Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

Thermal and solutal transport by Cattaneo-Christov model for the magnetohydrodynamic Williamson fluid with joule heating and heat source/sink

This article scrutinizes the 2-dimensional and boundary layer flow of magnetohydrodynamic Williamson fluid flowing on a stretchable surface with variable viscosity. The thermal and solutal rates are examined through the Cattaneo-Christov model with Joule heating, heat source/sink, and chemical reaction. The authors are motivated to conduct this study because of its practical and scientific significance in various processes, including polymer processing, textile industries, food industries, solar energy, biomedical science, wind turbine blades, oil spill clean-up, metal rolling, and forging. With the mentioned assumptions, the partial differential equations are achieved by using the basic governing laws, including momentum law, energy law, and concentration law. This non-linear system of equations is transmuted into ordinary differential equations by taking similarity transformations. The main novelty behind the conduction of this work is the numerical technique, namely the 'Adams-Milne (Predictor-Corrector)' method along with the Runge-Kutta technique on Matlab software, which has not previously been studied by any researcher in the literature. The analytical solution of the determined equations is not possible due to their highly non-linear nature; therefore the multistep numerical method namely the 'Adams-Milne (Predictor-Corrector)' method, along with the Runge-Kutta technique is used to determine the numerical results. The outcomes are noted due to numerous parameters for velocity, temperature, and concentration profiles. The explanation of graphical and numerical results is discussed here. The graphical impression of the Williamson parameter reveals that the velocity and temperature curves diminish for higher inputs of this parameter. The movement of fluid shows the declining behavior for the Hartmann number and viscosity parameter. The solutal and thermal findings due to Cattaneo-Christov heat and mass relaxation coefficients mark the reducing behaviour in respective field. The rise in reaction coefficient decreases the mass distribution. The analyses of comparison of results are also presented here.

Comparative Analysis of Darcy–Forchheimer Radiative Flow of a Water-Based Al2O3-Ag/TiO2 Hybrid Nanofluid over a Riga Plate with Heat Sink/Source

The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al2O3 and Ag) and (Al2O3 and TiO2) with a base fluid (H2O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient.

Bidirectional rotating flow of nanofluid over a variable thickened stretching sheet with non-Fourier's heat flux and non-Fick's mass flux theory

The flow of nanofluid over a variable thickened stretching sheet is studied in this article. Non-Fourier's heat flux and non-Fick's mass flux are incorporated for heat and mass flow analysis. Silver (Ag) and Copper (Cu) are considered nanoparticles with water as base fluid. The resulting equations are transformed into the dimensionless form using similarity transformation and solved by RK-4 with the shooting method. The impact of the governing parameters on the dimensionless velocity, temperature, concentration, skin friction coefficient, streamlines, and finally isotherms are incorporated. It is observed that increment in power-law index parameter uplifts the fluid flow, heat, and mass transfer. The increase in the magnitude of skin friction coefficient in (x-direction) with wall thickness parameter is high for nanofluid containing silver nanoparticles as compared to copper nanoparticles.

Theoretical analysis of SWCNT- MWCNT/H2O hybrid flow over an upward/downward moving rotating disk

The flow-through various disk movement has wide range of applications in manufacturing processes like, computer storage equipment’s, rotating machines, electronic and various types of medical equipment’s. Inspired from these applications, here we scrutinised the consequences of homogeneous-heterogeneous reactions and uniform heat source/sink on the three-dimensional (3D) hybrid SWCNT-MWCNT’s flow on time dependent moving upward/downward rotating disk. The renowned innovation of this paper is the application of the hybrid nanofluid made up of SWCNT and MWCNT’s. Heat generation/absorption effect for the disk that does not move up or down creates a dual flow on the disk. Alternatively, the rotation and upright motion of the disk creates a 3D flow on the surface which has not been considered in the open literature. The modelled PDE’s are reduced in to ODE’s by opting suitable similarity variables and boundary constraints. Here, we used RKF-45 method to obtain the numerical approximations by adopting shooting technique. The analysis of rate of heat transfer is done through graphs. Further, change in velocity, thermal and concentration profiles for various non-dimensional parameters are deliberated briefly and illustrated with the help of suitable plots. The results reveal that, the, rise in values of homogeneous and heterogeneous reaction parameters improve the rate of reaction which results in reduction of the distribution rate and diminishes the concentration gradient. An increase in expansion/contraction parameter enhances the velocity and thermal gradients.

Radiative flow of non Newtonian nanofluids within inclined porous enclosures with time fractional derivative

An unsteady convection-radiation interaction flow of power-law non-Newtonian nanofluids using the time-fractional derivative is examined. The flow domain is an enclosure that has a free surface located at the top boundaries. Also, the geometry is filled by aluminum foam as a porous medium and the overall thermal conductivity as well as the heat capacity are approximated using a linear combination of the properties of the fluid and porous phases. Additionally, the dynamic viscosity and thermal conductivity of the mixture are expressed as a function of velocity gradients with a fractional power. Marangoni influences are imposed to the top free surface while the bottom boundaries are partially heated. Steps of the solution methodology are consisting of approximation of the time fractional derivatives using the conformable definition, using the finite differences method to discretize the governing system and implementation the resulting algebraic system. The main outcomes reveled that as the fractional order approaches to one, the maximum values of the stream function, the bulk-averaged temperature and cup-mixing temperature are reduces, regardless values of the time.

A Finite Element Simulation of the Active and Passive Controls of the MHD Effect on an Axisymmetric Nanofluid Flow with Thermo-Diffusion over a Radially Stretched Sheet

The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology.

Variable Viscosity Effects on Unsteady MHD an Axisymmetric Nanofluid Flow over a Stretching Surface with Thermo-Diffusion: FEM Approach

The present study investigated the unsteady magnetohydrodynamic (MHD) nanofluid flow over a radially nonlinear stretching sheet along with the viscosity dependent on temperature, convective boundary condition, thermo-diffusion, and the radiation effects. Moreover, the nanofluid’s viscous effects were considered dependent on temperature and the exponential Reynolds model was considered in this context. It was additionally assumed that a uniform suspension of nanoparticles is present in the base fluid. The Buongiorno model, which involves the thermophoresis and Brownian motion effects, was considered. For the sake of a solution, the variational finite element method was selected with coding in MATLAB and the numerical results were contrasted with the published articles. The influence of various physical parameters on the velocity, temperature, and concentration profiles are discussed by the aid of graphs and tables. It was detected that the nanofuid viscosity parameter declines the fluid flow velocity, while, for the temperature and the concentration profiles, it accomplished the reverse phenomenon.

Thermo-Diffusion and Multi-Slip Effect on an Axisymmetric Casson Flow over a Unsteady Radially Stretching Sheet in the Presence of Chemical Reaction

The objective of this article is to investigate the impacts of thermo-diffusion effect on unsteady axisymmetric Casson flow over a time-dependent radially stretching sheet with a multi-slip parameter and the force of chemical reaction. We employed an established similarity transformation to this non-linear partial differential system to convert it into a system of ordinary differential equations. The numerical results are attained for this system by using KELLER-BOX implicit finite difference scheme. It has great reliability and accuracy even a very short time period for computational simulation. The impacts of influential flow parameters on fluid flow are sketched through graphs and the numerical results are thoroughly argued. The temperature, velocity and wall concentration control parameters are analyzed. (i) It is witnessed that chemical reaction is not favorable to enhance the velocity profile. (ii) Multi-slip parameters vary inversely with velocity profile. (iii) The fluid concentration in its boundary layer decreases with the increase of heavier species, the parameter of the reaction rate and the exponent of power law for fluids having Prandtl number = 10.0, 15.0, 20.0 and 25.0. Moreover, the skin-friction-coefficient factor and Nusselt-number are compared with the published work. A strong numerical solution agreement is being observed.

Keller-Box Analysis of Buongiorno Model with Brownian and Thermophoretic Diffusion for Casson Nanofluid over an Inclined Surface

The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and thermal radiations. Nonlinear ordinary differential equations are obtained from governing nonlinear partial differential equations by using compatible similarity transformations. The quantities associated with engineering aspects, such as skin friction, Sherwood number, and heat exchange along with various impacts of material factors on the momentum, temperature, and concentration, are elucidated and clarified with diagrams. The numerical solution of the present study is obtained via the Keller-box technique and in limiting sense are reduced to the published results for accuracy purpose.

Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.

Computation of Melting Dissipative Magnetohydrodynamic Nanofluid Bioconvection with Second-order Slip and Variable Thermophysical Properties

This paper studies the combined effects of viscous dissipation, first and second-order slip and variable transport properties on phase-change hydromagnetic bio-nanofluid convection flow from a stretching sheet. Nanoscale materials possess a much larger surface to volume ratio than bulk materials, significantly modifying their thermodynamic and thermal properties and substantially lowering the melting point. Gyrotactic non-magnetic micro-organisms are present in the nanofluid. The transport properties are assumed to be dependent on concentration and temperature. Via appropriate similarity variables, the governing equation with boundary conditions are converted to nonlinear ordinary differential equations and are solved using the BVP4C subroutine in the symbolic software MATLAB. The non-dimensional boundary value features a melting (phase change) parameter, temperature-dependent thermal conductive parameter, first as well as second-order slip parameters, mass diffusivity parameter, Schmidt number, microorganism diffusivity parameter, bioconvection Schmidt number, magnetic body force parameter, Brownian motion and thermophoresis parameters. Extensive computations are visualized for the influence of these parameters. The present simulation is of relevance in the fabrication of bio-nanomaterials for bio-inspired fuel cells.