The steady magnetohydrodynamic ternary hybrid nanofluid flow over a slender surface under the effects of activation energy, Hall current, chemical reactions, and a heat source has been reported. A numerical model is developed to increase the rate of energy transfer and boost the efficiency and outcome of heat energy dissemination for a diverse range of biological applications and commercial uses. The rheological properties and thermal conductivity of the base fluids are improved by framing an accurate combination of nanoparticles (NPs). The ternary hybrid nanofluid has been prepared, in the current analysis, by the dispersion of magnesium oxide, titanium dioxide (TiO2), and cobalt ferrite (CoFe2O4) NPs in the base fluid. The physical phenomena have been expressed in the form of a system of nonlinear PDEs, which are degraded to a dimensionless system of ODEs through the similarity replacement and numerically solved by employing the MATLAB software package bvp4c. The graphical and tabular results are estimated for velocity, mass, and energy curves vs distinct physical factors. It has been noticed that the variation in the magnetic effect enhances the energy profile while the increasing number of ternary nanocomposites (MgO, TiO2, and CoFe2O4) in water lowers the energy curve. Furthermore, the effect of both Lewis and Peclet numbers weakens the motile microbe’s profile.

https://aip.scitation.org/doi/pdf/10.1063/5.0144191

Motile micro-organism based trihybrid nanofluid flow with an application of magnetic effect across a slender stretching sheet: Numerical approach

Abstract The flow of a fluid across a revolving disc has several technical and industrial uses. Examples of rotating disc flows include centrifugal pumps, viscometers, rotors, fans, turbines, and spinning discs. An important technology with implications for numerous treatments utilized in numerous sectors is the use of hybrid nanofluids (HNFs) to accelerate current advancements. Through investigation of ternary nanoparticle impacts on heat transfer (HT) and liquid movement, the thermal properties of tri-HNFs were to be ascertained in this study. Hall current, thermal radiation, and heat dissipation have all been studied in relation to the use of flow-describing equations. The ternary HNFs under research are composed of the nanomolecules aluminum oxide (Al 2 O 3 ), copper oxide (CuO), silver (Ag), and water (H 2 O). For a number of significant physical characteristics, the physical situation is represented utilizing the boundary layer investigation, which produces partial differential equations (PDEs). The rheology of the movement is extended and computed in a revolving setting under the assumption that the movement is caused by a rotatingfloppy. Before the solution was found using the finite difference method, complicated generated PDEs were transformed into corresponding ODEs (Keller Box method). A rise in the implicated influencing factors has numerous notable physical impacts that have been seen and recorded. The Keller Box method (KBM) approach is also delivered for simulating the determination of nonlinear system problems faced in developing liquid and supplementary algebraic dynamics domains. The rate of entropy formation rises as the magnetic field parameter and radiation parameter increase. Entropy production rate decreases as the Brinkman number and Hall current parameter become more enriched. The thermal efficiency of ternary HNFs compared to conventional HNFs losses to a low of 4.8% and peaks to 5.2%. 

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Partial differential equations of entropy analysis on ternary hybridity nanofluid flow model via rotating disk with hall current and electromagnetic radiative influences

This article describes a two-dimensional steady laminar boundary layer flow and heat mass transfer caused by a non-Newtonian nanofluid due to a horizontally stretching sheet. The non-dimensional parameters take into consideration and regulate the effects of convective boundary condition, slip velocity, Brownian motion, thermophoresis and viscous dissipation. The thermal radiation, which affects the flow’s thermal conductivity and the nanofluid’s variable viscosity are also taken into consideration. We propose that a hot fluid could exist beneath the stretching sheet’s bottom surface, which could aid in warming the surface via convection. The physical boundary conditions are non-dimensionalized, as are the governing transport set of nonlinear partial differential equations. By using the shooting approach, numerical values for dimensionless velocity, temperature and nanoparticle concentration are achieved. Distributions of velocity, temperature and concentration are plotted against a number of newly important governing factors, and the outcomes are then provided in accordance with those graphs. Additionally, the local skin-friction coefficient, the local Sherwood number and the local Nusselt number are discussed in order to further clarify and thoroughly explain the current problem. In order to validate the numerical results, comparisons are made with previously published data in the literature. There is a really good accord. Additionally, the current work has implications in the nanofluid applications.

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Radiative MHD Nanofluid Flow Due to a Linearly Stretching Sheet with Convective Heating and Viscous Dissipation

This research aims to examine the combined effects of Cattaneo–Christov heat flux and heat generation/absorption on magnetohydrodynamic (MHD) nanoliquid (Fe3O4-Ethylene glycol) across a linearly stretchable bidirectional surface immersed in a permeable media. The characteristics of nanoliquid (viscosity and thermal conductivity) are a function of temperature and nanoparticle volume fraction. The problem is formulated by considering Corcione’s correlation which describes the effective viscosity and thermal conductivity of nanoliquid. The application of Corcione’s correlation on a bidirectional surface with a combination of MHD nanofluid comprising the unique combination of (Fe3O4-Ethylene glycol) makes this idea novel and is being presented for the first time. The implementation of appropriate similarity transformation leads to the transition of coupled momentum and energy equations into dimensionless ordinary differential equations (ODEs). These ODEs are numerically addressed by applying a well-known bvp4c method in MATLAB. The outcome of the arising parameters on the velocity and thermal field of nanoliquid are demonstrated graphically and numerically (drag force coefficient and Nusselt number) depicted through tables. It is observed that the porosity and velocity slip parameters combined with the volume fraction of nanoparticles decay velocity field. It is also comprehended that heat transmission augments by escalating the volume fraction of nanoparticles. A strong correlation is reflected in comparing the findings of the current analysis with the preceding literature. 

Application of Corcione correlation in a nanofluid flow on a bidirectional stretching surface with Cattaneo–Christov heat flux and heat generation/absorption


 This study emphasizes the aspects of heat transfer and transient thermal distribution through a rectangular fin profile when a stretching or shrinking mechanism is mounted on the surface of the fin. Furthermore, the effects of radiation, internal heat generation, and convection are all considered when developing the corresponding fin problem. The simulated time-dependent heat transfer equation is a partial differential equation (PDE) that can be represented by dimensionless arrangement using appropriate non-dimensional terms. The nonlinear dimensionless problem concerning the stretching/shrinking of a fin is numerically solved using the finite difference method (FDM), and the Levenberg-Marquardt method of backpropagation artificial neural network (LMM-BANN) has been used in this investigation. By varying the stretching/shrinking parameters, a set of data for the presented ANN is produced to discuss stretching and shrinking scenarios. The testing, training, and validation procedure of LMM-BANN, as well as correlation for verification of the validity of the proposed approach, establish the approximate solution to various scenarios. The suggested model LMM-BANN is then validated using regression interpretation, mean square error, and histogram explorations. The ANN results and the procured numerical values agree well with the current numerical results.

Artificial Neural Network Modeling for Predicting the Transient Thermal Distribution in a Stretching/Shrinking Longitudinal Fin

Numerical evaluation of Darcy Forchhemier hybrid nanofluid flow under the consequences of activation energy and second-order chemical reaction over a slender stretching sheet


 Stretching flow problems have several real-world applications in engineering, biological, and industrial fields. The real-world applications of the stretching sheet flow problems are continuous cooling of fiber, manufacturing of rubber and plastics sheets, metal-working processes, crystal growth processes, drawing of the filaments through a quiescent fluid, and consideration of the liquid's films and many others. The present problem focuses on the study of heat and mass transmission phenomena of the MHD flow of three-dimensional micropolar liquid over a bi-directional stretching surface. In the current analysis, the heat and mass transport mechanism are demonstrated by incorporating the Cattaneo-Christov heat and mass flux model. The microorganisms are only used to stabilize suspended nanoparticles via bioconvection, which is caused by the combination of magnetic field and a buoyancy force. The current model is demonstrated in the system of higher-order PDEs which are changed into nonlinear ODEs by the exploitation of appropriate similarity variables. For the analytical solution, the resulting nonlinear ODEs are simulated by employing the homotopy analysis scheme. The physical significance of velocities, microrotation, temperature, concentration, and microorganism profiles of the fluid via various embedded parameters are calculated and discussed in a graphical form. The Nusselt number, Sherwood number and microorganism density number are calculated via tables. Some major findings of the current problem are that the Nusselt number is weakened for the boosted estimation of radiation and thermal relaxation time parameter. The bioconvection Lewis and Peclet numbers raised the microorganism density number.

Effects of Soret and Dufour Numbers On the Three-Dimensional MHD Flow of Micropolar Fluid Containing Gyrotactic Microorganisms Over a Bi-Directional Stretching Sheet with Cattaneo-Christov Heat and Mass Flux Model

The Jeffrey fluid model is capable of accurately characterizing the stress relaxation behavior of non-Newtonian fluids, which a normal viscous fluid model is unable to perform. The primary objective of this paper is to provide a comprehensive investigation into the effects of MHD and thermal radiation on the 3D Jeffery fluid flow over a permeable irregular stretching surface. The consequences of the Darcy effect, variable thickness and chemical reaction are also considered. The phenomena have been modeled as a nonlinear system of PDEs. Using similarity substitution, the modeled equations are reduced to a dimensionless system of ODEs. The parametric continuation method (PCM) is used to determine the numerical solution to the obtained sets of nonlinear differential equations. The impact of physical parameters on temperature, velocity and mass profiles are presented through Figures and Tables. It has been noticed that the energy profile magnifies with the increment of porosity term, thermal radiation and heat source term, while diminishing with the flourishing upshot of power index and Deborah number. Furthermore, the porosity term and wall thickness parameter enhance the skin friction. 

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Numerical simulation of 3D Darcy–Forchheimer fluid flow with the energy and mass transfer over an irregular permeable surface

Bio-convection Eyring-Powell nanofluid through a spinning disk with a heated convective stretching sheet

This work presents the neutrosophic Maxwell distribution (NMD) as a novel probability distribution. The proposed model represents a generalized design of Maxwell distribution that provides more analytical flexibility for data, including all imprecise observations or some degree of vagueness within the dataset. Important reliability characteristics and distributional properties of NMD are developed under the notion of neutrosophy. The neutrosophic forms of some commonly used functions in applied statistics such as mean, variance, moment generating function, and shape coefficients are explored. In view of uncertainties involved in the processing data and indeterminacy in the defined parameters, an estimation framework using the maximum likelihood approach is established. Additionally, the quantile function is developed to validate the distributional properties of NMD. The efficiency of the neutrosophic estimate has been studied through a Monte Carlo simulation. Finally, real data on the incubation period of COVID-19 are considered for numerical illustration, and further extensions of the NMD for future research works are discussed.

Fuad S. Alduais

Papers

Numerical evaluation of Darcy Forchhemier hybrid nanofluid flow under the consequences of activation energy and second-order chemical reaction over a slender stretching sheet

Effects of Soret and Dufour Numbers On the Three-Dimensional MHD Flow of Micropolar Fluid Containing Gyrotactic Microorganisms Over a Bi-Directional Stretching Sheet with Cattaneo-Christov Heat and Mass Flux Model

Numerical simulation of 3D Darcy–Forchheimer fluid flow with the energy and mass transfer over an irregular permeable surface

Bio-convection Eyring-Powell nanofluid through a spinning disk with a heated convective stretching sheet

On Neutrosophic Extension of the Maxwell Model: Properties and Applications