Effect Of Nonlinear Thermal Radiation Research Articles

Effect of Nonlinear Thermal Radiation on MHD Boundary Layer Flow and Melting Heat Transfer of Micro-Polar Fluid over a Stretching Surface with Fluid Particles Suspension

A comprehensive numerical study is conducted to investigate effect of nonlinear thermal radiation on MHD boundary layer flow and melting heat transfer of micro polar fluid over a stretching surface with fluid particles suspension. Using suitable transformations, the governing equations of the problem are transformed in to a set of coupled nonlinear ordinary differential equations and then they are solved numerically using the Runge–Kutta–Fehlberg-45 method with the help of shooting technique. Authentication of the current method is proved by having compared with established results with limiting solution. The impact of the various stimulating parameters on the flow and heat transfer is analyzed and deliberated through plotted graphs in detail. We found that the velocity, angular velocity and temperature fields increase with an increase in the melting process of the stretching sheet. Also it is visualize that the shear stress factor is lower for micro polar fluids as compared to Newtonian fluids, which may be beneficial in flow and heat control of polymeric processing.

A computational analysis subject to thermophysical aspects of Sisko fluid flow over a cylindrical surface

The present analysis is devoted to probing the salient features of the mixed convection and non-linear thermal radiation effects on non-Newtonian Sisko fluid flow over a linearly stretching cylindrical surface. Properties of heat transfer are outlined via variable thermal conductivity and convective boundary conditions. The boundary layer approach is implemented to construct the mathematical model in the form of partial differential equations. Then, the requisite PDEs are transmuted into a complex ordinary differential system by invoking appropriate dimensionless variables. Solution of subsequent ODEs is obtained by utilizing the Runge-Kutta algorithm (fifth order) along with the shooting scheme. The graphical illustrations are presented to interpret the features of the involved pertinent flow parameters on concerning profiles. For a better description of the fluid flow, numerical variations in local skin friction coefficient and local Nusselt number are scrutinized in tables. From thorough analysis, it is inferred that the mixed convection parameter and the curvature parameter increase the velocity while temperature shows a different behavior. Additionally, both momentum and thermal distribution of fluid flow decrease with increasing values of the non-linearity index. Furthermore, variable thermal parameter and heat generation/absorption parameter amplify the temperature significantly. The skin friction is an increasing function of all momentum controlling parameters. The local Nusselt number also shows a similar behavior against heat radiation parameter and variable thermal conductivity parameter while it shows a dual nature for the heat generation/absorption parameter. Finally, the obtained results are validated by comparison with the existing literature and hence the correctness of the analysis is proved.

Effect of nonlinear thermal radiation on double-diffusive mixed convection boundary layer flow of viscoelastic nanofluid over a stretching sheet

BackgroundThe present exploration deliberates the effect of nonlinear thermal radiation on double diffusive free convective boundary layer flow of a viscoelastic nanofluid over a stretching sheet. Fluid is assumed to be electrically conducting in the presence of applied magnetic field. In this model, the Brownian motion and thermophoresis are classified as the main mechanisms which are responsible for the enhancement of convection features of the nanofluid. Entire different concept of nonlinear thermal radiation is utilized in the heat transfer process.MethodsAppropriate similarity transformations reduce the nonlinear partial differential system to ordinary differential system which is then solved numerically by using the Runge–Kutta–Fehlberg method with the help of shooting technique. Validation of the current method is proved by having compared with the preexisting results with limiting solution.ResultsThe effect of pertinent parameters on the velocity, temperature, solute concentration and nano particles concentration profiles are depicted graphically with some relevant discussion and tabulated result.ConclusionsIt is found that the effect of nanoparticle volume fraction and nonlinear thermal radiation stabilizes the thermal boundary layer growth. Also it was found that as the Brownian motion parameter increases, the local Nusselt number decreases, while the local friction factor coefficient and local Sherwood number increase.

Effects of Nonlinear Thermal Radiation, Non-Uniform Heat Source/Sink on MHD Stagnation Point Flow of a Casson Fluid Over a Nonlinear Stretching Sheet with Slip Conditions

Effects of Nonlinear Thermal Radiation, Non-Uniform Heat Source/Sink on MHD Stagnation Point Flow of a Casson Fluid Over a Nonlinear Stretching Sheet with Slip Conditions

Nonlinear thermal radiation and cubic autocatalysis chemical reaction effects on the flow of stretched nanofluid under rotational oscillations

Combined effects of nonlinear thermal radiation and cubic autocatalysis chemical reaction on the three dimensional flow of stretched nanofluid along a rotating sheet have been investigated in this paper. The flow field is assumed to be suspended with magnetic iron oxide nanoparticles (IONPs). Hamilton-Crosser model is applied to measure effective thermal conductivity of nanofluid. Rosseland approximation is employed to obtain the nonlinear radiative heat flux. For novelty and practical point of view, influence of fluctuating surface velocity and periodic surface temperature constraints are incorporated into the governing equations which in turn are made dimension free by employing suitable transformations. For numerical solutions, an explicit finite difference scheme has been proposed under the restrictions of derived stability conditions.

Numerical simulation of MHD mixed convection in alumina–water nanofluid filled square porous cavity using KKL model: Effects of non-linear thermal radiation and inclined magnetic field

This study examines the influence of non-linear thermal radiation and inclined magnetic field on mixed convection in a square porous cavity. Here, the cavity is saturated with alumina–water nanofluid. Darcy-Brinkman-Forchheimer-extended model has been adopted to formulate governing differential equations. After transforming equations to dimensionless form, these are solved by utilizing weighted residual Galerkin finite element method. Latest Koo-Kleinstreuer-Lee (KKL) model is employed for the evaluation of effective thermal conductivity and dynamic viscosity of nanofluid. Effect of pertinent parameters in specific ranges such as Richardson number (0.01 ≤ Ri ≤ 100), radiation parameter (0 ≤ Rd ≤ 5), temperature ratio parameter (1.1 ≤ Nr ≤ 1.4), inclined magnetic field parameter (0°≤ γ ≤ 90°), Darcy number (10−6 ≤ Da ≤ 10−3), porosity parameter (0.2 ≤ ϵ ≤ 0.8) and volume fraction of solid particles (0 ≤ ϕ ≤ 0.04) has been studied and presented in the form of streamlines, isotherms and plots. Moreover, kinetic energy and average temperature have also been taken into account for better understanding the flow philosophy. It is found that radiation parameter, temperature ratio parameter, Darcy number and porosity parameter augment heat transfer, kinetic energy and average temperature while inclined magnetic field parameter in selected aforementioned range declines heat transfer due to hot bottom wall.

Boundary Layer Flow and Heat Transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet embedded in a porous medium

AbstractAn analysis has been carried out to study the effect of nonlinear thermal radiation on slip flow and heat transfer of fluid particle suspension with nanoparticles over a nonlinear stretching sheet immersed in a porous medium. Water is considered as a base fluid with dust particles along with suspended Aluminum Oxide (Al

A mathematical model of MHD nanofluid flow having gyrotactic microorganisms with thermal radiation and chemical reaction effects

In this article, we have examined three-dimensional unsteady MHD boundary layer flow of viscous nanofluid having gyrotactic microorganisms through a stretching porous cylinder. Simultaneous effects of nonlinear thermal radiation and chemical reaction are taken into account. Moreover, the effects of velocity slip and thermal slip are also considered. The governing flow problem is modelled by means of similarity transformation variables with their relevant boundary conditions. The obtained reduced highly nonlinear coupled ordinary differential equations are solved numerically by means of nonlinear shooting technique. The effects of all the governing parameters are discussed for velocity profile, temperature profile, nanoparticle concentration profile and motile microorganisms' density function presented with the help of tables and graphs. The numerical comparison is also presented with the existing published results as a special case of our study. It is found that velocity of the fluid diminishes for large values of magnetic parameter and porosity parameter. Radiation effects show an increment in the temperature profile, whereas thermal slip parameter shows converse effect. Furthermore, it is also observed that chemical reaction parameter significantly enhances the nanoparticle concentration profile. The present study is also applicable in bio-nano-polymer process and in different industrial process.

Free Convective Nonaligned Non-Newtonian Flow with Non-linear Thermal Radiation

The present study explores the free convective oblique Casson fluid over a stretching surface with non-linear thermal radiation effects. The governing physical problem is modelled and transformed into a set of coupled non-linear ordinary differential equations by suitable similarity transformation, which are solved numerically with the help of shooting method keeping the convergence control of 10−5 in computations. Influence of pertinent physical parameters on normal, tangential velocity profiles and temperature are expressed through graphs. Physical quantities of interest such as skin friction coefficients and local heat flux are investigated numerically.

Mathematical modelling of nonlinear thermal radiation effects on EMHD peristaltic pumping of viscoelastic dusty fluid through a porous medium duct

Biologically-inspired propulsion systems are currently receiving significant interest in the aerospace sector. Since many spacecraft propulsion systems operate at high temperatures, thermal radiation is important as a mode of heat transfer. Motivated by these developments, in the present article, the influence of nonlinear thermal radiation (via the Rosseland diffusion flux model) has been studied on the laminar, incompressible, dissipative EMHD (Electro-magneto-hydrodynamic) peristaltic propulsive flow of a non-Newtonian (Jefferys viscoelastic) dusty fluid containing solid particles through a porous planar channel. The fluid is electrically-conducting and a constant static magnetic field is applied transverse to the flow direction (channel walls). Slip effects are also included. Magnetic induction effects are neglected. The mathematical formulation is based on continuity, momentum and energy equations with appropriate boundary conditions, which are simplified by neglecting the inertial forces and taking the long wavelength and lubrication approximations. The boundary value problem is then rendered non-dimensional with appropriate variables and the resulting system of reduced ordinary differential equations is solved analytically. The impact of various emerging parameters dictating the non-Newtonian propulsive flow i.e. Prandtl number, radiation parameter, Hartmann number, permeability parameter, Eckert number, particle volume fraction, electric field and slip parameter are depicted graphically. Increasing particle volume fraction is observed to suppress temperature magnitudes. Furthermore the computations demonstrate that an increase in particle volume fraction reduces the pumping rate in retrograde pumping region whereas it causes the opposite effect in the co-pumping region. The trapping mechanism is also visualized with the aid of streamline contour plots. Increasing thermal radiation elevates temperatures. Increasing Hartmann (magnetic body force) number decreases the size of the trapping bolus whereas the quantity of the does not effected. Conversely increasing particle volume fraction reduces the magnitude of the trapping bolus whereas the number of trapped bolus remains constant.

Combined Effects of Nonlinear Thermal Radiation and Internal Heat Generation/Absorption on Heat and Mass Transfer in a Thin Liquid Film on a Permeable Unsteady Stretching Surface with Convective Boundary Condition

An analysis has been carried out to study the combined effects of nonlinear thermal radiation and internal heat source/sink on heat and mass transfer in a thin liquid film over a permeable unsteady stretching sheet with suction/injection in the presence of chemical reaction. Since the momentum, energy and mass diffusion equations are highly non-linear, the problem is solved numerically. The governing equations are first reduced to a set of ordinary differential equations by using the similarity transformations and then the resulting nonlinear ordinary differential equations are solved using Runge–Kutta–Fehlberg method with shooting technique. The effects of various physical parameters on heat and mass transfer in a thin liquid film are presented graphically and in tabular forms. Numerical results are compared with the published results for some limiting cases. It is found that increase in the unsteadiness parameter leads to increase in the velocity distribution, temperature gradient and concentration gradient due to reduction in the thin film thickness. Also, increase in the thermal radiation parameter decreases the temperature gradient whereas reverse effect is seen on the concentration gradient by increasing the values of the Schmidt number.

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.

MHD Mixed Convection Flow of Burgers’ Fluid in a Thermally Stratified Medium

AbstractThis attempt addresses the effects of nonlinear thermal radiation and magnetohydrodynamics (MHD) in mixed convection flow of Burgers’ fluid over a stretching sheet embedded in a thermally stratified medium. A transformation method has been employed to reduce the nonlinear partial differential equation (PDE) into the nonlinear ordinary differential equation (ODE). The resulting nonlinear coupled ordinary differential equations are solved for the series solutions. Convergence of derived series solutions is explicitly explored. Physical interpretation of different parameters through graphs and numerical values of local Nusselt number is discussed.

A finite element investigation of the flow of a Newtonian fluid in dilating and squeezing porous channel under the influence of nonlinear thermal radiation

The influence of nonlinear thermal radiation on the flow of a viscous fluid between two infinite parallel plates is investigated. The lower plate is solid, fixed and heated, while the upper is porous and capable of moving toward or away from the lower plate. The effects of nonlinear thermal radiation are incorporated in the energy equation by using Rosseland approximation. The similarity transformations have been used to obtain a system of ordinary differential equations. A finite element algorithm, known as Galerkin method, has been employed to obtain the solution of the resulting system of differential equations. It is observed that the radiation parameter Rd increases the temperature of the fluid in all the cases considered. Same is the case with temperature ratio parameter θ w . The influence of the concerned parameters on the local rate of heat transfer is also displayed with the help of graphs.

Mixed convection two-phase flow of Maxwell fluid under the influence of non-linear thermal radiation, non-uniform heat source/sink and fluid-particle suspension

Abstract 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.

Unsteady three-dimensional flow of Casson–Carreau fluids past a stretching surface

In this study, we investigated the effects of nonlinear thermal radiation and non-uniform heat source/sink in unsteady three-dimensional flow of Carreau and Casson fluids past a stretching surface in the presence of homogeneous–heterogeneous reactions. The transformed governing equations are solved numerically using Runge–Kutta based shooting technique. We obtained good accuracy of the present results by comparing with the already published literature. The influence of dimensionless governing parameters on velocity, temperature and concentration profiles along with the friction factors, local Nusselt and Sherwood numbers is discussed and presented graphically. We presented dual solutions for flow, heat and mass transfer in Carreau and Casson fluids. It is found that the heat and mass transfer rate in Casson fluid is significantly high while compared with the Carreau fluid.

Opposing and Assisting Flow Characteristics of Radiative Casson Fluid due to Cone in the Presence of Induced Magnetic Field

In this study, we investigated the induced magnetic field and nonlinear thermal radiation effects on Casson fluid flow over a cone in the presence of chemical reaction. The coupled non-linear transformed governing equations are solved numerically using Runge-Kutta based shooting technique. We obtain good accuracy of the new results by comparing with the published results. In this study we presented dual solutions for opposing and assisting flows over a cone. The influence of dimensionless parameters on velocity, temperature and concentration profiles along with the friction factor coefficient, local Nusselt and Sherwood numbers are discussed with the help of graphs and tables. It is observed that the effect of induced magnetic field is highly significant while controlling the flow field.

Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation

This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.

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.

Numerical simulation for nonlinear radiative flow by convective cylinder

Present study explores the effect of nonlinear thermal radiation and magnetic field in boundary layer flow of viscous fluid due to nonlinear stretching cylinder. An incompressible fluid occupies the porous medium. Nonlinear differential systems are obtained after invoking appropriate transformations. The problems in hand are solved numerically. Effects of flow controlling parameters on velocity, temperature, local skin friction coefficient and local Nusselt numbers are discussed. It is found that the dimensionless velocity decreases and temperature increases when magnetic parameter is enhanced. Temperature profile is also increasing function of thermal radiation.