The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

In this work, a new heuristic computing design is presented with an artificial intelligence approach to exploit the models with feed-forward (FF) Gudermannian neural networks (GNN) accomplished with global search capability of genetic algorithms (GA) combined with local convergence aptitude of active-set method (ASM), i.e., FF-GNN-GAASM to solve the second kind of Lane–Emden nonlinear singular models (LE-NSM). The proposed method based on the computing intelligent Gudermannian kernel is incorporated with the hidden layer configuration of FF-GNN models of differential operatives of the LE-NSM, which are arbitrarily associated with presenting an error-based objective function that is used to optimize by the hybrid heuristics of GAASM. Three LE-NSM-based examples are numerically solved to authenticate the effectiveness, accurateness, and efficiency of the suggested FF-GNN-GAASM. The reliability of the scheme via statistical valuations is verified in order to authenticate the stability, accuracy, and convergence.

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“…In the future, the designed ANN-PSOIPA can be functional to apply to the biological models [58,59] and fluid dynamics models [60][61][62][63].…”

Section: Discussionmentioning

confidence: 99%

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

et al. 2021

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“…Boundary conditions are broken and got initial conditions with the shooting method, 64 here details are given.

\begin{matrix} left \\ f = m_{1}, \\ f' = m_{2}, f ″ = m_{3}, \\ f ‴ = m_{3}^{true'}, g = m_{4}, g' = m_{5}, \\ g ″ = m_{6}, g ‴ = m_{6}^{'}, θ = m_{7}, θ' = m_{8}, \\ θ ″ = m_{8}^{'}, ϕ = m_{9}, ϕ' = m_{10}, \\ ϕ ″ = m_{10}^{'} . \end{matrix}

m_{3}^{'} = \frac{[{(m_{2})}^{2} - (m_{1} + m_{4}) m_{3} + M m_{2} - normalΛ m_{7}]}{[\frac{(1 - {(w e_{1} m_{3})}^{n}) (n - 1) (1 - β *)}{(1 + {(w e_{1} m_{3})}^{n})} + β *]}

m_{8}^{'} = - Pr true(true(m_{1} + m_{4} true) m_{8} + N_{b} m_{8} m_{10} + N_{t} {m_{8}}^{2} - λ m_{7} true) - ε m_{8}^{2} - 3 R_{d} (1 + (θ_{f} - 1...

…”

Section: Methodsmentioning

confidence: 99%

Interpretation of infinite shear rate viscosity and a nonuniform heat sink/source on a 3D radiative cross nanofluid with buoyancy assisting/opposing flow

et al. 2021

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With respect to bionomical concerns and energy security, the performance of refrigeration systems should be enriched, which can be done by improving the characteristics of working liquids. Nanoliquids have attracted interest in the fields of engineering and industry due to their prominent thermophysical characteristics. Researchers have used nanoliquids as working liquids and noticed significant fluctuations in thermal execution. In this study, our prime aim was to study the impact of thermal radiation and varying thermal conductivity on a cross‐nanofuid with the addition of a nonuniform heat sink–source, chemical process, and activation energy (AE) together with effects of assisting and opposing buoyancy. Furthermore, the relationship of zero‐mass flux together with the mechanism of thermophoresis and Brownian motion is considered. Traditionalistic transformations gave the ordinary differential equations (ODEs), which are further dealt with the approach of the Shooting Scheme to change the boundary value problem (BVP) into an initial value problem (IVP) and a numerical comparison is made with the Matlab solver package bvp4c. Bvp4c is based upon a collocation scheme, which yields numeric outcomes for nonlinear ODEs with IVP. Impacts of the involved parameters on mass transfer profile, heat, and momentum fields are shown through graphs. Mass transfer of the cross nanofluid increases with increasing values of AE parameter. Values of physical quantities like drag forces, rate of transport of heat and mass in the case of assisting/opposing flow are tabulated. The drag force magnitudes are greater for enhancing values of M, a, and n, while on the other hand, the opposing tendency is seen for We1 and We2. The magnitude of the rate of heat transport (Nusselt number) falls for greater values of m, σ, δ, and Nt, but in contrast, it accelerates for E, Pr, and n.

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“…In this methodology, the first attempt was taken that both differential equations (18) and (19) are broken down into a system of five concurrent equations of first‐order bearing five strangers. For solving this system through R‐K F45 methodology, 37–42 the utilization of end conditions develops into two foreign initial conditions at η = 0 with the assistance of scheme of shooting. The most vital ingredient of this methodology is to pick the suitable finite delimited value of

η_{\infty}

.…”

Section: Methodsmentioning

confidence: 99%

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

et al. 2021

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Heat transport subject to nonlinear thermal radiation has multiple applications in physics, industry, engineering field, and space technology, such as aerodynamic rockets, solar power technology, large open water reservoirs, and gas‐cooled nuclear reactors. This effort studies the magnetohydrodynamic flow of cross fluid, which is a type of non‐Newtonian, along a heated surface. Furthermore, the transportation of heat in the fluid is induced by thermal radiation. Furthermore, the behavior of opposing/assisting flow and impact of nonuniform heat sink/source is scrutinized. The reserved suitable transformations are carried out to shift the ruling equations into nondimensional class. Through reserved transformations, two nonlinear partial differential equations are altered into corresponding nonlinear ordinary differential equations. Then a scheme of integration referred to as Runge–Kutta–Fehlberg is imposed to get a numerical solution of these. The impact of parameters are mentioned concisely on temperature and velocity profiles in the absence and presence of a magnetic parameter. It is proved that the presence of a magnetic field steps up the velocity and temperature as well.

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The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

Cited by 82 publications

References 64 publications

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

Evolutionary Integrated Heuristic with Gudermannian Neural Networks for Second Kind of Lane–Emden Nonlinear Singular Models

Interpretation of infinite shear rate viscosity and a nonuniform heat sink/source on a 3D radiative cross nanofluid with buoyancy assisting/opposing flow

On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow

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