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The present investigation aims to use entropy analysis to analyze the unsteady Magnetohydrodynamic (MHD) flow in a second-grade fuzzy hybrid Al 2 O 3 - Cu/SA nanofluid over an exponentially shrinking/stretching surface. The model for hybridization of the mixture of alumina Al 2 O 3 and copper (Cu) nanoparticles in the sodium alginate (SA) base fluid under heat source/sink, nonlinear thermal radiation, and viscous dissipation. The fundamental partial differential equations (PDEs) are simplified using an appropriate similarity conversion to generate the ordinary differential equations (ODEs). The analytical computation occurs in the MATHEMATICA program implementing the homotopy analysis method (HAM). In terms of code validity, our results are preferable to previous findings. The features of several parameters against the velocity, surface friction coefficient, entropy, temperature, and Nusselt number are described through graphs. According to our findings, the rise in the Brinkman and Reynolds numbers enhanced the total entropy of the system. Furthermore, the nanoparticle volume fraction and viscus dissipation magnifies the fluid temperature while retards the flow profile throughout the domain. Fluid velocity declined due to the Lorentz force using magnetic impact applications. The imprecision of nanofluid and hybrid nanofluid volume fractions was modelled as a triangular fuzzy number (TFN) [0%, 1%, 2%] for comparison. The double parametric approach was applied to deal with the fuzziness of the associated fuzzy parameters. The nonlinear ODEs convert into fuzzy differential equations (FDEs) and use HAM for the fuzzy solution. From our observation, the hybrid nanofluid displays the maximum heat transfer compared to nanofluids. This important contribution will support industrial growth, particularly in the processing and manufacturing sectors. The percentage increase in skin friction factor is 18.3 and 15.0 when α and β take input in the ranges of 0 ≤ α ≤ 0.8 and 0 ≤ β ≤ 1, respectively. [ABSTRACT FROM AUTHOR]

The significance of fuzzy volume percentage on the unsteady flow of MHD tangent hyperbolic fuzzy hybrid nanofluid towards an exponentially stretched surface is scrutinized. The heat transport mechanism is classified by Joule heating, nonlinear thermal radiation, boundary slippage, and convective circumstances. Ethylene glycol (EG) as a host fluid along with the nanomaterial's Cu and Al 2 O 3 are used for heat transfer analysis is also considered in this investigation. The nonlinear governing PDEs are meant to be converted into ODEs employing appropriate renovations. Then, a built-in MATLAB program bvp4c is employed to acquire the outcome of the given problem. The variation of flow rate, thermal heat, drag force and Nusselt number and their influence on fluid flow with heat transfer have been scrutinized through graphs. An increase in thermal radiation, power law index and nanoparticle volume friction heightens the heat transmission rate. Skin friction is diminished by swelling the power-law index, Weissenberg number, and ratio parameters, whereas it is increased by enhancing the magnetic parameter. The heat transfer rate upsurges with an increase in Weissenberg number and nanoparticle volume fraction. Also, the nanoparticle volume percentage is expressed as a triangular fuzzy number (TFN). The triangular membership function (MF) and TFN are regulated by the χ - cut parameter, which has a range of 0 to 1. In comparison to nanofluids, hybrid nanofluids have a higher heat transmission rate, according to the fuzzy analysis. This investigation has applications in the areas of paper manufacturing, metal sheet cooling and crystal growth. [ABSTRACT FROM AUTHOR]

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy Al 2 O 3 + Cu + TiO 2 /EO tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, Al 2 O 3 , Cu and TiO 2 have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination Al 2 O 3 + Cu + TiO 2 /EO. Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range 0.1 ≤ Mh ≤ 0.3 and wedge angle parameters 0.1 ≤ m ≤ 0.3 . For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal. [ABSTRACT FROM AUTHOR]

This contribution aims to optimize nonlinear thermal flow for Darcy-Forchheimer Maxwell fuzzy Al 2 O 3 + Cu + TiO 2 /EO tri-hybrid nanofluid flow across a Riga wedge in the context of boundary slip. Three types of nanomaterials, Al 2 O 3 , Cu and TiO 2 have been mixed into the basic fluid known as engine oil. Thermal properties with the effects of porous surface and nonlinear convection have been established for the particular combination Al 2 O 3 + Cu + TiO 2 /EO. Applying a set of appropriate variables, the set of equations that evaluated the energy and flow equations was transferred to the dimensionless form. For numerical computing, the MATLAB software's bvp4c function is used. The graphical display is used to demonstrate the influence of several influential parameters. It has been observed that flow rate decay with expansion in porosity parameter and nanoparticles volumetric fractions. In contrast, it rises with wedge angle, Grashof numbers, Darcy-Forchheimer, nonlinear Grashof numbers, and Maxwell fluid parameter. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increases in drag force for ternary hybrid nanofluid are 13.2 and 8.44 when the Modified Hartmann number takes input in the range 0.1 ≤ Mh ≤ 0.3 and wedge angle parameters 0.1 ≤ m ≤ 0.3 . For fuzzy analysis, dimensionless ODEs transformed into fuzzy differential equations and employed symmetrical triangular fuzzy numbers (TFNs). The TFN makes a triangular membership function (M.F.) that describes the fuzziness and comparison. This study compared nanofluids, hybrid nanofluids, and ternary nanofluids through triangular M.F. The boundary layer flow caused by a wedge surface plays a crucial role in heat exchanger systems and geothermal. [ABSTRACT FROM AUTHOR]

The significance of fuzzy volume percentage on the unsteady flow of MHD tangent hyperbolic fuzzy hybrid nanofluid towards an exponentially stretched surface is scrutinized. The heat transport mechanism is classified by Joule heating, nonlinear thermal radiation, boundary slippage, and convective circumstances. Ethylene glycol (EG) as a host fluid along with the nanomaterial's Cu and Al 2 O 3 are used for heat transfer analysis is also considered in this investigation. The nonlinear governing PDEs are meant to be converted into ODEs employing appropriate renovations. Then, a built-in MATLAB program bvp4c is employed to acquire the outcome of the given problem. The variation of flow rate, thermal heat, drag force and Nusselt number and their influence on fluid flow with heat transfer have been scrutinized through graphs. An increase in thermal radiation, power law index and nanoparticle volume friction heightens the heat transmission rate. Skin friction is diminished by swelling the power-law index, Weissenberg number, and ratio parameters, whereas it is increased by enhancing the magnetic parameter. The heat transfer rate upsurges with an increase in Weissenberg number and nanoparticle volume fraction. Also, the nanoparticle volume percentage is expressed as a triangular fuzzy number (TFN). The triangular membership function (MF) and TFN are regulated by the χ - cut parameter, which has a range of 0 to 1. In comparison to nanofluids, hybrid nanofluids have a higher heat transmission rate, according to the fuzzy analysis. This investigation has applications in the areas of paper manufacturing, metal sheet cooling and crystal growth. [ABSTRACT FROM AUTHOR]

The unsteady energy and mass transport of magnetohydrodynamics (MHD) second grade nanofluid via an exponentially extending surface with Dufour and Soret effects are investigated in this study. Variable thermal conductivity and mixed convection effects are used to investigate the heat transfer mechanism. There are also new characteristics such as slip flow, viscous dissipation, Brownian motion, nonlinear thermal radiation, and thermophoresis. In the problem formulation, the boundary-layer approximation is used. Using the suitable transformations, the energy, momentum, and concentration equations are generated into non-linear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). The effects of environmental parameters on velocity, temperature, and concentration profiles are graphically depicted. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison to a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio, and Brownian motion parameters. According to the findings, the slippery porous surface may be employed efficiently in chemical and mechanical sectors that deal with a variety of very viscous flows. [ABSTRACT FROM AUTHOR]

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina Al 2 O 3 and Copper Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids. [ABSTRACT FROM AUTHOR]