An enhancement in thermal performance of partially ionized fluid due to hybrid nano-structures exposed to magnetic field

This article considers ethylene glycol as a partially ionized base fluid whose rheological characteristics can be exhibited by Carreau stress-strain relations. This dispersion of nanoparticles (MoS2) and hybrid nanoparticles (a combination of (MoS2 and SiO2) in ethylene-glycol is considered and thermal performance of MoS2-Carreau nanofluid and hybrid nanofluid (MoS2-SiO2-ethylene glycol) are investigated numerically using FEM. The results are validated. The present theoretical analysis has shown that thermal performance of working fluid can be enhanced by the use of hybrid nano fluid rather than nano fluid. Unfortunately, shear stress on elastic surface exerted by hybrid nanofluid is greater than the shear stress exerted by nanofluid. Although the thermal performance of hybrid nano fluid is greater than the thermal performance of nanofluid but one must be cautious about strength of surface as it can afford sufficient stress otherwise thermal system may experience failure. Failure analysis prediction while using hybrid nanonfluid must be in mind. As ethylene glycol is partially ionized and its interaction with applied magnetic field induces Hall and ion slip currents. Due to Hall and ion slip currents, ethylene glycol experiences Hall and ion slip forces which are opposite to the Lorentz force of applied magnetic field. This Lorentz force is reduced Hall and ion slip forces. Consequently, the flow of ethylene glycol is accelerated when Hall and ion slip parameters are increased.This article considers ethylene glycol as a partially ionized base fluid whose rheological characteristics can be exhibited by Carreau stress-strain relations. This dispersion of nanoparticles (MoS2) and hybrid nanoparticles (a combination of (MoS2 and SiO2) in ethylene-glycol is considered and thermal performance of MoS2-Carreau nanofluid and hybrid nanofluid (MoS2-SiO2-ethylene glycol) are investigated numerically using FEM. The results are validated. The present theoretical analysis has shown that thermal performance of working fluid can be enhanced by the use of hybrid nano fluid rather than nano fluid. Unfortunately, shear stress on elastic surface exerted by hybrid nanofluid is greater than the shear stress exerted by nanofluid. Although the thermal performance of hybrid nano fluid is greater than the thermal performance of nanofluid but one must be cautious about strength of surface as it can afford sufficient stress otherwise thermal system may experience failure. Failure analysis prediction while...


I. INTRODUCTION
Transportation of heat energy is a key process in industrial manufacturing. The efficiency of a thermal cooling system depends upon the speed of transportation amount of heat transported. An enhancement of heat or cooling in natural or processes affect the money factors like energy storage, reduction of process time, etc. Therefore, an enhancement in the transportation of heat has become a major concern has thermal performance is the main focus. There are several techniques/methods of transportation in the process of heat. These methods include the use of the extended surface, cooling fins, metallic and non-metallic coating, displacement insertion, wireless of flow, vibration, injection suction, jet impingement, the use corrugated tubes and cooling tower packings, etc. Although above-mentioned methods for good for the enhancement of transportation of heat but the most recent and extensively used technique is the inclusion of nano-sized metallic structures in the base fluid. An enhancement in technology and synthesis of nanofluid at the industrial level has increased the imported of the nanofluid. In view of the applications of nanofluid several practical and experimental studies have been published. For example, Sheikholeslami et al. 1 considered Lorentz force and porous medium resistance to developed mathematical theory for an enhancement in the thermal performances due to aluminium particles and computed the solutions of modelled problems using Lattice Boltzmann method. Zhixiong et al. 2 numerically analysed the role of Copper oxide on the thermal performance of water in a duct Lattice Boltzmann method. Sadiq et al. 3 studied the combined effects of nano-sized metallic structures and free stream velocity. Saleem et al. 4 developed mathematical modelling to incorporate the simultaneous effects of Brownian motion and thermophoresis on transport of heat energy and concentration and solved the resulting models to examine the impact of Walter B parameter, rotation of cone and unsteadiness of the transportation mechanism. Ramzan et al. 5 discussed an enhancement in thermal ARTICLE scitation.org/journal/adv performance of couple stress fluid containing nano-structures under the mass flux conditions. Saleem et al. 6 performed optimized analysis for parameters affecting dissipation phenomenon in nanofluid. Dogonchi et al. 7 investigated the impact of nanoparticles on the transport of heat ene rgy in natural convection in cavity subjected to elliptical heater. They also studied the role of shape of nanostructures on the thermal performance of nanofluid. Dogonchi et al. 8 considered combined role of nano-structures, thermal radiations, resistance of porous medium, magnetic field during the transport of heat energy and solved the problems by FEM. Seyyedi et al. 9 performed numerical simulations in order to capture the role of nano-structures on the entropy generation in the presence of magnetic field. Dogonchi et al. 10 discussed the role of Carreau heater and nano-structures in working fluid and also in square cavity. Daniel et al. 11 analysed the role of stratification on convective transport of heat in nanofluid. Daniel et al. 12 simultaneously considered thermal radiation, viscous and Joule heating on transport phenomenon with double stratification. Daniel et al. 13 performed electromagnetic analysis of entropy generation in nanofluid emitting thermal radiations. Daniel et al. 14 modelled unsteady electromagnetics for heat transfer with double stratification and dissipation of heat and numerically solved the problems to investigate the role of key parameters. Daniel et al. 15 studied thermal stratification in convective heat transport in radiative nanofluid flow over a stretching sheet of nonuniform thickness. Daniel et al. 16 modelled the role of convective boundary conditions together with partial slip and computed solution of obtained problems to explore the underlying physics. Daniel et al. 17 numerically studied generation of entropy occurring heat transfer in EHD flow of nanofluid and also examined the impact of heat generation and absorption on transport of heat in slip flow over a permeable surface. Daniel et al. 18 analysed the role slip on the transport of momentum and heat in an unsteady convective flow when the impact of thermal radiation is remarkable. Daniel et al. 19 analysed the impact of wall permeable and magnetic field convective heat transfer in fluid experiencing partial slip. Daniel and Daniel 20 modelled the role of buoyancy, thermal radiation, permeability of sheet and magnetic field on convective transfer of heat and derived approximate series solutions in order to examine the impact of key parameters on convective heat transfer. Convective heat transfer in slip flow was modelled by Daniel et al. 21 and computed the solution of modelled problems using homotopy analysis method.
The advent of hybrid nanofluid and an excellent increase in their thermal performance have been received immense attractions. Therefore, researchers have proposed models for effective thermal properties in term of hybrid nanoparticles and some others have used proposed models to examine the impact of hybrid nanoparticles on the thermal performance of working fluids. For instance, For instance Chamkha et al. 22 explored the role of hybrid nanoparticles on the thermal performance of working fluid. Afridi et al. 23 analysed the role of hybrid nano-structures on an enhancement in thermal performance of working fluid dissipating heat during thermal changes. Sheikholeslami et al. 24 considered non-uniform magnetic field and dispersion of hybrid nanofluid to model the transport of heat in fluid enclosed in circular cavity and solved problems by FEM.
Partially ionized fluid exposed to the magnetic field exhibit totally different to characteristics than the characteristics of a natural fluid. Due to these different dynamics of partially ionized nanofluid, several investigators [25][26][27][28][29][30][31] have heat and mass transport in partially ionized fluids.
To the best of author's knowledge, no study on thermal performance partially ionized Carreau liquid fluid by hybrid nanoparticles exposed to magnetic field investigated so far. The complex mathematical models are solved by finite element method (FEM) and an efficient method. This method has been successfully implemented to complex problems of computational fluid dynamics (CFD). Simulations are carried out by indigenously developed computer program on personal computer. Eventually, the remarkable observations are noted and discussed.

II. MODELLING AND DIMENSIONAL ANALYSIS
We considered MoS 2 and (MoS 2 , SiO 2 ) as hybrid nano solid structures in ethylene glycol (Carreau liquid) over the horizontal sheet moving with velocity Vw = [a(x + y) n , b(x + y) n ]. A nonuniform temperature and magnetic field are considered as Tw = T∞ + A 1 T 0 (y + x) 2n , B 0 (x + y) n−1 2 k. Furthermore, MoS 2 and (MoS 2 , SiO 2 ) in ethylene glycol is determined to be plasma 34 and non-Newtonian in form of shear thinning. 35 The schematic representation is given by Fig. 1.
The boundary layer equations under consideration are Here nf stands the nanofluid and hnf stands hybrid nanofluid.
The change of variables Converts Eqs. (2)-(6) into the dimensionless form which are ARTICLE scitation.org/journal/adv Density Thermal conductivity Electrical thermal conductivity The wall shear stresses are expressed as The wall heat transfer rate is given by ) is the local Reynolds number. Further, the numerical values of thermophysical properties. 32,33 are given in Table I.

III. SOLUTION STRATEGY
The computational procedure is briefly described as under.
Step I: Problem domain is converted into finite number of the elements and gets linear type polynomial solution over each element. The weighted residual function is implemented to transformed strong form of the flow problem into weak form. Shape functions are used in flow problem to compute the approximate solution.
Step II: Stiffness matrices, force vector and boundary integral vector are computed according to the shape functions over each element. Finally, the global stiffness matrix is calculated over a whole domain and Picards scheme is used to transform system of non-linear equations into linear equations.
Step III: The solution of system of linear equations is computed iteratively under computational tolerance 10 −8 .
Step IV: FEM code is developed in MAPLE. The mesh-free analysis is carried out for the computational domain [0,7]. Several experiments are run for different grids and obtained numerical data is recorded in Table II. Table II predicts that computed solutions become mesh-free when domain is broken down into 300 elements.

Validation of results:
The results in special cases are compared with already published work. 36 This comparison is given in Tables III and IV.   TABLE II

IV. GRAPHICAL AND NUMERICAL DATA AND ITS DESCRIPTION
The mathematical models governing the transport phenomenon in the partially ionized Carreau liquid fluid containing nanoparticles (MoS 2 ) and hybrid nanoparticles (MoS 2 and SiO 2 ) are solved numerically in order to investigate their thermal performances. Numerical runs have provided very useful information regarding impact of hybrid nanoparticles on thermal efficiency of working fluid mixture (mixture of Carreau fluid, MoS 2 and SiO 2 ). The extracted information is displayed graphically and in the form of numerical data.

A. Dynamics of fluid flow
The impact of Weissenberg number We on the flow of nano and hybrid fluids is studied and obtained dynamics of flow is displayed by Figs. 2a and 2b. The solid curves are velocity curves for hybrid nanofluid whereas the dotted curves are velocity curves for nanofluid. Figs. 2a and 2b are lateral velocities under the influence of We. These Figs. predict that the flow of nano and hybrid nanofluids slows down when We is increased. It is also evident that velocity of Newtonian nano and hybrid nanofluid are greater than the velocity of Carreau nano and hybrid nanofluids. The momentum boundary layer thickness can be shortened by the use of Carreau fluids. This fact can be read by Figs. 2a and 2b. The behavior of nano and hybrid nanofluid under the change of magnetic intensity is also investigated and obtained behavior is represented by Fig. 3a and 3b. These Figs. clearly predict that the flow in both xand ydirections is slowed down when intensity of magnetic field is increased. This increase in the intensity of magnetic field also reduces the momentum boundary layer thickness see Figs. 3a and 3b. The behavior of Hall and ion slip currents on the velocity (f ′ , g ′ ) are studied and information is displayed in Figs. 4a-5b. One can easily study that the Hall and ion slip forces are favourable for flow in xdirection. It is also noted that enhancement in momentum boundary due to an increase in Hall and ions slip currents. However, this increasing impact of Hall and ion slip currents on nanofluid is more than the impact on hybrid nanofluid (see Figs. 4a, 4b, 5a and 5b).

B. Impact of parameters on temperature
The impact of Hall and ion slip parameters (βe, βi) on the temperature of fluid is also examined. Corresponding numerical data is represented by Figs. 6a and 6b. This graphical representation of data reveals that temperature decreases when Hall and ion slip parameters are increased. This decreasing trend is based on the fact that βe and βi appear in denominator of Joule heating terms and an increase in βe and βi results a decrease in the heat generated due to Ohmic dissipation phenomena. The thermal boundary layer thickness has also shown a decreasing behavior when βe and βi are increased. This implies that the use of partially ionized liquid in the presence of magnetic field helps in controlling the thermal boundary layer thickness. Thermal boundary layer thickness associated with natural liquid is greater them thermal boundary layer thickness in partially ionized liquid. The Eckert number (Ec) appears as coefficient of viscous dissipation term in the energy equation and increase in (Ec) corresponding to enhancement in the dissipation heat. Consequently, temperature of the fluid rises. This fact is shown by Fig. 7. Since Ec appears in the viscous dissipation term of energy equation and an increase Ec corresponds to an increase in rate of work done by the friction force. According to first law of thermodynamics, this work done is used to increase the internal energy of the fluid. Consequently temperature increases.

C. Wall shear stresses and wall heat flux
The role of Hall and ion slip parameters and power law index on the wall shear stress, wall heat and mass flux are studied for nano and hybrid nanofluids. Wall shear stresses have shown reduction when the parameter (We) is varied. However, an enhancement in wall heat flux is analysed (see Table V). Furthermore, wall shear stresses for Newtonian fluid are less than the wall shear stresses for Carreau liquid (We ≠ 0). However, the case of Newtonian fluid is less than that for Carreau fluid. The above-noted observations are valid for both nano and hybrid nanofluid. It is also noted from that Table V. That wall shear stresses for nanofluid have low values when compared with those for hybrid nanofluid. Moreover, the wall heat flux for the case of hybrid nanofluid is greater than that for the case of nanofluid (see Table V). Table V predicts that the wall shear stresses and wall heat flux for nano and hybrid nanofluid increase when the hall parameter βe is enhanced whereas

ARTICLE
scitation.org/journal/adv  βi has shown an increasing trend on the wall shear stresses and decreasing trend on wall shear stresses. The impact of power law index (m) on the wall shear stresses and wall heat flux is also given by Table V.

V. CONCLUSION
The ethylene glycol is partially ionized and exhibits shear thinning/shear thickening behaviour. Therefore, thermal performance of nano-ethylene glycol and hybrid nano-ethylene glycol by considering ethylene glycol as a partially ionized liquid is investigated numerically. Several numerical experiments are conducted to analyse the behaviour of key parameters on the thermal performances of nano-ethylene glycol and hybrid nano-ethylene glycol. The key observations are listed below.
• The present theoretical analysis has shown that thermal performance of working fluid can be enhanced by the use of hybrid nano fluid rather than nano fluid • Unfortunately, shear stress on elastic surface exerted by hybrid nanofluid is greater than the shear stress exerted by nanofluid. Although the thermal performance of hybrid nano fluid is greater than the thermal performance of nanofluid but one must be cautious about strength of surface as it can afford sufficient stress otherwise thermal system may experience failure. Failure analysis prediction while using hybrid nanonfluid must be in mind. • As ethylene glycol is partially ionized and its interaction with applied magnetic field induces Hall and ion slip currents. Due to Hall and ion slip currents, ethylene glycol experiences Hall and ion slip forces which are opposite to the Lorentz force of applied magnetic field. This Lorentz force is reduced Hall and ion slip forces. Consequently, the flow of ethylene glycol is accelerated when Hall and ion slip parameters are increased • Joule heating and viscous dissipation have shown an increasing impact on the temperature because heat dissipated as a result of Ohmic and friction phenomenon adds to the fluid and its temperature rises • It is observed that thermal performance of partially ionized hybrid nanofluid is greater than that of partially ionized nanofluid