Presence Of Nonlinear Thermal Radiation Research Articles

The Rotating Flow of Magneto Hydrodynamic Carbon Nanotubes over a Stretching Sheet with the Impact of Non-Linear Thermal Radiation and Heat Generation/Absorption

The aim of this research work is to investigate the innovative concept of magnetohydrodynamic (MHD) three-dimensional rotational flow of nanoparticles (single-walled carbon nanotubes and multi-walled carbon nanotubes). This flow occurs in the presence of non-linear thermal radiation along with heat generation or absorption based on the Casson fluid model over a stretching sheet. Three common types of liquids (water, engine oil, and kerosene oil) are proposed as a base liquid for these carbon nanotubes (CNTs). The formulation of the problem is based upon the basic equation of the Casson fluid model to describe the non-Newtonian behavior. By implementing the suitable non-dimensional conditions, the model system of equations is altered to provide an appropriate non-dimensional nature. The extremely productive Homotopy Asymptotic Method (HAM) is developed to solve the model equations for velocity and temperature distributions, and a graphical presentation is provided. The influences of conspicuous physical variables on the velocity and temperature distributions are described and discussed using graphs. Moreover, skin fraction coefficient and heat transfer rate (Nusselt number) are tabulated for several values of relevant variables. For ease of comprehension, physical representations of embedded parameters such as radiation parameter ( R d ) , magnetic parameter ( M ) , rotation parameter ( K ), Prandtl number ( P r ), Biot number ( λ ) , and heat generation or absorption parameter ( Q h ) are plotted and deliberated graphically.

Thermophysical properties of unsteady 3D flow of magneto Carreau fluid in the presence of chemical species: a numerical approach

In this article, we establish a mathematical relation for unsteady 3D flow of a magneto-Carreau liquid over a bidirectional stretched surface. The impact of convective heat transfer for magneto-Carreau liquid is investigated in the presence of non-linear thermal radiation and heat absorption/generation. Additionally, in this analysis, the proposed model of heterogeneous–homogeneous processes with equivalent diffusivities for reactant and autocatalysis is considered. The modeled boundary layer equations are reduced to a system of nonlinear ordinary differential equations using the appropriate transformation. The resulting equations are then solved by utilizing two different techniques, namely the bvp4c function in Matlab and homotopy analysis method (HAM). The numerical data for the velocity, temperature and concentration fields are graphically sketched and characteristics of the relevant parameters are deliberated in detail. Moreover, the velocity gradients and the rate of heat transfer at the stretched surface for different values of the pertaining parameters are given in tabulated form. It is observed that the temperature profile enhance for higher values of magnetic parameter M and heat generation parameter $$(\delta >0)$$ , whereas it decline for augmented values of heat absorption $$(\delta <0)$$ parameter. In addition, the concentration profile decline for increasing values of homogeneous reaction parameter $$k_{1}$$ and unsteadiness parameter S. To see the validity of the numerical computations, we compared these results of the numerical techniques bvp4c with an efficient analytical method, namely the homotopy analysis method (HAM) and perceived an outstanding correlation between these techniques.

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.

Couple Stress Effects on Three Dimensional Flow of Magnetite–Water Based Nanofluid Over an Extended Surface in Presence of Non-linear Thermal Radiation

The present study discloses the three dimensional flow and heat transfer of water-based nanofluid tempted by an extendable surface subject to the effects of couple stress and thermal radiation. Fe $$_{3}$$ O $$_{4}$$ nanoparticles in water-based couple stress nanofluid are considered. The consequence of nonlinear thermal radiation is sought. Using appropriate similarity transformations, governing partial differential equations are reduced to ordinary differential equations and these equations are solved numerically by means of shooting technique with the assistance of Runge–Kutta method. Effects of controlling parameters on velocity, temperature, local skin friction coefficient and local Nusselt number are discussed in detail. It is observed that fluid velocities decrease due to increase in couple stress parameter and also with the rise in nanoparticle volume fraction. Thickness of thermal boundary layer increases with the rise in couple stress parameter.

Slip Flow of Nanofluid Over A Stretching Vertical Cylinder in the Presence of Non-Linear Thermal Radiation and Non-Uniform Heat Source/Sink

An analysis is performed to study axisymmetric mixed convective boundary layer flow of a nanofluid over a vertical stretching circular cylinder in the presence of non-linear radiative heat flux. The effects of non-uniform heat source/sink and slip flow are also taken into consideration. Water as conventional base fluid containing nanoparticles of Copper (Cu) is used. By means of similarity transformations, the governing partial differential equations are reduced into highly non-linear ordinary differential equations and then solved analytically using Homotopy Analysis Method (HAM). A comparison is made with the available results in the literature and our results are in very good agreement with the known results. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that, the thermal boundary layer is thicker for non-linear thermal radiation problem when compared with that of linear thermal radiation. It also found that heat transfer rate at the surface decreases with the increase in both space and time dependent heat source/sink parameters.

Buoyancy effects on the radiative magneto Micropolar nanofluid flow with double stratification, activation energy and binary chemical reaction

A mathematical model has been developed to examine the magneto hydrodynamic micropolar nanofluid flow with buoyancy effects. Flow analysis is carried out in the presence of nonlinear thermal radiation and dual stratification. The impact of binary chemical reaction with Arrhenius activation energy is also considered. Apposite transformations are engaged to transform nonlinear partial differential equations to differential equations with high nonlinearity. Resulting nonlinear system of differential equations is solved by differential solver method in Maple software which uses Runge-Kutta fourth and fifth order technique (RK45). To authenticate the obtained results, a comparison with the preceding article is also made. The evaluations are executed graphically for numerous prominent parameters versus velocity, micro rotation component, temperature, and concentration distributions. Tabulated numerical calculations of Nusselt and Sherwood numbers with respective well-argued discussions are also presented. Our findings illustrate that the angular velocity component declines for opposing buoyancy forces and enhances for aiding buoyancy forces by changing the micropolar parameter. It is also found that concentration profile increases for higher values of chemical reaction parameter, whereas it diminishes for growing values of solutal stratification parameter.

Numerical exploration of the combined effects of non-linear thermal radiation and variable thermo-physical properties on the flow of Casson nanofluid over a wedge

PurposeThe effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue.Design/methodology/approachSelected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique.FindingsThe velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail.Research limitations/implicationsThis study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies.Originality/valueIt is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

Numerically framing the impact of radiation on magnetonanoparticles for 3D Sisko fluid flow

A numerical investigation is carried out to study the three-dimensional Sisko fluid flow in the presence of nonlinear thermal radiation and convective boundary conditions over a bidirectional stretching surface. In addition, the impact of newly suggested model for nanofluid is considered that requires nanoparticles volume fraction at the wall to be passively rather than strongly controlled. The numerical solutions for resulting flow, heat, and mass transfer have been computed utilizing the two different techniques, namely, the bvp4c function in Matlab and shooting method with Runge–Kutta–Fehlberg and Newton–Raphson methods. It is perceived that the temperature profile declines as the power-law index enhances. Furthermore, it is anticipated from the graphs that the concentration profile decays as the Brownian motion parameter rises, while the opposite behavior is observed for the thermophoresis parameter. In addition, these results are more prominent for shear-thinning fluids when compared with shear-thickening fluids. To see the validity of the numerical computations, we compare the results of the shooting technique with the bvp4c and perceived an excellent agreement. The numerical solutions obtained in the limiting cases have shown an admirable agreement with the existing literature

Unsteady radiative stagnation point flow of MHD carreau nanofluid over expanding/contracting cylinder

The unsteady magnetohydrodynamic (MHD) stagnation point flow of Carreau nanofluid over an expanding/contracting cylinder in the presence of nonlinear thermal radiation is investigated numerically in this article. Recently devised model for nanofluid namely Buongiorno’s model involving Brownian motion and thermophoresis is considered in the present problem. Additionally, zero nanoparticle mass flux condition at the boundary is considered. Mathematical problem is developed with the help of momentum, energy and nanoparticle concentration equations using suitable transformation variables. The numerical results for the transformed highly nonlinear ordinary differential equations are presented for both cases of stretching and shrinking cylinder in shear thinning as well as shear thickening fluids. For numerical computations, an effective numerical solver namely bvp4c package is used. Effects of involved controlling parameters on the velocity, temperature and nanoparticle concentration are examined. Numerical computations for the skin friction coefficient and Nusselt number are also executed. It is interesting to note that the temperature and nanoparticle concentration are higher in shrinking cylinder case when compared to stretching cylinder case. Additionally, the rate of heat transfer (Nusselt number) is a decreasing function of the unsteadiness, radiation and thermophoresis parameters in stretching and shrinking cylinder both for shear thickening and shear thinning fluids.

Analysis of boundary layer formed on an upper horizontal surface of a paraboloid of revolution within nanofluid flow in the presence of thermophoresis and Brownian motion of 29 nm CuO

In the industry, the thickness of many surfaces can be described as non-uniform. To a reasonable extent, an upper half surface of a horizontal object with variable thickness can be described as a paraboloid of revolution. In this article, a modified version of a buoyancy-induced model is considered to account for the force which drives the flow of 29nm CuO-water nanofluid along its upper horizontal surface in the presence of nonlinear thermal radiation. The case of unequal diffusion coefficients of reactant A (bulk fluid) and B (high concentration of catalyst at the surface) in the presence of a gyrotactic microorganism is considered. It is assumed that there exist a significant difference between nanoparticle mass density and base fluid density. Governing equation suitable to unravel the thermophoresis which takes place within the boundary layer is presented. Since chemical reactant, B is of higher concentration at the surface more than the concept earlier described as cubic autocatalytic, hence the suitable schemes herein described as isothermal quartic autocatalytic reaction and first order reaction. The dynamic viscosity and thermal conductivity are assumed to vary with volume fraction (ϕ) and suitable models for the case 0≤ϕ≤0.9 are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for a limiting case. Numerical analysis of many emerging parameters is illustrated graphically and discussed.

MHD Boundary Layer Behaviour over a Moving Surface in a Nanofluid under the Influence of Convective Boundary Conditions

The present work provides an analysis of the hydro-magnetic nanofluid boundary layer over a moving surface with variable thickness in the presence of nonlinear thermal radiation and convective boundary conditions. The governing partial differential equations system that describes the problem is converted to a system of ordinary differential equations by the similarity transformation method; such a system is solved numerically. The velocity, temperature, and nanoparticle concentration of the boundary layer are plotted and investigated in details. Moreover, the surface skin friction, rate of heat and mass transfer are deduced and explained in detail.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

Magnetohydrodynamic three-dimensional nonlinear convection flow of Oldroyd-B nanoliquid with heat generation/absorption

Abstract The present article investigates the magnetohydrodynamic (MHD) three-dimensional nonlinear convective flow of an Oldroyd-B nanofluid over a stretching sheet. Heat transfer analysis is reported in the presence of nonlinear thermal radiation and heat generation/absorption. The effects of Brownian motion and thermophoresis are considered in energy and concentration expressions. Meaningful solutions are established for the velocity, temperature and concentration. It is observed that both components of velocity show opposite behavior for mixed convection parameter, ratio of concentration to thermal buoyancy forces and ratio parameter. Local Nusselt and Sherwood numbers are analyzed for the pertinent parameters. Temperature and heat transfer rate are enhanced for thermal radiation and temperature ratio parameters. It is observed that the impact of Brownian motion on the temperature and nanoparticle concentration is quite reverse.

Effect of Temperature Dependent Viscosity on MHD Radiative Nanofluid Flow Caused by Heated/Cooled Cone

In this study, we investigated the temperature dependent viscosity effect on magnetohydrodynamic nanofluid flow caused by a heated/cooled cone in the presence of nonlinear thermal radiation and irregular heat source/sink. The transformed governing equations using similarity variables are solved numerically using Runge-Kutta based shooting technique. We demonstrated solutions for Al2O3-water and TiO2-water nanofluid cases. The effects of various dimensionless parameters on velocity and temperature profiles along with the skin friction coefficient and the local Nusselt number are discussed and presented with the help of graphs and tables. It is found that the viscous variation parameter help to control the velocity as well as the temperature field and regulates the friction factor and heat transfer rate.

Influence of Non-linear Thermal Radiation on MHD Double-Diffusive Convection Heat and Mass Transfer of a Non-Newtonian Fluid in a Porous Medium

The present paper deals with the problem of steady, magnetohydrodynamic laminar double-diffusive convection heat and mass transfer of a micropolar fluid over a vertical permeable semi-infinite plate embedded in a uniform porous medium in the presence of non-linear thermal radiation. In addition, the present model allows the influence of heat generation/absorption and first-order chemical reaction. The governing equations are solved efficiently by Runge–Kutta–Fehlberg method with shooting technique. The effects of thermal buoyancy ratio, Schmidt number, chemical reaction parameter, heat generation/absorption and surface suction/injection on the fluid velocity, microrotation, temperature and solute concentration are analyzed. It is found that increase in the inverse Darcy number results in decrease in the velocity and microrotation distributions whereas reverse effects are seen on the temperature and concentration distributions. Also, it is observed that with increase in the magnetic parameter there is decrease in the velocity and microrotation gradient whereas reverse effects are noticed on the temperature and concentration distributions.

Soret and Dufour Effects in Three-Dimensional Flow of Jeffery Nanofluid in the Presence of Nonlinear Thermal Radiation

Soret and Dufour Effects in Three-Dimensional Flow of Jeffery Nanofluid in the Presence of Nonlinear Thermal Radiation

Comparison between the flow of two non-Newtonian fluids over an upper horizontal surface of paraboloid of revolution: Boundary layer analysis

Boundary layer flow of two non-Newtonian fluids past an upper horizontal surface of a paraboloid of revolution (uhspr) in the presence of nonlinear thermal radiation is investigated. A new concept of parameterization is introduced to achieve comparison between the flows of both fluids (i.e. switch momentum governing equation from Williamson fluid to Casson fluid). In this study, it is assumed that buoyancy and stretching at the wall induce Casson and Williamson fluid flow over this kind of surface which is neither a perfect horizontal/vertical nor inclined/cone. Influence of space dependent internal heat source is accommodated in the energy equation. The case of unequal diffusion coefficients of reactants A and B (high concentration of catalyst on uhspr) is considered. Since chemical reactant B is of higher concentration at the surface more than the concept described as cubic autocatalytic, the suitable schemes are herein described as isothermal quartic autocatalytic reaction and first order reaction. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge-Kutta technique along with shooting method. Comparisons of the effects of some parameters on the flow profiles are illustrated graphically and discussed.

Effect of nonlinear thermal radiation on non-aligned bio-convective stagnation point flow of a magnetic-nanofluid over a stretching sheet

The current study covers the relative study of non-aligned magnetohydrodynamic stagnation point flow of a nanofluid comprising gyrotactic microorganisms across a stretching sheet in the presence of nonlinear thermal radiation and variable viscosity. The governing equations transitioned as nonlinear ordinary differential equations with suited similarity transformations. With the assistance of Runge-Kutta based shooting method, we derived solutions. Results for oblique and free stream flow cases are exhibited through plots for the parameters of concern. In tabular form, heat and mass transfer rate along with the local density of the motile microorganisms are analyzed for some parameters. It is found that local density of the motile microorganisms is highly influenced by the Biot and Peclet numbers. Rising values of the magnetic field parameter, Biot number, thermal radiation parameter and thermophoresis parameter increase the thermal boundary layer. Bioconvection Peclet number and bioconvection Lewis number have tendency to reduce the density of the motile microorganisms. It is also found that thermal and concentration boundary layers become high in free stream flow when compared with the oblique flow.

Suspended Particle Effect on Slip Flow and Melting Heat Transfer of Nanofluid Over a Stretching Sheet Embedded in a Porous Medium in the Presence of Nonlinear Thermal Radiation

Suspended Particle Effect on Slip Flow and Melting Heat Transfer of Nanofluid Over a Stretching Sheet Embedded in a Porous Medium in the Presence of Nonlinear Thermal Radiation

Buoyancy induced model for the flow of 36 nm alumina-water nanofluid along upper horizontal surface of a paraboloid of revolution with variable thermal conductivity and viscosity

The motion of nanofluid (water and 36nm alumina nanoparticles) along upper horizontal surface of a paraboloid of revolution in the presence of nonlinear thermal radiation, Lorentz force and space dependent internal heat source within thin boundary layer is investigated theoretically. It is assumed that buoyancy induces the flow over this kind of surface which is neither a horizontal/vertical nor cone/wedge, hence suitable buoyancy model for this case of fluid flow is presented. The viscosity and thermal conductivity are assumed to vary with volume fraction and suitable models for the case 0%≤ϕ≤0.8% are adopted. The transformed governing equations are solved numerically using Runge-Kutta fourth order along with shooting technique (RK4SM). Good agreement is obtained between the solutions of RK4SM and MATLAB bvp5c for limiting case. The influence of pertinent parameters are illustrated graphically and discussed. It is found that temperature and velocity functions are maximum at higher values of internal space dependent heat source. Local heat transfer rate is maximum at smaller values of internal space dependent heat source.