Nonlinear Radiation Effects Research Articles

Nonlinear Radiation and Variable Viscosity Effects on Free Convection of a Power-Law Nanofluid Over a Truncated Cone in Porous Media With Zero Nanoparticles Flux and Internal Heat Generation

Abstract This study used numerical analysis to investigate the effects of nonlinear radiation and variable viscosity on free convection of a power-law nanofluid over a vertical truncated cone in porous media with Rosseland diffusion approximation considering zero nanoparticles flux and internal heat generation. The internal heat generation is of an exponential decaying form and the viscosity of the fluid is assumed to follow Reynolds viscosity model. The surface boundary conditions of vertical truncated cone is maintained at the uniform wall temperature (UWT) and the zero nanoparticle flux (ZNF) to cause the results to be more realistic and useful. The nanofluid model considered the effects of Brownian motion and thermophoresis. The nonsimilar governing equations are obtained by using a suitable coordinate transformation and then solved by Keller box method (KBM). Comparisons with previously published work obtained good agreement. Graphical and tabular presentations of numerical data for the dimensionless temperature profile and the local Nusselt number were presented for main parameters: dimensionless streamwise coordinate, thermophoresis parameter, Lewis number, radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and internal heat generation coefficient. The local Nusselt number increased when the following parameters were increased: radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and dimensionless streamwise coordinate. In contrast, the local Nusselt number decreased when the following parameters were increased: internal heat generation coefficient, thermophoresis parameter, and Lewis number. Besides, the physical aspects of the problem are discussed in details.

Effect of nonlinear radiation on 3D unsteady MHD stagnancy flow of Fe3O4/graphene–water hybrid nanofluid

ABSTRACT Three-dimensional unsteady magnetohydrodynamic stagnancy flow of hybrid nanoliquid, with nonlinear radiation and uneven heat rise/sag, is studied hypothetically. We considered Fe3O4/graphene nanoparticles embedded in water. The physical problem is modelled mathematically and resolved using Runge–Kutta Fourth order with a shooting procedure. Influences of pertinent parameters on the flow and energy transport are noted numerically and graphically. Moreover, the wall friction and the local Nusselt number are computed and a comparative analysis of nano/hybrid nanofluids is performed with the help of streamlines and isotherms. It is found that the drive and energy transport of nano/hybrid nanofluid is highly influenced by the variation in the particle volume fraction as well as unsteadiness factor. Also, the average temperature of nanofluid in the saddle stagnation region is higher than that of hybrid nanofluid.

Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy

The main motive of this work is to study the effects of nonlinear radiation and mixed convection for the Casson nanofluid through the thin needle. Mass transfer is further characterized by activation energy. Temperature-dependent viscosity and a variable magnetic field are assumed for the current problem. The consequences of the physical framework on the velocity, temperature and species including the impact of radiative heat flux are discussed. The partial differential equations of the physical model are achieved using the concept of boundary layer approximation and are remolded into the ordinary differential mathematical statement which is coupled nonlinear, by substituting specific similarity transformations. By making the use of built-in MATLAB bvp4c function, the results are calculated and arranged in the manner of graphs and tables. The effects of different physical parameters of our interest such as the Casson fluid parameter, Brownian motion, Prandtl number, buoyancy ratio parameter, thermal radiation, thermophoresis parameter, Schmidt number and relaxation time are examined for the velocity, concentration and temperature profiles.

Convective heat transport in a heat generating MHD vertical layer saturated by a non-Newtonian nanofluid: a bidirectional study

PurposeIn this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.Design/methodology/approachInfinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.FindingsThe impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (βT, βC), mixed convection parameter (α), Hartmann number (M2), Weissenberg number (We), nonlinear radiation parameter (NR), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.Originality/valueThe velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

Non-similar radiative bioconvection nanofluid flow under oblique magnetic field with entropy generation

Motivated by exploring the near-wall transport phenomena involved in bioconvection fuel cells combined with electrically conducting nanofluids, in the present article, a detailed analytical treatment using homotopy analysis method (HAM) is presented of non-similar bioconvection flow of a nanofluid under the influence of magnetic field (Lorentz force) and gyrotactic microorganisms. The flow is induced by a stretching sheet under the action of an oblique magnetic field. In addition, nonlinear radiation effects are considered which are representative of solar flux in green fuel cells. A second thermodynamic law analysis has also been carried out for the present study to examine entropy generation (irreversibility) minimization. The influence of magnetic parameter, radiation parameter and bioconvection Rayleigh number on skin friction coefficient, Nusselt number, micro-organism flux and entropy generation number (EGN) is visualized graphically with detailed interpretation. Validation of the HAM solutions with published results is also included for the non-magnetic case in the absence of bioconvection and nanofluid effects. The computations show that the flow is decelerated with increasing magnetic body force parameter and bioconvection Rayleigh number whereas it is accelerated with stronger radiation parameter. EGN is boosted with increasing Reynolds number, radiation parameter and Prandtl number whereas it is reduced with increasing inclination of magnetic field.

Nonlinear self-focusing in strongly magnetized pair plasma.

An intense radiation field can modify plasma properties and the corresponding refractive index and lead to nonlinear propagation effects such as self-focusing. We estimate the corresponding effects in pair plasmas for circularly polarized waves, in both unmagnetized and strongly magnetically dominated cases. First, in the unmagnetized pair plasma the ponderomotive force does not lead to charge separation but to density depletion. Second, for astrophysically relevant plasmas of pulsar magnetospheres [and possible loci of fast radio bursts (FRBs)], where the cyclotron frequency ω_{B} dominates over the plasma frequency ω_{p} and the frequency of the electromagnetic wave ω_{B}≫ω_{p},ω, we show that (i) there is virtually no nonlinearity due to changing effective mass in the field of the wave; (ii) the ponderomotive force is F_{p}^{(B)}=-m_{e}c^{2}/4B_{0}^{2}∇E^{2}, which is reduced by a factor (ω/ω_{B})^{2} if compared to the unmagnetized case (B_{0} is the external magnetic field and E is the electric field of the wave); and (iii) for a radiation beam propagating along a constant magnetic field in the pair plasma with density n_{±}, the ponderomotive force leads to the appearance of circular currents that lead to a decrease of the field within the beam by a factor ΔB/B_{0}=2πn_{±}m_{e}c^{2}E^{2}/B_{0}^{4}. Applications to the physics of FRBs are discussed; we conclude that for the parameters of FRBs, the dominant magnetic field completely suppresses nonlinear self-focusing or filamentation.

A shear flow investigation for incompressible second grade nanomaterial: Derivation and analytical solution of model

A theoretical study of entropy generation (EG) has been conducted in flow of second grade nanomaterial in the presence of Darcy Forhheimer porous space. MHD stagnation point flow with nonlinear mixed convection is examined. Joule heating, nonlinear radiation, Brownian diffusion, dissipation and thermophoresis effects are accounted in the modeling of energy expression. Entropy rate is calculated. The chemical reaction is considered for mass transport with activation energy is addressed. The nonlinear flow expressions are analytical tackled for series development via homotopy method. Flow parameters are graphically discussed. Skin friction and Nusselt number are graphically interpreted and discussed. The obtained outcomes addressed that the velocity decreases against magnetic variable. Thermal field and layer thickness growths via radiation and Eckert number. Key observations are listed.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects

BackgroundIn last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls. MethodsBuilt-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem. ResultsImpacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles. ConclusionsHere the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

Non-linear radiation and chemical reaction effects on slip flow of Williamson nanofluid due to a static/moving wedge: a revised model

In the present study, heat and mass transfer characteristics of unsteady, two-dimensional stagnation-point flow of Williamson nanofluid along a static/moving wedge in the presence of velocity slip and chemical reaction effects are investigated. The Rosseland approximation is adopted for thermal radiation effects and Buongiorno model is used for incorporating the effects of Brownian diffusion and thermophoresis. The wall of wedge is heated by the convection current from hotter fluid and revised model is also considered in this study. The governing boundary-layer equations are altered into a coupled non-linear ordinary differential equations using suitable transformations and then tackled numerically employing Runge–Kutta–Fehberg method with shooting technique. The effects of intricate physical parameters on the dimensionless velocity, temperature, nanoparticle concentration profiles as well as skin friction coefficient and local Nusselt number are explored graphically and discussed in detail. Verification of present code is achieved via benchmarking with previously published results, and generally, very excellent agreement is revealed. Our study reveals that the intensifying values of temperature ratio parameter enhances the nanofluid temperature and thermal boundary-layer thickness. The rate of heat transfer is seen to be higher with the growth of Prandtl number and Biot number. Moreover, the nanoparticle concentration is decreased as the Brownian motion and Schmidt number increasing.

Second law analysis of Blasius flow with nonlinear Rosseland thermal radiation in the presence of viscous dissipation

In the present article, we perform the second law analysis of classical Blasius flow accounting the effects of nonlinear radiation and frictional heating. The two-dimensional boundary layer momentum and energy equations are converted to self-similar equations using similarity transformations. The set of resultant ordinary differential equations are solved numerically. The numerical results obtained from solutions of dimensionless momentum and energy equations are used to calculate the entropy generation number and Bejan number. The velocity profile f'(ξ), temperature distribution θ(ξ), entropy production number Ns and Bejan number Be are plotted against the physical flow parameters and are discussed in detail. Further, for the sake of validation of our numerical code, the obtained results are reproduced using Matlab built-in boundary value solver bvp4c resulting in an excellent agreement. It is observed that entropy generation is increasing function of heating parameter, Prandtl number, Eckert number and radiation parameter. Further, it is observed that entropy generation can be minimized by reducing the operating temperature ΔT=Tw−T∞.

Heat and Mass Transfer of MHD Dissipative Casson Nanofluid Flow over a Stretching or Shrinking Sheet with Multiple Slip Boundary Conditions

The present study concerns steady two-dimensional laminar mixed convective boundary layer Casson nanofluid flow along a stretching or shrinking sheet with multiple slip boundary conditions in a non-Darcian porous medium. The effect of viscous dissipation and non-linear radiation are considered. The governing partial differential equations, together with boundary conditions are transformed into a system of dimensionless coupled ordinary differential equations. Galerkin weighted residual method is then employed to solve the transformed coupled ordinary differential equations. The effect of various controlling parameters on dimensionless velocity, temperature, nanoparticle volume fraction, velocity gradient, temperature gradient and nanoparticle volume fraction gradient are presented graphically and discussed. The present approach is validated by comparing the result of this work and those available in the literature, and they are found to be in excellent agreement.

Convective heat transfer during the flow of Williamson nanofluid with thermal radiation and magnetic effects

Recently, several studies have been presented to show that nanofluids are amongst the best tools for the enhancement of heat transfer characteristics. It has been experimentally verified that nanofluids are a new type of enhanced working fluids, engineered with enhanced thermo-physical properties. Therefore, we present a novel study to develop and understand a mathematical model for a non-Newtonian Williamson fluid flow in the presence of nanoparticles. This study aims at describing the thermal characteristics of nanoparticles via Rosseland approximation to illustrate the non-linear radiation effects. Convective heat transfer model alongside Brownian motion are studied for the electrically conducting nanofluids flow. A set of partial differential equations for Williamson nanofluid flow has been derived by basic conservation laws, i.e., momentum, energy and concentration conservations. These equations are initially converted to ordinary differential equations by employing non-dimensional quantities. The numerical simulation of these equations is performed using the Runge-Kutta-Fehlberg scheme. The corresponding important physical parameters have been produced as function of the unsteadiness parameter, Weissenberg number, magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, Biot number, velocity slip parameter and Lewis number. The examination is done to investigate the impact of the above-said parameters on momentum, thermal and concentration boundary layers. It is concluded from our computations that the nanofluids velocity and temperature accelerate when the Brownian motion parameter rises. Results proved that temperature gradient enhances with increase of solid particle concentration, while it decreases with increasing magnetic field. Finally, a comparison of the obtained numerical solution against previous literature is presented which shows satisfactory agreement.

Heat transfer analysis of Casson dusty fluid flow along a vertical wavy cone with radiating surface

A boundary layer analysis is presented to analyze the effect of non-linear surface radiation on Casson-dusty particulate suspension flow past a vertical wavy cone. Stefan-Boltzmann law is employed in the boundary conditions to express the contribution of surface radiative heat flux. Appropriate sets of transformations are used to convert the governing equations into non-dimensional, non-conserved form and then numerical scheme is applied to obtain the solutions. Our numerical results are shown graphically under the variation of important non-dimensional parameters. Comparison is also established with the available literature and it is observed that our results are in good agreement. From this study it is noticed that amplitude of the wavy cone, a, and half-angle of the cone, ϕ, increase the rate of heat transfer. Furthermore, large values of Casson rheological parameter β results in considerable enchantment in fluid velocity but an opposite behavior is noticed on temperature profiles.

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.

Non-linear radiation effects on magnetic/non-magnetic nanoparticles with different base fluids over a flat plate

This work investigates the two-dimensional steady convective boundary layer flow and heat transfer of Newtonian/non-Newtonian base fluids with magnetic/non-magnetic nanoparticles over a flat plate which incorporates non-linear thermal radiation and slip effects. We considered magnetite and aluminium oxide as magnetic and non-magnetic nanoparticles suspending inside the two sorts of base fluids specifically Water and Sodium Alginate. For physical significance we analyzed the behavior on non-Newtonian profiles by employing Casson model individually. The particular intrigue lies in looking the impacts of non-linear thermal radiation on the behavior of the flow. The solution of wide class of boundary value problems are facilitated by the change of the partial differential equations administering the flow utilizing similarity transformations into ordinary differential equations. The ODE’s are numerically handled by applying fourth order Runge-Kutta integration scheme in association with shooting procedure. The novel results for the dimensionless velocity and temperature inside the boundary layer are exhibited graphically for various parameters that describe the flow. A graphical demonstration is given for the skin friction coefficient and the local Nusselt number.

Dual solutions for nanofluid flow past a curved surface with nonlinear radiation, Soret and Dufour effects

Present work explores the numerical study of heat and mass transfer in nanofluid flow past a curve shaped stretchable (linearly/nonlinearly) geometry. The impact of Lorentz force caused by magnetic field, nonlinear radiation due to high temperature near the surface, frictional heating by virtue of viscous dissipation and cross diffusion by virtue of concentration and temperature differences are pondered while formulating the problem. The thermo physical properties of water and silver nanoparticles are used for calculations. Hamilton-Crosser model is considered for effective thermal conductivity of nanofluid. Shooting method and R.K. fourth order algorithm are adopted to solve the nonlinear coupled differential equations of the problem. The concentration, temperature and velocity fields are studied graphically for distinct values of flow parameters. Numerical values also calculated to know the impact of same parameters on mass and heat transfer coefficients. Results depict that mass and heat transfer performance in the flow via nonlinear curved surface is better when compared with the flow over linearly curved surface. As usually Eckert number and temperature ratio parameter boosts the fluid temperature in the present flow situation also.

Nonlinear radiation effect on MHD Carreau nanofluid flow over a radially stretching surface with zero mass flux at the surface

A mathematical model is envisaged to study the axisymmetric steady magnetohydrodynamic (MHD) Carreau nanofluid flow under the influence of nonlinear thermal radiation and chemical reaction past a radially stretched surface. Impact of heat generation/absorption with newly introduced zero mass flux condition of nanoparticles at the sheet is an added feature towards novelty of the problem. Further, for nanofluid the most recently organized model namely Buongiorno’s model is assumed that comprises the effects thermophoresis and Brownian motion. Utilizing suitable self-similar transformations, the set of partial differential equations with high nonlinearity are converted into a dimensionless system of ordinary differential equations. Set of these transmuted equations are numerically solved by MATLAB built-in function bvp4c. Impact of germane parameters on all involved profiles are plotted to examine the heat and mass transfer characteristics. This study reveals that the temperature distribution is an escalating function of the heat generation and nonlinear radiation parameters. Also, it is noted that the incrementing values of chemical reaction parameter lowers the nanoparticles concentration profile. A comparison of the present investigation with already published explorations in limiting case is also added to authenticate the presented results; hence reliable results are being presented.

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

Abstract The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

Heat generation/absorption and nonlinear radiation effects on stagnation point flow of nanofluid along a moving surface

Abstract In this study, heat generation/absorption effects are studied in the presence of nonlinear thermal radiation along a moving slip surface. Uniform magnetic field and convective condition along the stretching surface are adjusted to deal the slip mechanisms in term of Brownian motion and thermophoresis for nanofluid. The mathematical model is constructed in the form of coupled partial differential equations. By introducing the suitable similarity transformation, system of coupled nonlinear ordinary differential equations are obtained. Finite difference approach is implemented to obtain the unknown functions of velocity, temperature, nanoparticle concentration. To deduct the effects at the surface, physical quantities of interest are computed under the effects of controlled physical parameters. Present numerical solutions are validated via numerical comparison with existing published work for limiting cases. Present study indicates that due to increase in both Brownian motion and thermophoresis, the Nusselt number decreases while Sherwood number shows the gradual increase.

Thermal deposition on magnetohydrodynamic nanofluidic transport of viscoplastic fluid with microrotations

Background and objectivesThe prime focus of this investigation is to explore nonlinear radiation effects on MHD micropolar Casson fluid over a stretching surface. Impact of microrotation on flow and heat transfer characteristics has been examined under the influence of thermophoresis and Brownian motion phenomenon. MethodologyThe prevailing nonlinear coupled system of equations is solved numerically by means of shooting algorithm keeping the iterative precision up to six decimal places. Influence of sundry parameters on velocity profile, temperature and concentration profiles are portrayed through graphs and discussed analytically. Physical quantities of practical engineering significance such as skin friction coefficient, local heat and mass flux at the surface are computed and discussed physically. ConclusionThe obtained physical results revealed some significant facts such as increasing magnetic field strength accelerates microrotation and temperature profiles while it decreases local heat and mass flux at the wall. Nusselt and Sherwood numbers can be enhanced by increasing thermal radiation factor for the case of strong concentration. Thermophoretic phenomenon leads to an increase in concentration profile of the fluid.