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A study has been carried out to obtain solutions for heat and mass transfer in a forced magnetohydrodynamic convective flow of an electrically conducting incompressible fluid over a permeable flat plate embedded in a porous medium with thermal convective surface boundary conditions due to thermal radiation, temperature dependent viscosity, and thermal conductivity taking into account the first-order homogeneous chemical reaction. A scaling group of transformations has been applied to the governing equations. The transformed self-similar nonlinear ordinary differential equations, along with the boundary conditions, have been solved numerically using a fourth-order Runge–Kutta method and a Shooting technique. The effect of various relevant parameters on the flow field, temperature, concentration, wall skin friction, heat flux, and wall mass flux has been elucidated through graphs and tables. A comparison with previously published results has been presented.

This work is focused on the examination of the effect of thermal radiation on the heat and mass transfer characteristics of an incompressible electrically conducting fluid squeezed between two parallel plates in the presence of a transverse magnetic field. Using the similarity transformation, the governing system of nonlinear partial differential equations is transformed into similarity equations which are solved numerically using the Nachtsheim and Swigert shooting iteration technique together with the Runge–Kutta sixth-order integration scheme. Numerical results are presented through graphs and tables for pertinent parameters to show interesting aspects of the solution.

An exact solution of the problem of the unsteady free convection flow of a viscous elec- trically conducting incompressible fluid in the presence of thermal radiation and under the influence of uniform magnetic field applied normal to the plate near an infinite vertical plate, which moves at a time dependent velocity, is presented here by the Laplace transform technique. The fluid is also assumed to be gray; emitting absorbing but non scattering medium and the optically thick radiation limit is considered. The solutions of the present problem were obtained in closed forms with arbitrary magnetic field parameter (M), radiation parameter (F), Prandtl number ( r P ), thermal Grashof number ( r G ), etc. Some important applications of physical interest for different type motion of the plate are discussed. Applying numerical values into the expressions of analytical solution, we also discussed the vertical air flows — the usual phenomenon at plumes into the atmosphere.

In this paper, effects of viscous and Joulean dissipations on hydro-magnetic convection flow on an incompressible fluid with temperature dependent viscosity over a stretching surface have been studied numerically using MATLAB 6.1. The results for velocity and temperature distribution, local skin friction coefficient, and surface heat flux coefficients have been investigated and discussed for different values of the parameters encountered in the equations.

In this article, we scrutinized the impact of nonlinear thermal radiation and an externally applied magnetic field over a rotating upward or downward disk on an unsteady 3D hybrid nanofluid flow in the presence of SWCNT(single-walled carbon nanotube)+ F e 3 O 4 (ferrosol ferric oxide) and MWCNT(multi-walled carbon nanotube)+ F e 3 O 4 with water as a base fluid. The foremost partial differential equations (PDEs) with boundary conditions of the flow model are converted into ordinary differential equations (ODEs) by considering suitable transformations and then solved numerically by using RKF-45 by implementing a shooting technique. Fluid flow characteristics are explored for various parameters and presented using graphs and charts. The results show that an increase in the radiation parameter causes an upsurge in the thermal field in the fluid flow of MWCNT+ F e 3 O 4 -water/SWCNT+ F e 3 O 4 -water hybrid nanofluid. The thermal profile and axial velocity profile of MWCNT+ F e 3 O 4 and SWCNT+ F e 3 O 4 with water-based hybrid nanofluid increase as magnetic parameter values rise but radial and azimuthal velocity profiles decrease. Also, the Nusselt number for MWCNT + F e 3 O 4 -water hybrid nanofluid is 0.35% less than SWCNT + F e 3 O 4 -water hybrid nanofluid. [ABSTRACT FROM AUTHOR]

Purpose: Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis. Design/methodology/approach: Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H2O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach. Findings: There is no fund for the research work. Social implications: This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells. Originality/value: This investigation unfolds the hydrothermal changes of radiative water-based Fe3O4-Ag-MgO-H2O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study. [ABSTRACT FROM AUTHOR]

The current article addressed an unsteady motion of nanofluid due to a rotating stretchable disk. Darcy–Forchheimer porous field is taken in this study with adjustable porosity and variable permeability. Also, nonlinear thermally radiative and melting heat mechanisms are considered. Leading equations are changed into dissoluble form by some proper similarity functions and the solutions are attained via the Runge–Kutta method of order 4 in conjunction with the shooting process. The power of main parameters on general profiles, i.e., radial velocity, cross-radial velocity, temperature, concentration, streamline, isotherms, and so forth are obtained through pictures. Also, the nature of engineering coefficients in the lower boundary is calculated through three dimensional plots. It is detected that variable porosity and variable permeability have opposite behavior in every situation. Melting parameter upsurges velocity and reduces temperature of the fluid. [ABSTRACT FROM AUTHOR]

In this paper, the impact of thermal slip and slip velocity on ZrO2 (Zirconia)–water nanofluid flow through a vertically heated permeable stretching sheet surrounded by a porous medium has been deliberated. The concept of thermal radiation is assimilated into the study. Using similarity transformations, the concerned governing flow model is changed into nonlinear ODEs and gets a solution by the R-K method. The consequence of numerous pertinent parameters in the fluid flow arena is deliberated by employing graphical and tabular approaches. The current investigation will be supportive of understanding the thermal features of heat transfer nanofluids. Outcomes of the present effort are compared with that of previously published works and found a commendable level of settlement. Our analysis sightsees that Zirconia–water achieves high temperatures due to thermal radiation. Also, it is found that Zirconia–water nanofluid lessens the heat transfer rate related to their base fluid. [ABSTRACT FROM AUTHOR]

An analysis exploring the influence of second-order slip mechanism on nanofluid flow passing over a permeable stretching surface is investigated. Additionally we have captured the flow features including the presence of realistic thermal and solutal boundary conditions. Applying the similarity transformation procedure leads us to convert the partial differential flow related equations into nonlinear ordinary ones. After that we solved them numerically using the fourth-order Runge-Kutta method in conjunction with the shooting technique. Parametric study has been performed through tables and diagrams to highlight the consequence of velocity, temperature, and concentration profile. Moreover, a statistical attempt is made to illustrate the correlation of physical parameters within the flow system. Key words: stretching flows, nanofluid, second-order slip, statistical correlation, thermal and mass convection. Nous presentons une analyse qui explore l'influence du mecanisme de glissement du second ordre surun nano-fluide s'ecoulant sur une surface permeable en etirement. Nous determinons aussi les caracteristiques de l'ecoulement, incluant la presence d'une limite realiste thermale et solutale. Une transformation de similarite permet de transformer les equations differentielles aux derivees partielles pour l'ecoulement en equations differentielles ordinaires. Ces dernieres sont solutionnees par la methode de Runge-Kutta du 4e ordre, avec l'aide de la methode de tir. Nous presentons une etude parametrique via tables et diagrammes pour souligner l'importance de la vitesse, de la temperature et du profil de concentration. De plus, nous faisons un essai statistique pour illustrer la correlation des parametres physiques dans le systeme en ecoulement. [Traduit par la Redaction] Mots-cles: nano-fluide, glissement du second ordre, ecoulement d'etirement, correlation statistique, convexion thermale et massique., 1. Introduction The term nanofluid, after its first use by Choi [1], continues to catch a keen interest in engineering, science, and technology owing to its diverse applications and gifted [...]

The present exploration talks to a steady and incompressible chemically reacting hybrid-nanofluid rotating flow toward a stretchable sheet in presence of activation energy and magnetic field. We have chosen kerosene oil as base fluid and two nanoparticles specifically Al2O3 and Cu for hybrid-nanofluid and Al2O3 for regular nanofluid. Relative studies of imprint factors between hybrid nanofluid and customary nanofluid have been implemented for our present article. The leading system of PDEs subject to their compatible boundary conditions are renovated into a system of ODEs and then resolved by the Runge–Kutta–Fehlberg quadrature method with shooting practice. The stimulus of ignite flow parameters on the flow precise is carried off accurately through figures, bar diagrams and tables. Our analysis conveys that the primary velocity profiles for both hybrid and regular nanofluid diminish with intensifying values of Hartmann number and rotational parameter, however secondary velocity profile enhances with augmentation of the rotational parameter. Temperature profiles of both category fluids lead to increase with growing values of radiation parameter and Hartmann number, whereas opposite phenomena observe for concentration profiles with improving values of chemical reaction parameter. Again, rate of heat transfer diminishes sharply for leading Hartmann number. [ABSTRACT FROM AUTHOR]

The target of this article is to perceive the effects of the externally applied magnetic force on an unsteady nanofluid flow in the occurrence of carbon nanotubes with water as a base fluid. The flow is caused by a rotating and wavy spinning permeable disk where the disk is continuously moving vertically upward and downward. 3D nanofluid flow is created by a spinning and vertically moving disk. A study of the passive and active mass flux of nanoparticles is presented in this work. The problem is solved by the Runge–Kutta–Fehlberg 45 (RKF 45) method in the mathematical software MAPLE. The outcomes of the present work are compared to the results communicated previously. The physical measures are exemplified pictorially in thermal and concentration fields. 2D contour phenomenon and 3D flow conceptions for some pertinent parameters − 1.5 ≤ β ≤ 1.5 , 0 ≤ M ≤ 1.4 , 0.1 ≤ N b ≤ 0.7 , 0.1 ≤ N t ≤ 0.7 , − 0.3 ≤ S ≤ 1 are also sketched. There is a slight difference in temperature and concentration profiles between MWCNTs and SWCNTs. It is detected that in the presence of active and passive control, the thermal energy profile shows decreasing behaviour by the fluctuating parameter; however, the concentration profile exhibits dual nature under passive control. [ABSTRACT FROM AUTHOR]