Influence Of Nonlinear Thermal Radiation Research Articles

Non-linear radiative heat transfer analysis during the flow of Carreau nanofluid due to wedge-geometry: A revised model

In this article, an innovative revised Buongiorno's model is employed to investigate the flow of Carreau nanofluids generated by a wedge-shaped geometry. Moreover, heat and mass transfer characteristics are explored under the influence of non-linear thermal radiation. At first, the developed flow equations are made dimensionless via suitable transformations and then resulting set of nonlinear ordinary differential equations are solved numerically using built-in MATLAB solver bvp4c. It is observed that the solution of current flow problem is highly dependent on the contribution of several physical parameters like Weissenberg number, power-law index, wedge angle parameter, velocity ratio parameter, non-linear radiation parameter, suction parameter, Brownian motion and thermophoresis parameters, Lewis and Prandtl numbers. Detailed analysis for the novel results of dimensionless velocity, temperature and nanoparticles concentration with in the boundary layer region is exhibited graphically. The core physical implication of the computed results is that the thermal boundary layer is thinned by higher radiation parameter. This study reveals that an enhancement in the local Nusselt number is noted with higher temperature ratio parameter. On the other hand, an incremental skin friction ate the wall can be achieved by growing values of power-law index. The obtained data is distinguished with earlier studies and admirable agreement has been noted.

Cross Diffusion Effects on Heat and Mass Transfer Micropolar Fluid Flow Past a Stretching Surface

Through this study, we investigated the influence of nonlinear thermal radiation, Soret and Dufour effects on unsteady mixed convection boundary flow of micropolar fluid past a stretching sheet. The governing equations of the flow, heat and mass transfer are transformed into a system of nonlinear ordinary differential equations by using self-similarity transformation and solved numerically using bvp4c Matlab package. The influence of various non-dimensional governing parameters on velocity, microrotation, temperature and concentration profiles are discussed and presented with the help of the graphs. Also computed the friction factor, heat and mass transfer rates and presented through tables. Result indicates by increasing the radiation parameter, an improvement is observed in both friction factor and mass transfer rates. .

The combined influence of nonlinear thermal radiation and thermal stratification on the dynamics of micropolar fluid along a vertical surface

PurposeThe purpose of this paper is to consider the problem of thermal destratification facing engineers and scientists during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force. This paper provides an insight into the non-linear transfer of thermal radiation within the boundary layer.Design/methodology/approachSimilarity transformation and parameterization of the non-linear partial differential equation are carried out. The approximate analytical solution of the governing equation which models the free convective flow of strong and weak concentration of micro-elements in a micropolar fluid over a vertical surface is presented.FindingsIt is observed that the velocity and temperature distribution are decreasing properties of thermal stratification parameter St. Maximum local skin friction coefficients are ascertained at an epilimnion level (St=0) when the magnitude of thermal radiation is small. Thermal stratification parameter has no significant effect on the temperature distribution in the flow near a free stream.Originality/valueThe relationship between stratification of temperature and the transfer of thermal energy during the problem of thermal destratification facing engineers and scientist during the motion of fluids which consist of rigid and randomly oriented particles suspended in a viscous medium under the influence of Lorentz force is unravelled in this paper.

Non Linear Radiative Flow of a Micropolar Nanofluid through a Vertical Channel with Porous Collapsible Walls

In this paper we discuss the MHD unsteady flow of a micropolar nanofluid through a vertical channel with expanding/contracting walls under the influence of nonlinear thermal radiation considering weak permeability. The PDEs of the governing problem are reduced into a set of ODEs by using self-similar transformations and are then solved numerically. Influence of flow parameters such as wall dilation ratio, permeability Reynolds number, micropolar parameters, thermal radiation parameter, nanofluid parameters etc. on the flow, thermal energy and volume fraction of nanoparticles has been discussed in detail. We trust that the results of this study are not only useful for industrial applications but also present a basic understanding of the physical model.

Influence of nonlinear thermal radiation on rotating flow of Casson nanofluid

Abstract The heat and mass transfer of rotating Casson nanofluid flow is incorporated in the present study. Influence of magnetic field, nonlinear thermal radiation, viscous dissipation and Joule heating effects are taken into the account. A set of nonlinear ordinary differential equations are obtained from the governing partial differential equations with the aid of suitable similarity transformations. The resultant equations are solved for the numerical solution using Runge-Kutta-Fehlberg fourth-fifth order method along with shooting technique. The impact of several existing physical parameter on velocity, temperature and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that, velocity component decreases and temperature component increases for rotating parameter.

Dual stratification effects on double-diffusive convective heat and mass transfer of a sheet-driven micropolar fluid flow

The intent of this study is to analyse the influence of nonlinear thermal radiation, thermophoresis, second order slip and magnetic field on the doubly stratified flow of a non-Newtonian micropolar fluid induced by a stretched sheet along with transport of thermal energy and mass species. The radiative heat flux term is modified using the non-linear Rosseland diffusion approximation. The partial differential equations governing the physics of the problem are recast into a set of coupled non-linear ordinary differential equations by using appropriate similarity transformations and later they are solved numerically using RKF-45 algorithm along with shooting technique. Results of the numerical solution are illustrated graphically for several sets of values of the governing parameters. Comparison of our results with the available results in literature for some special cases reveals close agreements. The results indicate that material parameter boosts the velocity and micro-rotation. The temperature ratio parameters that arise due to non-linear thermal radiation are seen to have opposite effect on temperature. It is seen that for strong thermal stratification reverse flow takes place accompanied by an undershoot in temperature. Excessive mass stratification and weaker molecular diffusivity resulted in a significant undershoot of species concentration.

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.

Flow of a radioactive Casson fluid through a deformable asymmetric porous channel

PurposeThe purpose of this study is to investigate numerically the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with deformable porous walls.Design/methodology/approachTwo numerical schemes, namely, Galerkin’s method (GM) and Runge–Kutta–Fehlberg (RKF) method have been used to obtain solutions after reducing the governing equations to a system of nonlinear ordinary differential equations.FindingsHeat transfer rate falls at the upper wall owing to the decreasing values of the permeability parameter. However, at the lower wall, the same rate rises. Increment in θw increases the rate of heat transfer at both walls. Nusselt number also increases with the increasing values of Rd. Rd also uplifts the temperature distribution, except for the case where it falls near the lower wall owing to the contraction coupled with injection.Originality/valueIt is confirmed that the presented work is original.

Effects of Variable Thermal Conductivity and Non-linear Thermal Radiation Past an Eyring Powell Nanofluid Flow with Chemical Reaction**Supported by the World Class 300 Project (No. S2367878) of the SMBA (Korea)

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.

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.

Influence of Nonlinear Thermal Radiation and Magnetic Field on Three-Dimensional Flow of a Maxwell Nanofluid

Influence of Nonlinear Thermal Radiation and Magnetic Field on Three-Dimensional Flow of a Maxwell Nanofluid

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.

Influence of non-linear thermal radiation on 2D unsteady flow of a Williamson fluid with heat source/sink

Abstract The present article reports a new mathematical formulation for a time dependent flow of a non-Newtonian Williamson fluid model by taking into account the impacts of infinite shear rate viscosity. By incorporating the constitutive relation of Williamson fluid model the basic conservation equations are obtained for two dimensional boundary layer flow. In addition, the heat transfer characteristics for flow filed over a stretching surface has been explored within the sight of thermal radiation and heat sink or source. The Rosseland approximation is being employed for non-linear thermal radiation impacts in the presence of convective heat transfer mode. The current work aims at revealing the solution of equations describing the flow of Williamson fluid by mean of employing the dimensionless approach. Therefore, the leading nonlinear momentum and energy equations are rendered into a set of simultaneously ordinary differential equations via non-dimensional variables with associated physical boundary conditions. Numerical treatment of these reduced conservation equations has been conducted by utilizing the Runge-Kutta Fehlberg integration scheme. We have examined the influence of various physical variables, like, the unsteadiness parameter, Weissenberg number, viscosity ratio parameter, Biot number, radiation parameter, temperature ratio parameter, Prandtl number and heat source/sink parameter on momentum and thermal boundary layers, which is illustrated by means of graphs and tables. The results suggest that the impact of larger viscosity ratio parameter lead to higher fluid velocity while the converse is true for the temperature field. It is noted that the greater unsteadiness parameter results in a significant enhancement in the friction factor. In addition, an increase in thermal radiation as well as temperature ratio parameters improves the heat transfer performance in fluid flow. The work of previous researchers is correlated with the findings of this paper in some special cases in the absence of Weissenberg number and viscosity ratio parameter for different values of unsteadiness parameter. A reasonably accurate predictions are achieved in this comparison.

MHD flow and nonlinear radiative heat transfer of Sisko nanofluid over a nonlinear stretching sheet

Abstract The problem of heat and mass transfer of Siskonanofluid flow over a nonlinear stretching sheet under the influence of nonlinear thermal radiation and chemical reaction is considered. suitable set of similarity transformations are implemented to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. An efficient Runge–Kutta–Fehlberg fourth–fifth order method along with shooting technique is employed to solve the reduced equations. The influence of several emerging physical parameters on velocity, temperature and concentration profiles for both linear and nonlinear stretching sheet in the presence of linear and nonlinear thermal radiation has been studied and analyzed through plotted graphs and tables in detail. It is found that the Nusselt and Sherwood number are high in case of nonlinear stretching sheet than linear. Further, it is observed that the nonlinear thermal radiation has more influence on temperature profiles than linear.

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.

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.

Influence of nonlinear thermal radiation on the viscous flow through a deformable asymmetric porous channel: A numerical study

A numerical investigation has been made to study the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with deformable porous walls. Two numerical schemes, namely, Galerkin's method [GM] and Runge-Kutta-Fehlberg [RKF] method have been employed to obtain the solutions after reducing the governing equations to a system of nonlinear ordinary differential equations. A good agreement has been found in both the solutions. Flow behavior under the influence of arising parameters has been discussed in details with the help of suitable graphs. It is seen that the thermal radiation increases not only the rate of heat transfer at the wall but it also affects the temperature profile quite significantly. The last section summarizes the observations and conclusions made after the study.

Influence of nonlinear thermal radiation and variable viscosity on hydromagnetic heat and mass transfer in a thin liquid film over an unsteady stretching surface

This paper describes the influence of nonlinear thermal radiation on magnetohydrodynamic heat and mass transfer in a thin liquid film over a permeable unsteady stretching surface with temperature-dependent viscosity with convective boundary condition in the presence of heat source/sink and chemical reaction. The momentum, energy and mass-diffusion equations are highly non-linear. Thus the problem is solved numerically using Runge–Kutta–Fehlberg method with shooting technique. The shooting technique is essential to convert the boundary value problem to an initial value type. The results reveal 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. Further, increase in the value of magnetic parameter results in a decrease in the velocity profile and increase in the temperature and concentration gradient. Also, increase in the thermal radiation parameter decreases the temperature gradient. But there is decrease in the value of the concentration gradient by increasing the value of the Schmidt number.

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.