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In this paper, single-phase homogeneous nanofluid model is proposed to investigate the natural convection of magneto-hydrodynamic (MHD) flow of Newtonian Cu–H2O nanoliquid in a baffled U-shaped enclosure. The Brinkman model and Wasp model are considered to measure the effective dynamic viscosity and effective thermal conductivity of the nanoliquid correspondingly. Nanoliquid's effective properties such as specific heat, density and thermal expansion coefficient are modeled using mixture theory. The complicated PDS (partial differential system) is treated for numeric solutions via the Galerkin finite element method. The pertinent parameters Hartmann number (1 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106) and nanoparticles volume fraction (0% ≤ ϕ ≤ 4%) are taken for the parametric analysis, and it is conducted via streamlines and isotherms. Excellent agreement between numerical results and open literature. It is ascertained that heat transfer rate enhances with Rayleigh number Ra and volume fraction ϕ, however it is diminished for larger Hartmann number Ha.

The characteristics of Stefan blowing effects in a magneto-hydrodynamic flow of a Casson fluid past a stretching sheet are investigated. The effects of radiation, heat source/sink, Newtonian heating, Arrhenius activation energy and binary chemical reaction are considered for heat and mass transfer analysis. The homotopy analysis method (HAM) was utilised to solve the transformed non-dimensionalized equations analytically. The impact of various physical parameters affecting the flow are investigated. Further, the relationship of various parameters on the skin friction and rate of heat and mass transfer was explored using correlation and probable error. A sensitivity analysis was carried out based on the Response Surface Methodology to analyse the effect of Stefan blowing parameter, magnetic parameter and stretching/shrinking parameter on the reduced Nusselt number and reduced Sherwood number. A constant positive sensitivity for the reduced Nusselt number towards the Stefan blowing parameter for all levels of magnetic parameter and stretching/shrinking parameter was found. Further, the reduced Sherwood number indicated a negative sensitivity towards the Stefan blowing parameter.

A detailed investigation of two-dimensional mixed convection flow of non-Newtonian fluid due to convectively heated stretching sheet in the presence of dust particles is conducted. The influence of viscous dissipation, nonlinear thermal radiation and non-uniform heat source/sink is considered in the heat transport equation. To simulate the nonlinear thermal radiation effect, the Rosseland approximation has been used. The governing equations are transformed into a set of self-similar nonlinear ordinary differential equations by means of suitable similarity transformations, which are then solved numerically by using Shooting method. The influence of pertinent parameters on the velocity and temperature distributions of both fluid and particle phases inside the boundary layer is observed and discussed in detail. Further, the features of skin friction coefficient and Nusselt number for different values of the governing parameters are also analysed and discussed. Moreover, the numerical results of present study and those existing ones are tabulated for some limiting case. Keywords: Upper-convected Maxwell fluid, Boundary layer flow, Non-uniform heat source/sink, Convective boundary condition, Dusty fluid, Numerical solution

The combined effects of nonlinear thermal convection and radiation in 3D boundary layer flow of non-Newtonian nanofluid are scrutinized numerically. The flow is induced by the stretching of a flat plate in two lateral directions. The mechanism of heat and mass transport under thermophoretic and Brownian motion is elaborated via implementation of the thermal convective condition. The prevailing two-point nonlinear boundary value problem is reduced to a two-point ordinary differential problem by employing suitable similarity transformations. The solutions are computed by the implementation of homotopic scheme. At the end, a comprehensive parametric study has been conducted to analyze the typical trend of the solutions. It is found that the nanoparticle volume fraction and temperature profiles are stronger for the case of solar radiation in comparison with problem without radiation. Keywords: Non-linear convection, Nonlinear density temperature (NDT), Nonlinear thermal radiation, Three dimensional flow, Maxwell fluid, Nanoparticles

Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect. Keywords: Marangoni convection, Exponential space dependent heat source (ESHS), Cross-diffusion, Magnetohydrodynamics, Casson fluid, Joule heating

This paper deals with the thermal Marangoni convection effects in magneto-Casson liquid flow through suspension of dust particles. The transpiration cooling aspect is accounted. The surface tension is assumed to be fluctuating linearly with temperature. The fluid and dust particle’s temperature of the interface is chosen as a quadratic function of interface arc length. The governing problem is modelled by conservation laws of mass, momentum and energy for fluid and dust particle phase. Stretching transformation technique is utilized to form ordinary differential equations from the partial differential equations. Later, the numerical solutions based on Runge-Kutta-Fehlberg method are established. The momentum and heat transport distributions are focused on the outcome of distinct governing parameters. The results of Nusselt number is also presented and discussed. It is established that the heat transfer rate is higher in the case of dusty non-Newtonian fluid than dusty Newtonian fluid. The rate of heat transfer can be enhanced by suspending dust particles in a base liquid. Keywords: Marangoni convection, Dusty fluid, Casson fluid, Two-phase flow, Runge-Kutta-Fehlberg method

The impact of Marangoni convection on dusty Casson fluid boundary layer flow with Joule heating and viscous dissipation aspects is addressed. The surface tension is assumed to vary linearly with temperature. Physical aspects of magnetohydrodynamics and thermal radiation are also accounted. The governing problem is modelled under boundary layer approximations for fluid phase and dust particle phase and then Runge-Kutta-Fehlberg method based numeric solutions are established. The momentum and heat transport mechanisms are focused on the result of distinct governing parameters. The Nusselt number is also calculated. It is established that the rate of heat transfer can be enhanced by suspending dust particles in the base fluid. The temperature field of fluid phase and temperature of dust phase are quite reverse for thermal dust parameter. The radiative heat, viscous dissipation and Joule heating aspects are constructive for thermal fields of fluid and dust phases. The velocity of dusty Casson fluid dominates the velocity of dusty fluid while this trend is opposite in the case of temperature. Moreover qualitative behaviour of fluid phase and dust phase temperature/velocity are similar. Keywords: Marangoni convection, Dusty fluid, Casson fluid, Joule heating, Viscous dissipation, Two-phase flow, Thermal radiation

The exponential space dependent heat source (ESHS) process is utilized to explore the thermal transport characteristics of Marangoni convective flow in a Cu-H2O nanoliquid due to an infinite disk. Flow is driven by linear temperature. Five distinct nanoparticle shapes such as sphere, tetrahedron, column, hexahedron and lamina are accounted. Impacts of Joule heating, radiation and viscous dissipation are also retained. Hamilton-Crosser’s expression is employed to deploy effective thermal conductivity of nanoliquid. Multi degree partial differential equations system is reduced by Kármán transformations and then solved via shooting method. It is figured out that the heat transfer rate is enhanced for stronger Marangoni convection and nanoparticle volume fraction. Also, shape of the nanoparticles significantly affects the flow fields. Keywords: Nanofluid, Magnetohydrodynamics, Marangoni convection, Joule heating, Exponential space dependent heat source, Disk flow

Impacts of Hall current and irregular heat generation/consumption on two-phase flow of dusty-nanofluid are scrutinized. Particulate nanofluid saturates the stretched surface. Heat transfer mechanism is studied via radiative heating and viscous dissipation aspects. The nanoliquid is a carrier fluid and dust (micro-sized fine particles) particles are suspended in it. Governed equations are remodeled in the form of ordinary differential system using stretching transformations. Numeric solutions are developed via Runge-Kutta-Fehlberg scheme. The influence of pertinent parameters on both nanofluid and particle phase flow fields are studied through graphs. The friction factor and Nusselt number are also studied. It is established that the Hall current has a significant impact on thermal flow fields. The irregular heat generation/consumption aspect is constructive for the heating process. AMS Subject Classification (2000): 76T15, 80A20, Keywords: Dusty nanofluid, Irregular heat generation, consumption, Hall current, Mixed convection

The current study compacts with effect of nonlinear convection and radiation on tangent hyperbolic fluid flow of through a convectively heated vertical surface. The converted set of boundary layer equations are solved numerically by Runge-Kutta-Fehlberg method. The effect of various pertinent parameters on flow and heat transfer characteristics are discussed with tabulated numerical values and deliberate figures. Additionally, the skin friction coefficient and Nusselt number are also presented. We noticed that, the skin friction factor and heat transfer rates are higher in presence of nonlinear convection than its absence. Further, velocity profile decreases by increasing power law index but establishes opposite results for skin friction. Keywords: Tangent hyperbolic fluid, Nonlinear convection, Nonlinear thermal radiation, Heat source, Numerical solution

Numerical investigation of three-dimensional flow of an electrically conducting nanofluid over a bidirectional stretching surface is proposed here. The slip flow over a convectively stretching sheet is considered. The flow is caused due to a non-linear stretching surface and Lorenz force. Water and copper nanoparticles are used to form nanoliquid. Suitable transformations are employed to reduce the conservation equations into nonlinear coupled, multidegree ordinary differential equations. Resultant nonlinear two-point boundary value problem is numerically integrated using Runge-Kutta-Fehlberg fourth-fifth order method. Computed results are verified with existing results under limiting cases. The influences of pertinent parameters on different flow fields are evaluated and presented via graphical and tabular form. It is found that the thermal radiation and convective heating at boundary stabilizes the thermal boundary layer growth. Keywords: Nanofluid, Magnetohydrodynamic, Stretching surface, Viscous dissipation, Convective boundary condition

Impact of induced magnetic field over a flat porous plate by utilizing incompressible water-copper nanoliquid is examined analytically. Flow is supposed to be laminar, steady and two-dimensional. The plate is subjected to a regular free stream velocity as well as suction velocity. Flow formulation is developed by considering Maxwell–Garnetts (MG) and Brinkman models of nanoliquid. Impacts of thermal radiation, viscous dissipation, temperature dependent heat source/sink and first order chemical reaction are also retained. The subjected non-linear problems are non-dimensionalized and analytic solutions are presented via series expansion method. The graphs are plotted to analyze the influence of pertinent parameters on flow, magnetism, heat and mass transfer fields as well as friction factor, current density, Nusselt and Sherwood numbers. It is found that friction factor at the plate is more for larger magnetic Prandtl number. Also the rate of heat transfer decayed with increasing nanoparticles volume fraction and the strength of magnetism. Keywords: Induced magnetic field, Nanoliquids, Heat source/sink, Series expansion method, Chemical reaction, Thermal radiation

Melting and exponential space dependent internal heat source effects on magnetohydrodynamic of upper convected Maxwell liquid towards a horizontal flat surface are addressed. The combined effect of Brownian motion and thermophoresis in nanofluid modeling are retained. The Cattaneo-Christov heat flux model is imposed. Impacts of thermal and solutal stratifications are also accounted. A set of similarity variables are utilized to form ordinary differential system from the prevailing partial differential equations. The problem of ordinary differential system is analyzed numerically through Runge-Kutta-Fehlberg based shooting method. Graphical results of pertinent parameters on the velocity, temperature and nanoparticle concentration are studied. Skin friction coefficient, local Nusselt number and Sherwood number are also addressed.

Nonlinear convective flow of magneto-Carreau-Casson liquids past a deformable surface under the aspects of heterogeneous and homogeneous reactions is investigated. The present phenomenon also included the interaction of nonlinear radiation, Ohmic and Joule dissipations. At moderate to high temperature, the nonlinear convection and radiation are significant. The governed nonlinear system is illustrated numerically via Runge-Kutta based shooting scheme in the domain [0,∞). Role of significant parameters on flow fields as well as on the fiction factor, heat and mass transportation rates are determined and discussed in depth. Comparison is done for distinct flow fields of Carreau and Casson fluids. It is evaluated that the velocities of Casson liquid are higher in comparison to Carreau fluid model. However, liquid temperature for Casson fluid model is weaker in comparison to Carreau fluid. Keywords: Carreau fluid, Casson fluid, Nonlinear thermal radiation: Nonlinear convection, Homogeneous–heterogeneous reaction

The problem of conjugate effects of heat and mass transfer over a moving/stationary vertical plate has been studied under the influence of applied magnetic field, thermal radiation, internal heat generation/absorption and first order chemical reaction. The fluid is assumed to be electrically conducting water based Cu-nanofluid. The Tiwari and Das model is used to model the nanofluid, whereas Rosseland approximation is used for thermal radiation effect. Unified closed form solutions are obtained for the governing equations using Laplace transform method. The velocity, temperature and concentration profiles are expressed graphically for different flow pertinent parameters. The physical quantities of engineering interest such as skin friction, Nusselt number and Sherwood number are also computed. The obtained analytical solutions satisfy all imposed initial and boundary conditions and they can be reduced to known previous results in some limiting cases. It is found that, by varying nanoparticle volume fraction, the flow and heat transfer characteristics could be controlled.

A steady two-dimensional hydromagnetic stagnation-point flow of an electrically conducting nanofluid past a stretching surface with induced magnetic field, melting effect and heat generation/absorption has been analyzed numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The nonlinear partial differential equations are transformed into ordinary differential equations using suitable similarity transformations, before being solved numerically. Effect of pertinent parameters on different flow fields are determined and discussed in detail through several plots and a table. Obtained numerical results are compared and found to be in good agreement with previously published results in a limiting sense. Further, in the absence of melting and magnetic field effect, the skin friction co-efficient results are compared with exact solutions, which are reported earlier.