Thermal inspection for viscous dissipation slip flow of hybrid nanofluid (TiO2–Al2O3/C2H6O2) using cylinder, platelet and blade shape features

Hybrid nanofluid are the modified class of nanofluids with extra high thermal performances and present different applications in automotive cooling, heat transfer devices, solar collectors, engine applications, fusion processes, machine cutting, chemical processes etc. This thermal research explores the heat transfer assessment due to hybrid nanofluid with of different shape features. The thermal inspections regarding the hybrid nanofluid model are justified with aluminium oxide and titanium nanoparticles. The base liquid properties are disclosed with ethylene glycol material. The novel impact of current model is the presentation of different shape features namely Platelets, blade and cylinder. Different thermal properties of utilized nanoparticles at various flow constraints are reported. The problem of hybrid nanofluid model is modified in view of slip mechanism, magnetic force and viscous dissipation. The heat transfer observations for decomposition of TiO2–Al2O3/C2H6O2 is assessed by using the convective boundary conditions. The shooting methodology is involved for finding the numerical observations of problem. Graphical impact of thermal parameters is observed for TiO2–Al2O3/C2H6O2 hybrid decomposition. The pronounced observations reveal that thermal rate enhanced for blade shaped titanium oxide-ethylene glycol decomposition. The wall shear force reduces for blade shaped titanium oxide nanoparticles.

www.nature.com/scientificreports/ efficiency, domestic refrigerator freezers, cooling of electronics and transformer oil, boosting diesel generator efficiency, military and space, solar water heating, nuclear reactors, cooling of heat exchanging devices, and so on are only a few of the uses. Nanofluids have a wide range of applications because they can improve heat transfer performance when compared to pure liquids, earning them the moniker next-generation heat transfer fluids. Suspending metal particles in fluids to increase thermal conductivity is a well-known technique. Choi 1 predicted first invention on nanomaterials and introduction the concept of nanofluids. Buongiorno 2 presented the fascinating description related to slip mechanisms of the nanofluid that depends upon Brownian motion and thermophoresis characteristics. Hayat et al. 3 presented suggestion about consideration of Maxwell nanofluid persuaded through the way of stretching surface which possessed variable thickness. Sui et al. 4 proposed the investigations of modification of diffusion theories that can be used to analyze the phenomenon of mass and heat worked in Maxwell nanomaterial. Hsiao 5 worked to theoretically investigate the flow of nanoparticles having characteristics of viscous dissipation and also thermal radiation. Turkyilmazoglu 6 investigated the consequences of nanofluid flow having single phase in a circular jet. Ahmad et al. 7 investigated the generation of heat and absorption characteristics in nanofluid of rate type persuaded by the rotating disk and the formulated problems are numerically solved by shooting method. For channel with a zero-mass flux rate, Turkyilmazoglu 8 addressed the nanofluid thermal attention. Tlili et al. 9 20 tested the Hall features while addressing the enhanced heat transfer impact due to nanomaterials. The hybrid nanomaterial is the more impressive class of nanofluid justifying the enhanced thermal mechanism. This hybrid class contains properties of base fluid with decomposition of two different nanoparticles. It is experimentally observed that more strengthened thermal performances are observed when heat transfer inspection is observed with hybrid nanofluids. Owing to such unique thermal impact, the special applications of hybrid class are noted in photovoltaic systems, thermal management systems, automotive cooling systems, energy storage devices, coating of materials, heat transfer objects etc. Different studies in recent years are predicted for hybrid nanofluids. Bibi et al. 21 discussed the shape features of hybrid nanoparticles due to thin liquid layer. Saeed et al. 22 endorsed the hybrid nanofluid thermal effectives due to spinning of moving regime. Ibrahim and Gamachu 23 observed the entropy generation enrollment while inspecting the novel thermal outcomes of hybrid nanofluid. Alhadri et al. 24 performed the computations by using the Response surface technique for a hybrid nanofluid problem conveying the classical heating impact. Dero et al. 25 justified the stable thermal determination of hybrid nanofluid impacted by dissipation consequences. The shape features endorsing thermal classification of hybrid nanofluid was observed by Shanmugapriya et al. 26 . Mostafizur et al. 27 depicted the solar application for hybrid nanofluid in cooling systems. Haneef et al. 28 reported the progressive on set of hybrid nanoparticles via numerical approach. The gyrating channel surface flow containing the copper nanoparticles with ethylene glycol was invested by Das et al. 29 . Rana et al. 30 reported the hybrid nanofluid flow due to copper nanoparticles with radiative heat flux. The role of quadratic thermal radiation for hybrid nanofluid with ethylene glycol base material for rotating sphere was focused in the model of Rana et al. 31 . Later on, Rana et al. 32 worked out the Artificial neutral network framework for the hybrid nanofluid problem with elliptical fins. Ullah et al. 33 explained the multiple shape consequences regarding the hybrid nanofluid with Darcy Forchheimer impact. Guedri et al. 34 suggested the biomedical significance of aluminium and iron oxide nanoparticles against the blood base fluid. Mahmood et al. 35 reported the Joule heating mechanism of hybrid nanoparticles with spinning sphere. Qadeer et al. 36 continued the irreversibility mechanism of hybrid nanofluid in the divergent channel. Alqahtani et al. 37 enrolled the dissipative fact for hybrid nanofluid with stretched disk.
This thermal research explores the heat transfer assessment due to hybrid nanofluid with of different shape features. Titanium oxide (TiO 2 ) and aluminium oxide (Al 2 O 3 ) tiny materials are used for endorsing the hybrid nanofluid thermal prospective. The justification of base liquid is observed with ethylene glycol (C 2 H 6 O 2 ) liquid. The novel impact of current model is the presentation of different shape features namely Platelets, blade and cylinder. The microscopic view thermal visualization of nanoparticles is observed. Different thermal properties of hybrid nanofluid are observed with interreference of viscous dissipation, external magnetic force and heating source. The contribution of slip has also been observed for controlling of thermal transport phenomenon. The convective boundary assumptions are entertained for uprising the thermal impact. The shooting numerical technique is used to present the numerical outcomes. Various tables are developed for report the shape features assessment and thermal observations of proposed model. The enhanced thermal applications of ethylene glycol are important in different industrial and manufacturing processes.

Hybrid nanofluid model
Flow constraints and governing equations. The heat transfer enhancement due to hybrid nanofluid with different shape features is observed due to radially stretched surface. The nanofluid flow having velocity U(r, t) = ar 1−ct occurs along a radial direction and pressure gradient plays no part in the fluid flow field. The where T 0a ambient temperature. The flow configuration is presented in Fig. 1. Following flow assumptions are assumed for model the problem: • An unsteady 2-D hybrid nanofluid model in radially stretched surface framework is utilized.
• The flow is subject to the variable magnetic field. The role of induced magnetic force is neglected under the hypothesis of small magnetic Reynolds number hypothesis. • Different shaped nanoparticles of Tio 2 andAl 2 o 3 are submerged into ethylene glycol (EG) base fluid for a comprehensive relative analysis. • The effects of viscous dissipation and internal heat generation are considered to modify the problem.
• The mathematical structure is based on polar coordinate (r, θ, z).
• All physical entities are independent of θ against the rotational flow and the velocity field is in the form v = [u(r, z), 0, w(r, z)] , where u and w are velocity components along the radial(r) and axial(z) directions, respectively.
The governing equations of problem are [21][22][23] : The corresponding boundary conditions for the given system of differential equations are 23 : www.nature.com/scientificreports/ With density (ρ nf ) , thermal diffusivity (α nf ) , volume fraction φ , thermal conductivity (k s ) , shape factor of nanoparticles (nm) , viscosity (v nf ) and electrical conductivity (σ nf ) , thermal effeciency k nf and viscosity ( µ nf ). Moreover,φ, (ρCp) nf , D 1 , and D 2 are volume fraction, heat capacitance and viscosity enhancement coefficients of the nanofluid, respectively. Thermal features and shape features of hybrid nanoparticles. The characteristics of TiO 2 and Al 2 O tiny materials with EG base material are reflected via Table 1. The shape factor and viscosity of different shapes nanoparticles are given in Table 2.
Dimensionless variables. Endorsing the new variables 21-23 : where η is an independent variable, aRe = .˙r U v f is a local Reynolds number, and ψ is a stream function As a result, the velocity components are calculated as: By utilizing the relationship defined in Eqs. (6) to (8), Equation (1) is identically satisfied and equations (2) and (3) along with boundary conditions defined in Eq. (4) take the following form: Subject to the boundary conditions f The non-dimensional physical parameters such like magnetic number M , internal heat generation Q , Unsteadiness parameter S , Prandtl number Pr , Eckert number Ec and Biot factor Bi are defined as: Shear stress and Heat transfer rate can be defined as: The dimensionless form is:

Numerical simulations
The numerical outcomes are preserved via BVP4C algorithm. The first order system is: with: The numerical results are presented with accuracy of 10 -4 .

Thermal impact of parameters
A numerical solution of the dimensionless mathematical model is obtained using the BVP4C technique. Significant parameters such as the M magnetic parameter, S unsteadiness parameter, φ solid volume fraction, Ec Eckert number, Bi Biot number and Q internal heat generation parameter is all given special attention. In addition, there is a detailed result for skin friction and heat transfer coefficient. Figures 2, 3, 4 are drawn to investigate the influence of significant physical parameters such as velocity slip parameter K, Magnetic parameter M and unsteadiness parameter S on velocity distribution. Figure 2 signifies the assessment of slip factor K on velocity field for various shapes of TiO 2 andAl 2 O 3 anoparticles dispersed in ethylene glycol (EG) . Physically, the dragging of the stretching sheet is only partially coupled to the fluid under the slip parameter. The slip velocity increases while fluid velocity drops as K increases. It is worth noting that K has significant influence on the solutions. Furthermore, the enhancing and declining rate of velocities are noted for platelet shaped TiO 2 − EG and Blade shaped Al 2 O 3 − EG nanofluids. Figure 3 impacted the magnetic parameter association to velocity profile of two distinct nanoparticles TiO 2 andAl 2 O 3 for different shapes such as blade, cylinder and platelet. It is noticed that greater values of the magnetic parameter generate more Lorentz force, which causes the fluid velocity to slow and the velocity profile to drop. Figure 4 illustrates fluctuated pattern in velocity for S. The movement of the boundary layer thickness is slowed as S increases, resulting in a decrease in velocity profile for both type of nanofluids having various shapes of TiO 2 and Al 2 O 3 nanoparticles.    www.nature.com/scientificreports/ means unsteadiness significantly influence the temperature profile. Figure 7 depicts the effect of the internal heat generating parameter Q on temperature profile. It is observed that boosted onset of θ is noticed for larger Q. It is due to the fact that positive values of Q shows the temperature storage within the fluid that plays a vital role to enhance the fluid temperature. The viscous dissipation impact on temperature is visualized in Fig. 8. The temperature increases for rising values of EC for Al 2 O 3 − EG and TiO 2 − EG nanofluids. The increase in viscous dissipation indicates enhancement in the kinetic energy in the fluid which improves the temperature distribu-   www.nature.com/scientificreports/ tion. Figure 9 depicts the influence of volumetric fraction φ on θ . The rescaling values to φ declined the thermal phenomenon for Al 2 O 3 − EG and TiO 2 − EG . Such observations are associated to the rising values of φ thermal conductivity which rapidly transfer the. Figure 10 illustrates the influence of Biot number Bi on temperature profile. It is observed that temperature gradient for both BiAl 2 O 3 − EG and TiO 2 − EG nanofluids upsurges for Bi . Such enhanced inspection is due to larger heat transfer coefficient.

Assessment of velocity profile.
Variation of skin friction. Table 3 shows the influence of parameters like S , M and K on skin friction for multi-shape TiO 2 andAl 2 O nanoparticles. The analysis of this table reveals that grad force enhanced when S and

Conclusions
The heat transfer analysis due to modified hybrid nanofluid has been numerically studied due to radially stretching sheet. The aluminium oxide and titanium nanoparticles are used with ethylene glycol base material. The blade, cylinder and platelets shaped nanoparticles are focused. The analysis has been observed in view internal heat generation, viscous dissipation and velocity slip effects. The significant observations are: • With larger unsteady parameter, the velocity pattern reduced.
• The increasing velocity rate is claimed for platelet shaped titanium oxide-ethylene glycol suspension.
• The nanoparticles volumetric friction, velocity slip parameter and unsteadiness parameter reduce the heat transfer phenomenon. • The internal heat generation, viscous dissipation and convective boundary conditions are seen to increase the nanofluid temperature. • The unsteadiness parameter and Biot number effectively improves the heat transfer rate.
• The magnitude wall shear force controls due to slip parameter.
• The titanium oxide nanoparticles with a blade shape present enhanced heat transfer rate.