Abstract:
This article presents to evaluating the sway of thermal radiation and
chemical reaction on MHD flow of Ag/SWCNT – Water based Maxwell hybrid
nanoliquid over a vertical cone by considering Cattaneo - Christov heat
flux, convective boundary condition and suction parameter. By using
appropriate transformations the nonlinear partial differential equations
are converted into ordinary differential equations. The governing
dimensionless equations are solved by using an optimized and extensively
validated Finite element method. The sway of dissimilar parameter on
hydrodynamic, thermal and solutal boundary layer is perceived and the
results are laid out graphically. Additionally, the values of skin –
friction coefficient, Nusselt number and Sherwood numbers are authorized
for different values of pertinent parameters and results are
demonstrated in tabular form. Comparison of the present problem results
with existing results shows good agreement. The key observations are
summarized as the velocity grows with \((\phi 1)\), Temperature
increases for Biot number \((\text{Bi})\) and Skin – friction
coefficient, Sherwood number declines, nevertheless Nusselt number
escalates as values of Deborah number \((\alpha)\) improves.
Keywords: Cattaneo – Christov heat flux; Convective boundary
condition; Suction parameter; \(Ag/SWCNT\ \) Water Maxwell hybrid
nanoliquid; FEM.\(\ \)
1. Introduction
Nanoliquids are one new kind of heat transfer fluid containing a small
quantity of nanosized particles (<100 nm) that are uniformly
suspended in a fluids. Nanoliquids play an important role for various
heat transfer applications. They are used to give better thermal
performance than natural convectional fluids due to the presence of
suspended nanoparticles with high thermal conductivity. Furthermore,
several researchers reported that enhancement in the heat transfer rate
with the use of various nanoliquids in various application compared to
conventional fluids. Choi et al. [1] presented the fundamental
limits of convectional heat conduction model by suspending nanoliquids
and measured that high thermal conductivity is anomalously greater than
theoretical predictions and which are nonlinear with nanotube loadings.
Nabati Shoghl et al. [2] investigated thermophysical properties of
water based nanoliquid and results showed that enhancement in electrical
conductivity and viscosity of base fluid by suspending nanoparticles.
Sundar et al. [3] demonstrated experimental study of thermal
conductivity and viscosity of nanoliquids with nano diamond particles,
however, the density and specific heat were estimated theoretically and
reported that at 1.0 vol % the thermal conductivity enhancements of
12.7% and 22.8%, at 1.0 vol% the viscosity enhancement of 1.57 times
and 1.8 times were observed at temperatures of 293 K and 333K than the
general liquid. Many experimental and theoretical studies have been
focused on enhancement of thermal conductivity of different nanoliquids
by several authors [4 – 7]. Patil et al. [8] inspected
non-linear mixed convection flow and heat transfer analysis of
nanoliquid over vertical cone and found that rates of heat transfer is
low for the nanoliquid compared to the ordinary mixture of liquid.
Ramzan et al. [9] perceived the impact of thermal radiation
parameter on steady flow, heat and mass characteristics and entropy
analysis of nanoliquid made up of carbon nanotubes over a vertical cone
and detected deterioration in the rates of velocity with improving
values of bio-convection Rayleigh number.
To know the knowledge of heat exchange mechanism in applications of
nanoliquid in various situations, heat conduction model has been
proposed by Fourier. Later, Cattaneo presented the modified Fourier’s
law for heat conduction in an inflexible body by considering thermal
relaxation time, which is called as Maxwell - Cattaneo law. After that,
Christov focused to the theory of nanoliquids by employing Oldroyd upper
- convected derivative rather than Maxwell time derivative while dealing
with Cattaneo type theory of nanoliquid. Several authors described MHD
boundary layer flow, heat and mass transfer analysis of different
nanoliquids by using Cattaneo - Christov heat flux model. Ahmad Khan et
al. [10] demonstrated in their work on heat and mass transfer flow
in upper – convected Maxwell fluid over an exponentially stretching
surface with Cattaneo – Christov heat flux model and found that the
fluid velocity is impedes as the thermal relaxation time values rises.
Ghalambaz et al. [11] studied natural convection flow of
Al2O3–water nanoliquids over a vertical cone by considering variable
thermal conductivity by using Tiwari-Das model. Heat and mass transfer
analysis of Burgers nanoliquid flow through stretched sheet with
Cattaneo – Christov heat flux model examined by Waqas et al. [12].
Hayat et al. [13] analyzed three dimensional rotating flow of
Jeffery fluid over stretching sheet with Cattaneo – Christov heat flux
model and noted that retardation in velocity sketches with rising values
of ratio of relaxation parameter. The sway of Catteneo – Christov heat
flux on mass and heat transfer analysis of various nanoliquids over
different geometries instead of conventional Fourier’s law deliberated
by several authors [14 – 17]. Saleem et al. [18] cognized the
impact of Cattaneo – Christov heat flux and heat generation/absorption
on heat and mass transfer analysis over stretching sheet with optimal
homotopy analysis method. Khan et al. [19] probed that the sway of
homogeneous-heterogeneous chemical reaction on heat and fluid flow of
Sisko fluid over bidirectional stretching sheet and conclude that fluid
temperature and velocity is decreasing function with higher values of
thermal relaxation parameter. Ali et al. [20] demonstrated MHD
boundary layer flow of Casson nanoliquid over a cone, wedge and plate by
considering Cattaneo – Christov heat flux model with nonlinear
radiation effects and variable source/sink and found that heat transfer
performance and local Nusselt number enhances with step-up values of
thermal relaxation parameter over a wedge compared with flows over a
plate and cone. Jayachandra babu et al. [21] studied MHD flow, mass
and heat transfer analysis over three geometries (plate, wedge, cone) by
inspecting Cattaneo - Christov heat flux model with the impact of
thermophoresis and Brownian motion and detected that Sherwood number and
Nusselt number highly influenced over cone by the thermal relaxation
parameter. Mamatha et al. [22] demonstrated theoretically unsteady,
MHD flow on heat and mass transfer characteristics by considering
thermal radiation and Cattaneo-Christov heat flux by dispersing grapheme
nanoparticles in dusty fluids. Iqbal et al. [23] analyzed the
influence of Cattaneo – Christov mass and heat flux on nanoliquid flow
over circular cone.
Recently, so many authors interested to describes the behavior of hybrid
nanoliquid as a part of new generation of engine oil. These nanoliquids
has several application in MRI scanning, optical modulators etc.,
Behseresht et al. [24] explored thermo physical properties of
nanoliquid filled with porous media over a vertical cone. Nadeem et al.
[25] studied third Grade fluid flow over a rotating vertical cone in
the presence of thermophoresis and Brownian motion by using Homotopy
analysis method. Reddy et al. [26] studied MHD boundary layer flow,
mass and heat transfer characteristics of nanoliquids filled with Al2O3
and Ag nanoparticles over Vertical cone and concluded that fluid
velocity rises, whereas the temperature and concentration decelerates
when the values of (\(\phi\)) improves. The impact of thermophoresis and
Brownian motion on heat and mass transfer analysis flow of Jeffery,
Maxwell and Oldroyd-B nanoliquids over a cone in the presence of
non-uniform heat source/sink was explored by Raju et al. [27] and
concluded that impact of magnetic field is more influenced in Maxwell
nanoliquid than Jerry and Oldroyd-B nanoliquids. Siddiqa et al. [28 -
29] proposed bio convection mass and heat transfer analysis of
nanoliquids over vertical wavy cone filled with gyrotactic
microorganisms. Reddy et al. [30] probed the sway of chemical
reaction on heat and mass transfer flow of nanoliquid over a vertical
cone by using Buongiorno model and found that temperature and
concentration sketches are escalated as the values of thermophoresis
rises. Oyelakin et al. [31] perceived mass and heat transfer
properties of Casson nanoliquid flow over a vertical cone with
Cattaneo-Christov heat flux model under the convective boundary
condition. Dinarvand et al. [32] discussed MHD convective boundary
layer flow, mass and heat transfer analysis of water – based nanofluid
suspended with Copper, alumina and titania nanoparticles over rotating
down point cone by using Tiwari-Das model. Sreedevi et al. [33]
analyzed the sway of chemical reaction and suction/injection on MHD
boundary layer flow, mass and heat transfer characteristics of water –
based nanoliquid containing SWCNT and MWCNT nanoparticles over a
vertical cone with convective boundary condition and found that all
values of rates of mass transfer, rates of heat transfer and velocity
rates escalates with improving values of Biot number. Recently, several
authors [34 – 38] studied the impact of various pertinent
parameters on boundary layer flow, mass and heat transfer analysis of
different hybrid nanoliquids over several geometries.
Recently, several articles investigate the fluid flow, mass and heat
transfer characteristics of different nanoliquids over several
geometries. No studies have been analyzed to examine mass and heat
analysis of Maxwell hybrid nanoliquid over a vertical cone with Catteneo
- Christov heat flux model under the convective boundary condition.
Hence, we examine the sway of different parameters on Maxwell hybrid
nanoliquid flow, heat and mass transfer analysis over a vertical cone
and calculated local skin – friction coefficient, Sherwood and Nusselt
numbers.