
demonstrate
impact
thermophysical
parameters
on
velocity
profiles.
Journal of Nanotechnology,
Journal Year:
2025,
Volume and Issue:
2025(1)
Published: Jan. 1, 2025
The
nanofluids
and
their
advanced
models
(ternary
tetra
nanofluids)
possess
an
outstanding
thermal
mechanism
attract
engineers
industrialists
with
prominent
features.
Tetra
have
high
conductivity;
thus,
by
inserting
nanoparticles
in
the
base
fluids,
effective
conductivity
of
heat
transfer
fluids
is
enhanced.
A
framework
has
now
been
illuminated
throughout
this
work
to
scrutinize
behavior
chemical
reactions
radiation
on
water‐based
magnetohydrodynamics
(MHD)
biviscous
Bingham
flow
nanofluid
(Al
2
O
3
–Fe
4
–TiO
–Cu/H
O)
over
accelerated
plate
through
a
porous
medium
presence
slip
conditions,
source/sink,
viscous
dissipation.
overall
physical
problem
designed
form
nonlinear
partial
differential
equation,
which
then
altered
into
highly
ordinary
equation
via
proper
dimensionless
variable.
These
equations
are
solved
analytically,
along
associated
boundary
conditions.
flow,
energy,
mass
problems
were
examined
especially
transport
phenomena
performed
for
both
prescribed
surface
temperature
(PST)
flux
(PHF)
cases,
was
also
evaluated
two
different
namely
concentration
(PSC)
(PMF)
then,
these
solutions
demonstrated
terms
confluent
hypergeometric
function.
There
plots
showing
how
variables
affected
velocity
concentration,
skin
friction,
rate
transmission.
dual
solution
found
velocity,
temperature,
profiles.
finding
discloses
that
performance
magnetic
parameter,
fluid
parameters
experience
slowdown
impact
corresponding
velocities
cases
stretching
boundaries.
For
magnitude
field
parameter
increases
increasing
profile
second
solution,
whereas
reverse
trend
observed
first
solution.
Advanced Theory and Simulations,
Journal Year:
2025,
Volume and Issue:
unknown
Published: May 2, 2025
Abstract
This
research
aimed
to
analyze
the
effects
of
both
without
aggregation
and
with
nanoparticles
(i.e.,
titania‐ethylene
glycol
)
on
velocity
temperature
profiles
over
a
permeable
MHD
stretching/shrinking
sheet
permeability
parameter
thermal
radiation
.
For
purpose
studying
nanoparticle
aggregation,
improved
Maxwell‐Bruggeman
Krieger‐Dougarty
models
are
applied.
By
applying
similarity
transformation,
simple
partial
differential
equations
that
arise
from
mathematical
modeling
transformed
into
nonlinear
ordinary
equations.
The
calculated
equation
is
then
numerically
solved
using
Runge‐Kutta‐Fehlberg
4th‐5th
(RKF45)
order
method
shooting
technique
analytically
via
Adomian
decomposition
(ADM).
validation,
outcomes
this
inquiry
linked
those
available
in
literature.
In
addition,
acquired
analytical
ADM
data
compared
numerical
RKF45,
homotopy
analysis
(HAM)‐package
values,
given
It
found
skin
friction
coefficient
also
lower
presence
than
absence
such
effects.
Furthermore,
when
shrinking,
heat
transport
(HT)
decreases
increases,
respectively,
stretching.
reduces
HT
coefficient.
Contemporary Mathematics,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1707 - 1737
Published: April 17, 2024
This
study
investigates
sodium
alginate-based
nano-lubricants
with
added
copper
and
aluminum
oxides.
The
thermal
performance
of
nano
(Al2O3),
hybrid
(Al2O3
+
CuO)
ternary
CuO
TiO2)
nanofluids
is
studied
compared
in
this
article.
Due
to
the
significant
impact
higher
stream
rates,
nanofluid
crucial
domains
such
as
petroleum
engineering.
A
Sutterby
nanoflow
model
past
a
stretching
sheet
embedded
permeable
media
considered.
In
fluid,
effects
radiation,
hotness
source/sink,
inclined
magneto-convection
under
Stefan
blowing,
chemical
reaction
are
assumed.
highest-order
nonlinear
partial
differential
equation
handled
by
utilizing
similarity
function,
producing
new
set
ordinary
equations.
derived
equations
then
quantitatively
analyzed
using
bvp4c
approach
MATLAB.Graphical
representations
several
features
for
specific
non-dimensional
variables,
including
heat
transfer,
Sherwood,
drag
coefficient,
velocity,
temperature,
concentration,
presented.
An
increase
curve
observed
due
source/sink
parameter;
however,
Nusselt
number
exhibits
opposite
pattern.
participation
Nb
thermophoresis
force
led
greater
radiation.
For
Sc
Kr,
mass
transfer
ratio
lower.
results
show
very
good
congruence
when
literature.
Our
also
prove
that
transfers
more
from
system
than
or
nanofluid.
With
an
rate
energy
rises,
while
local
skin
friction
coefficients
tendency
direction.
International Journal of Numerical Methods for Heat & Fluid Flow,
Journal Year:
2024,
Volume and Issue:
unknown
Published: Sept. 27, 2024
Purpose
In
recent
times,
ternary
hybrid
nanofluid
has
garnered
attention
from
scientist
and
researchers
due
to
its
improved
thermal
efficiency.
This
study
aims
delve
into
the
examination
of
(Al
2
O
3
–Cu–TiO
/water),
particularly
concerning
axisymmetric
flow
over
a
nonlinearly
permeable
stretching/shrinking
disk.
addition,
investigation
convective
boundary
conditions
radiation
effects
is
also
considered
within
context
described
problem.
Design/methodology/approach
Mathematical
formulations
representing
this
problem
are
reduced
set
ordinary
differential
equations
(ODEs)
using
similarity
transformation.
The
MATLAB
value
solver
then
used
solve
obtained
ODEs.
impact
physical
parameters
such
as
suction
parameter,
nonlinear
nanoparticle
volumetric
concentration
Biot
number
on
profiles
well
quantities
illustrated
in
graphical
form.
Findings
findings
revealed
flux
for
shrinking
disk
approximately
1.33%,
significantly
higher
when
compared
linearly
Moreover,
existence
dual
solutions
attributed
unveiled,
with
first
solution
being
identified
stable
reliable
through
temporal
stability
analysis.
Practical
implications
Understanding
behavior
applications
engineering,
energy
systems
materials
research.
may
help
develop
optimize
like
heat
exchangers
cooling
systems.
Originality/value
dynamics
across
gains
less
linear
geometries.
Many
natural
industrial
processes
involve
changes
shapes
or
sizes.
shrinking/stretching
disks
therefore
essential
various
fields
processing,
biomedical
engineering
environmental
sciences.
Hence,
highlights
composed
alumina
),
copper
(Cu)
titania
(TiO
).
Besides,
tackles
complex
involving
multiple
factors
suction,
conditions.
Analyzing
can
provide
valuable
insights
real-world
phenomena
where
interact.