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Three-dimensional flow of non-Newtonian nanofluid with nonlinear thermal radiation and heat absorption is established numerical analysis. We are taken that, the nonlinear thermal radiation and heat absorption on porous stretching sheet. Moreover, we have to consider the Magnetohydrodynamic and convective conditions within the fluid motion on stretching surface. The similarity variables are implemented to translate the nonlinear PDE into a set of coupled system of ODE which are solved numerically via RKF (“Runge-Kutta-Fehlberg”) 4th order based on shooting procedure. We obtained the dimensionless parameters on velocity, temperature and concentration profiles and as well as skin friction coefficient, Nusselt number and Sherwood numbers are discussed through graphs. In this study, we found interesting results, that is the non-Newtonian fluids is most significant on velocity, temperature, and heat transfer rate is high significant in non-newtonian case when compared with nanofluid case with various statistical values of Pr (“Prandtl number”), θw (“Temperature ratio parameter”) and Nt (“Thermophoresis parameter”), respectively.

A numerical technique for the nonlinear thermal radiation effect on 3D (“Three Dimensional”) nanofluid (NFs) motion through shrinking or stretching surface with convective boundary condition is examined. In this investigation we use the convective and velocity slip conditions. The governing equations were converted into a set of couple non-linear ODE’s by suitable similarity transformations. The converted nonlinear equations are obtained by applying R-K-F (“Range-Kutta-Fehlberg”) procedure along with shooting technique. The physical parameters are explained graphically on velocity, temperature and concentration. Moreover, we found the coefficient of skin friction, rate of heat transfer with various nanofluid parameters. It is very good agreement when compared with previous study.

This work explores the heat transfer flow characteristics of an incompressible non-Newtonian Jeffrey fluid over a stretching/shrinking surface with thermal radiation and heat source. The sheet is linearly stretched in the presence of a transverse magnetic field with convective boundary conditions. Appropriate similarity variables are used to transform the basic governing equations (PDEs) into ODEs. The resulting equations are solved by utilizing MATLAB bvp4c. The impact of distinctive physical parameters and dimensionless numbers on the flow field and heat transfer is analysed graphically. It is noticed that the measure of heat raised with increasing the Biot number and opposite effect with the rise of the suction parameter.

A mathematical model has been established to study the effect of heat source on magnetohydrodynamic 3D chemically reacting couple stress nanofluid flow generated due to the stretching surface. The ...

This work examines the effects of non-linear thermal radiation and Joule heating on MHD three-dimensional visco-elastic nanofluid flow due to a surface stretching in lateral directions. A coupled nonlinear differential system is generated from the boundary layer equations by using self-similarity variables and is then solved numerically by using most powerful shooting technique with Runge Kutta method of fourth order. The computational results for the flow variables are plotted graphically and are discussed in detail for various governing parameters that emerged in the analysis. It is observed that the momentum of the visco elastic nanofluid is better than that of a viscous fluid. Thicker thermal and concentration boundary layers are formed for increasing nonlinear thermal radiation and temperature ratio parameters. Also the results are in very good agreement with the outcomes available in the literature as a particular case. This model may play a significant role in the field of manufacturing and engineering applications.

The present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

The aim of the current article is to demonstrate heat transfer characteristics of Williamson nanofluid flow through a stretching surface with a porous medium in two lateral directions. Heat generation, nonlinear thermal radiation, viscous dissipation, Joule heating, and chemical reaction are also considered in time-independent boundary layer equations of heat and concentration. One more significant boundary condition is the melting condition which is introduced in this study for the purpose of more heat generation and suitable transformations by the satisfied continuity equation are selected, These are used to translate the coupled time-independent partial differential equations into a coupled nonlinear system of ordinary differential equations. The translated equations are computed as numerical solutions by utilizing the Runge–Kutta–Fehlberg (R–K–F) fourth-order algorithm with the help of a shooting procedure in matlab (bvp4) programming. The significance of physical emerging nondimensional parameters is predicted through graphs and discussed numerically in detail on mass of conservation, temperature, and concentration. The numerical values of the coefficient of the skin friction are displayed through a table with large enhanced values of nondimensional parameters and heat transfer rate explained in detail through graphs.

The objective of this numerical analysis is to describe the motion of a magnetohydrodynamic non-Newtonian fluid flow generated by a linear stretching surface with porous medium. The shear stresses defined for Casson fluid model are reduced into the form of nonlinear ODEs with the help of similarity transformations. The translated equations are solved numerically by applying shooting technique along with RKF algorithm. The results are examined for distinct values of physical parameters and are displayed through graphs. It is found that the magnetic field and heat generations are responsible for high heat transfer rate in the fluid flow.

The influence of heat source and radiation on magnetohydrodynamic, chemically reacting non-Newtonian nanofluid flow generated by a moving surface is analysed in this study. This nanofluid mathematical model is defined based on Brownian motion and thermophoresis effects. The similarity variables are adopted to convert the governing flow equations into coupled ODE’s and hence solved by the RKF method with shooting technique. The distribution of different flow parameters on the flow, energy and species concentration is discussed and displayed graphically. The results revile that the drag coefficient and rate of heat transfer of the liquid along x-axis decrease for higher values of stretching parameter. In addition, the suction parameter shows an opposite behaviour on the above-said flow variables. The outcomes appear to be same with those of outstanding publicised results as a special limiting case.

The effects of viscous dissipation and heat source on MHD flow and heat transfer from a warm, electrically conducting fluid to melting surface parallel to a constant free stream are investigated numerically. This model constitutes highly non-linear governing equations which are transformed using similarity variables and are then solved by fourth order Runge–Kutta scheme along with shooting method. The influence of the various interesting parameters on the velocity and temperature fields within the boundary layer is discussed and explained graphically. It is noticed that the melting phenomenon rises the skin friction coefficient and declines the Nusselt number at the solid interface. Keywords: Viscous dissipation, MHD, Boundary layer flow, Heat source, Moving surface

A mathematical model is established to examine the influence of viscous dissipation and joule heating on magnetohydrodynamic (MHD) flow of an incompressible viscoelastic nanofluid over a convectively heated stretching sheet. Brownian motion and thermophoresis effects have been introduced in this nanofluid model. The governing equations are transformed into ODE’s by using suitable similarity conversions and are then solved numerically by the most robust shooting technique. The significance of numerous physical flow constraints is performed for, and distributions through graphs. It is noticed that, the increases for higher values of and reduces for rising values of heat source and Biot numbers. An outstanding contract was found between our numerical results and previously publicised results.

The numerical analysis of 3D magnetohydrodynamic Darcy-Forchheimer nanofluid flow with nonlinear thermal radiation is explored. Utilizing suitable similarity transformations, the governing PDEs are transformed into nonlinear ODEs. The resulting equations are then solved numerically by the most robust shooting technique with RK method of fourth order. The effect of various parameters like radiation, temperature ratio, Forchheimer and porosity parameters on θ(η) and ϕ(η), skin friction coefficient, and rate of heat transfer is discussed graphically. It is observed that the heat transfer rate reduces and skin friction coefficient increases for the rise of Fr and λ.

The present work nonlinear thermal radiation and chemical reaction effect on three-dimensional MHD flow of permeable medium analysed. We are considering introduce the Darcy-Forchheimer law along with axial and transverse velocity. Using suitable transportations the nonlinear partial differential equations are converted into ordinary differential equations. These equations are solved numerically by 4th Runge-Kutta-Fehlberg scheme with shooting procedure. We are getting unique numerical solution for distinct physical variables temperature and concentration fields are depicted. Also the heat transfer and skin friction coefficients drawn through numerical data. We are finding great results of the velocity profiles behaviors opposite trend of porosity and Forchheimer parameters, the profiles of and behavior reverse trend follows other than chemical reaction parameter, both directions of skin friction coefficient and heat transfer rates reduction.

The unsteady magnetohydrodynamic (MHD) mass transfer flow of an incompressible, electrically conducting nanofluid past a porous stretching sheet has been considered. In this study we considered three different types of water based nanofluids viz., copper (Cu), aluminum oxide Al2O3, and titanium dioxide (TiO2). By using appropriate similarity transformations, the governing partial differential equations of momentum and concentration are converted into a set of non-linear ordinary differential equations. The resulting equations are then solved numerically by using shooting method along with R-K fourth order scheme. The effects of diverse flow physical parameters on the flow fields and mass transfer are illustrated graphically. It is found that the influence of unsteady parameter on skin friction coefficient and Sherwood number is opposite.