RETRACTED ARTICLE: Second-order convergence analysis for Hall effect and electromagnetic force on ternary nanofluid flowing via rotating disk

Shahzad, Faisal; Jamshed, Wasim; Din, Sayed M. El; Shamshuddin, Md.; Ibrahim, Rabha W.; Raizah, Zehba; Adnan, Adnan

doi:10.1038/s41598-022-23561-7

Cited by 38 publications

(10 citation statements)

References 73 publications

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“…The system of equations, that is, conservation laws are used to model the rotational flow problem, and the governing partial differential equations under steady‐state conditions are as follows 22,30,43 :

\frac{\partial u}{\partial r} goodbreak+ \frac{u}{r} goodbreak+ \frac{\partial w}{\partial z} goodbreak= 0,

u \frac{\partial u}{\partial r} goodbreak+ w \frac{\partial u}{\partial z} goodbreak- \frac{v^{2}}{r^{2}} goodbreak= goodbreak- \frac{\partial p}{\partial r} goodbreak+ \frac{μ_{italichnf}}{ρ_{italichnf}} ((), \frac{\partial^{2} u}{\partial r^{2}} goodbreak+ \frac{1}{r} \frac{\partial u}{\partial r} goodbreak- \frac{u^{2}}{r^{2}} \frac{\partial^{2} u}{\partial z^{2}}) goodbreak+ \frac{{((), ρβ)}_{italichnf}}{ρ_{italichnf}} g ((), T goodbreak- T_{\infty}) goodbreak- \frac{σ_{italichnf}}{ρ_{italichnf}} B_{0}^{2} u,

u \frac{\partial v}{\partial r} goodbreak+ w \frac{\partial v}{\partial z} goodbreak- \frac{uv}{r} goodbreak= \frac{μ_{italichnf}}{ρ_{italichnf}} ((), \frac{\partial^{2} v}{\partial r^{2}} goodbreak+ \frac{1}{r} \frac{\partial v}{\partial r} goodbreak- \frac{v}{r^{2}} \frac{\partial^{2} u}{\partial z^{2}}) goodbreak+ \frac{{((), ρβ)}_{italichnf}}{ρ_{italichnf}} g ((), T goodbreak- T_{\infty}) goodbreak- \frac{σ_{italichnf}}{ρ_{italichnf}}

…”

Section: Mathematical Analysismentioning

confidence: 99%

“…The system of equations, that is, conservation laws are used to model the rotational flow problem, and the governing partial differential equations under steadystate conditions are as follows 22,30,43 :…”

Section: Propertiesmentioning

confidence: 99%

“…Sharma et al 27 discussed the Coriolis effect with forced convective heat transfer on steady ferrohydrodynamic flow past a rotating porous disk in viscous dissipation. Some exciting investigations have been carried out for rotating disks in various flow aspects, the results of which can be found in previous studies 28–32 …”

Section: Introductionmentioning

confidence: 99%

“…Some exciting investigations have been carried out for rotating disks in various flow aspects, the results of which can be found in previous studies. [28][29][30][31][32] Mixed convection is the name given to the phenomenon that takes place when a combination of free and forced convection systems coincide with subsidizing to both the fluid flow and heat transfer characteristics of a system. This can take place when free and forced convection systems coincide to subsidize to both the fluid flow and heat transfer characteristics of a system.…”

Section: Introductionmentioning

confidence: 99%

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Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk

Kulkarni¹

2023

Asia-Pacific J Chem Eng

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The primary objective of the present numerical analysis is to investigate the effect of a mixed convection flow around a disk containing hybrid nanofluid as graphene oxide (GO)‐molybdenum disulfide (MoS2) nanoparticles and water (H2O). This study examines the impacts of surface suction/injection, slip effect, magnetohydrodynamic effect, the shape of nanoparticles, and heat transfer characteristics, on a disk is analyzed. This research applies to disk‐shaped structures in aeronautical engineering, geophysics, and nuclear engineering, such as core catchers in nuclear power plant steam turbines, waxy crude oils or food products in centrifugal pumps, turbo‐machinery, and other industrial processes. Nonlinear partial differential equations (PDEs) with subjected surface restrictions represent this study's governing equations. It's a PDE. The Von Karman transformation can simplify PDEs into non‐dimensional ordinary differential equations, which can be solved using the MATLAB bvp5c function. The research findings indicate that the presence of hybrid nanoparticles results in a significant increase in the heat transfer rate compared to that of the nanoliquid. Increasing the strength of the magnetic field slows down the flow of a hybrid nanofluid. The gradient value pronounces impacts with increasing slip factor. The heat transfer rate increases significantly with the increase of sphericity of the nanoparticles.

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\frac{\partial u}{\partial r} goodbreak+ \frac{u}{r} goodbreak+ \frac{\partial w}{\partial z} goodbreak= 0,

u \frac{\partial u}{\partial r} goodbreak+ w \frac{\partial u}{\partial z} goodbreak- \frac{v^{2}}{r^{2}} goodbreak= goodbreak- \frac{\partial p}{\partial r} goodbreak+ \frac{μ_{italichnf}}{ρ_{italichnf}} ((), \frac{\partial^{2} u}{\partial r^{2}} goodbreak+ \frac{1}{r} \frac{\partial u}{\partial r} goodbreak- \frac{u^{2}}{r^{2}} \frac{\partial^{2} u}{\partial z^{2}}) goodbreak+ \frac{{((), ρβ)}_{italichnf}}{ρ_{italichnf}} g ((), T goodbreak- T_{\infty}) goodbreak- \frac{σ_{italichnf}}{ρ_{italichnf}} B_{0}^{2} u,

u \frac{\partial v}{\partial r} goodbreak+ w \frac{\partial v}{\partial z} goodbreak- \frac{uv}{r} goodbreak= \frac{μ_{italichnf}}{ρ_{italichnf}} ((), \frac{\partial^{2} v}{\partial r^{2}} goodbreak+ \frac{1}{r} \frac{\partial v}{\partial r} goodbreak- \frac{v}{r^{2}} \frac{\partial^{2} u}{\partial z^{2}}) goodbreak+ \frac{{((), ρβ)}_{italichnf}}{ρ_{italichnf}} g ((), T goodbreak- T_{\infty}) goodbreak- \frac{σ_{italichnf}}{ρ_{italichnf}}

…”

Section: Mathematical Analysismentioning

confidence: 99%

Section: Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk

Kulkarni¹

2023

Asia-Pacific J Chem Eng

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“…Finally, further research can be considered by incorporating different nanoparticles in the fluid to study their thermal enhancement under a vertical plate for hybrid and ternary hybrid nanofluids. The G-FEM could be a potential utilization for future science and technology challenges [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] .…”

Section: Discussionmentioning

confidence: 99%

Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate

Goud

Reddy

Jamshed

et al. 2022

Sci Rep

Self Cite

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This research aims to establish the MHD radiating convective nanofluid flow properties with the viscous dissipation across an exponentially accelerating vertical plate. As the plate accelerates, its temperature progressively increases. There are two separate types of water-based nanofluids that include copper ($$Cu$$ Cu ) and titanium dioxide ($$Ti{O}_{2}$$ T i O 2 ) nanoparticles, respectively. The most crucial aspect of this investigation is finding a closed-form solution to a nonlinear coupled partial differential equations scheme. Galerkin finite element method (G-FEM) is used to figure out the initial managing equations. Utilizing graphs, the effect of the flow phenomenon's contributing variables as well as the influence of other factors is determined and depicted. In the part dedicated to the findings and discussion, the properties of these emergent parameters are described in more depth. Nonetheless, the thermal radiation and heat sink factors increase the thermal profile. In addition, the greater density of the copper nanoparticles cause the nanoparticle volume fraction to lessen the velocity delineation.

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Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium

Kumar,

Nandkeolyar

2023

Z Angew Math Mech

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The goal of the research presented in this paper is to examine how a magnetic field affects the unsteady flow of an incompressible nanofluid over a spinning disc that is inclined and stretched while the flow is embedded in a non‐Darcy porous medium. Furthermore, the heat transmission mechanism takes into account Joule heating and viscous dissipation. By imposing thermal radiation to enhance the heat transmission system under the effects of convection, the current article becomes more realistic. A set of nonlinear partial differential equations and associated boundary conditions defines the mathematical problem. Using an appropriate similarity transformation, the mathematical model is converted into a set of nonlinear ordinary differential equations with boundary conditions, which are then solved numerically by the Spectral Quasi Linearization Method (SQLM). Graphs and tables for various flow parameters illustrate the complete results for the exploration of dimensionless velocity and temperature. Regression analysis is used to statistically estimate the local Nusselt number and the skin friction coefficients. From the numerical results, it is found that when the magnetic parameter is increased, the flow velocity in the radial and tangential directions decreases due to the Lorentz force. With the variation of the Forchheimer number, the fluid flow in both directions decreases with increasing inertia coefficient. By increasing the magnetic parameter and Eckart number, the temperature of the fluid increases. The performed quadratic regression analysis reveals that the permeability of the medium and the generated Lorentz force are significant for the skin friction coefficient in the radial direction, whereas the stretching parameter and Forchheimer number are significant for the skin friction coefficient in the tangential direction. Thermal radiation and convective heating are found to significantly affect the heat transfer coefficient.

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RETRACTED ARTICLE: Second-order convergence analysis for Hall effect and electromagnetic force on ternary nanofluid flowing via rotating disk

Cited by 38 publications

References 73 publications

Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk

Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk

Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate

Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium

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RETRACTED ARTICLE: Second-order convergence analysis for Hall effect and electromagnetic force on ternary nanofluid flowing via rotating disk

Cited by 38 publications

References 73 publications

Mixed convective magnetized GO‐MoS2/H2O hybrid nanofluid flow about a permeable rotating disk

Mixed convective magnetized GO‐MoS2/H2O hybrid nanofluid flow about a permeable rotating disk

Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate

Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium

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Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk

Mixed convective magnetized GO‐MoS₂/H₂O hybrid nanofluid flow about a permeable rotating disk