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.