Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

Effect of Nonlinear Thermal Radiation on Boundary Layer Flow of Viscous Fluid over Nonlinear Stretching Sheet with Injection/Suction

The present study reveals the effect of nonlinear thermal radiation and magnetic field on a boundary layer flow of a viscous fluid over a nonlinear stretching sheet with suction or an injection. Using suitable similarity transformations, governing partial differential equations were reduced to higher order ordinary differential equations and further these are solved numerically using of Keller-Box method. Effect of flow controlling parameter on velocity, temperature and nanoparticle fluid concentration, local skin friction coefficient, local Nusselt number and local Sherwood numbers are discussed. It is found that the dimensionless velocity decreases and temperature, concentration are increased with the increasing of magnetic parameter. The temperature profile is an increasing function of thermal radiation when it is increasing.

Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel

The main aim of the present work is to investigate the flow and heat transport properties of non-Newtonian Casson-Williamson fluid through an upright microchannel along with entropy generation analysis,and explore the effects of convective boundary conditions,Couette-Poiseuille flow,and nonlinear radiation.The movement of liquid is scrutinized with the Hall effect and exponential heat source.The rheological characteristics of the Casson-Williamson fluid model are also considered.By considering the desirable similarity variables,the equations of motion are reduced to nonlinear ordinary differential equations.The Runge-Kutta-Fehlberg fourth-fifth order method along with the shooting method is adopted to solve these dimensionless expressions.The detailed investigation is pictorially displayed to show the influence of effective parameters on the entropy generation and the Bejan number.One of the major tasks of the exploration is to compare the Casson fluid and the Williamson fluid.The results show that the rate of heat transfer in the Casson fluid is more remarkable than that in the Williamson fluid.

Nonlinear three-dimensional stretched flow of an Oldroyd-B fluid with convective condition, thermal radiation, and mixed convection

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer as- sumptions are taken into account to govern the mathematical model of the flow analy- sis. Some suitable similarity variables are introduced to transform the partial differen- tial equations into ordinary differential systems. fifth-order techniques with the shooting method The Runge-Kutta-Fehlberg fourth- and are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non- linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

MHD Flow and Nonlinear Thermal Radiative Heat Transfer of Dusty Prandtl Fluid over a Stretching Sheet

Boundary layer flows and melting heat transfer of a Prandtl fluid over a stretching surface in the presence of fluid particle suspensions has been investigated.The converted set of boundary layer equations are solved numerically by RKF-45 method.Obtained numerical results for flow and heat transfer characteristics are deliberated for various physical parameters.Furthermore,the skin friction coefficient and Nusselt number are also presented in Tabs.2 and 3.It is found that the heat transfer rates are advanced in occurrence of nonlinear radiation compered to linear radiation.Also,it is noticed that velocity and temperature profile increases by increasing Prandtl parameter.

Buoyancy driven Flow of a Second-Grade Nanofluid flow Taking into Account the Arrhenius Activation Energy and Elastic Deformation:Models and Numerical Results

The buoyancy driven flow of a second-grade nanofluid in the presence of a binary chemical reaction is analyzed in the context of a model based on the balance equations for mass,species concentration,momentum and energy.The elastic properties of the considered fluid are taken into account.The two-dimensional slip flow of such non-Newtonian fluid over a porous flat material which is stretched vertically upwards is considered.The role played by the activation energy is accounted for through an exponent form modified Arrhenius function added to the Buongiorno model for the nanofluid concentration.The effects of thermal radiation are also examined.A similarity transformations is used to turn the problem based on partial differential equations into a system of ordinary differential equations.The resulting system is solved using a fourth order RK and shooting methods.The velocity profile,temperature profile,concentration profile,local skin friction,local Nusselt number and local Sherwood number are reported for several circumstances.The influence of the chemical reaction on the properties of the concentration and momentum boundary layers is critically discussed.

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.

Influence of construction interfaces on dynamic characteristics of roller compacted concrete dams

To study the influence of construction interfaces on dynamic characteristics of roller compacted concrete dams(RCCDs),mechanical properties of construction interfaces are firstly analyzed. Then, the viscous-spring artificial boundary(VSAB) is adopted to simulate the radiation damping of their infinite foundations, and based on the Marc software, a simplified seismic motion input method is presented by the equivalent nodal loads. Finally, based on the practical engineering of a RCC gravity dam, effects of radiation damping and construction interfaces on the dynamic characteristics of dams are investigated in detail. Analysis results show that dynamic response of the RCC gravity dam significantly reduces about 25% when the radiation damping of infinite foundation is considered. Hot interfaces and the normal cold interfaces have little influence on the dynamic response of the RCC gravity dam.However, nonlinear fracture along the cold interfaces at the dam heel will occur under the designed earthquake if the cold interfaces are combined poorly. Therefore, to avoid the fractures along the construction interfaces under the potential super earthquakes,combination quality of the RCC layers should be significantly ensured.

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 distributionθ(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 temperatureΔT=T_(w)−T_(∞).

Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes,radiation effects and chemical reactions.The main aim of this research is to address entropy generation due to magnetic field,nonlinear thermal radiation,viscous dissipation,thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk.The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow,heat and mass transfer,while the second law of thermodynamics is used to analyze the entropy and irreversibility.The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method.The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks.The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks.Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks.The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion.The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant.It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip.The current results present many applications in the lubrication phenomenon,heating processes,cooling of devices,thermal engineering,energy production,extrusion processes etc.

Frequency-doubled vortex beam emitter based on nonlinear Cherenkov radiation

In this work, we propose a new scheme to generate frequency-doubled vortex beams from a radially poled Li Nb O3 micro-ring resonator based on nonlinear Cherenkov radiation. The near-infrared fundamental wave is resonant in the micro-ring, while the second harmonic is emitted from the resonator along the Cherenkov phase-matching direction. The topological charge of the emitted second-harmonic vortex beam is determined by both the azimuthal order of the whispering galley modes and the number of nonlinear grating elements. The field distribution and the conversion efficiency of the emitted vortex beam are investigated.

Effects of Variable Thermal Conductivity and Non-linear Thermal Radiation Past an Eyring Powell Nanofluid Flow with Chemical Reaction

Present analysis discusses the boundary layer flow of Eyring Powell nanofluid past a constantly moving surface under the influence of nonlinear thermal radiation. Heat and mass transfer mechanisms are examined under the physically suitable convective boundary condition. Effects of variable thermal conductivity and chemical reaction are also considered. Series solutions of all involved distributions using Homotopy Analysis method(HAM) are obtained.Impacts of dominating embedded flow parameters are discussed through graphical illustrations. It is observed that thermal radiation parameter shows increasing tendency in relation to temperature profile. However, chemical reaction parameter exhibits decreasing behavior versus concentration distribution.

Significance of activation energy and Wu's slip features in Cross nanofluid with motile microorganisms

The current article investigates the impact of the bioconvection in an unsteady flow of magnetized Cross nanofluid with gyrotactic microorganisms and activation energy over a linearly stretched configuration.The analysis has been performed by utilizing the realistic Wu's slip boundary and zero mass flux conditions.The effects of nonlinear thermal radiation and the activation energy are also addressed.The governing flow equations are deduced to a dimensionless form by considering suitable transformations which are numerically targeted via a shooting algorithm.The physical visualization of each physical parameter governing the flow problem has been displayed graphically for distribution of velocity,temperature,concentration and motile microorganisms.The numerical treatment for the variation of skin friction coefficient,local Nusselt number,local Sherwood number and motile density number is performed in tabular forms.

Falkner-Skan aspects of a radiating(50%ethylene glycol D 50%water)-based hybrid nanofluid when Joule heating as well as Darcy-Forchheimer and Lorentz forces affect significantly

Falkner-Skan aspects are revealed numerically for a non-homogeneous hybrid mixture of 50%ethylene glycol-50%water,silver nanomaterials Ag,and molybdenum disul-fide nanoparticles MoS2 during its motion over a static wedge surface in a DarcyForchheimer porous medium by employing the modified Buongiorno model.The Brownian and thermophoresis mechanisms are included implicitly along with the thermophysical properties of each phase via the mixture theory and some efficient phenomenological laws.The present simulation also accounts for the impacts of nonlinear radiative heat flux,magnetic forces,and Joule heating.Technically,the generalized differential quadrature method and Newton-Raphson technique are applied successfully for solving the resulting nonlinear boundary layer equations.In a limiting case,the obtained findings are validated accurately with the existing literature outcomes.The behaviors of velocity,temperature,and nanoparticles volume fraction are discussed comprehensively against various governing parameters.As crucial results,it is revealed that the temperature is enhanced due to magnetic field,linear porosity,radiative heat flux,Brownian motion,thermophoresis,and Joule heating effects.Also,it is depicted that the hybrid nanoliquids present a higher heat flux rate than the monotype nanoliquids and liquids cases.Moreover,the surface frictional impact is minimized via the linear porosity factor.Furthermore,the surface heat transfer rate receives a prominent improvement due to the radiative heat flux inclusion.

SPLITTING A CONCAVE DOMAIN TO CONVEX SUBDOMAINS

We examine a steady-state heat radiation problem and its finite element approximation in Rd, d = 2, 3. A nonlinear Stefan-Boltzmann boundary condition is considered. Another nonlinearity is due to the fact that the temperature is always greater or equal than 0[K]. We prove two convergence theorems for piecewise linear finite element solutions.