Effect Of Nonlinear Thermal Radiation Research Articles

Nonlinear Approximation for Mixed Convection Flow From a Vertical Plate With Exponentially Decaying Internal Heat Generation and Nonlinear Thermal Radiation

Abstract This study considered dynamic features of mixed convection flow over a vertical plate influenced by nonlinear thermal radiation and exponentially decaying internal heat generation. The importance of the nonlinear density variation with temperature (NDT) and convective heating is also analyzed. The governing equations are transformed into ordinary differential equations using the similarity variables and solved in MAPLE 2022 by a Runge–Kutta Ferhlberg fourth-fifth order scheme. The results obtained show that, with an increase in the convection process, the internal heat generation convects more fluid away and consequently reduced the rate of heat flowing back into the plate. For a weak internal heat generation λx=0.5, the plate temperature is less than one (1) and the heat is observed to flow from the plate into the fluid on the surface of the right plate. Furthermore, for weak convection and nonlinear thermal radiation effects, the rate at which the heat flows into the plate increases with the convective heat transfer parameter increase. However, for a strong nonlinear thermal radiation effect, the rate at which the heat flows out of the plate increases. The flow feature is not only governed by the rate of internal heat generation but the generation as well reverses the heat flow from the plate since the temperature of the near the plate surface T is much higher than the environmental temperature Tf.

Significance of binary chemical reaction with activation energy in magneto-bioconvection flow of a Powell Eyring nanofluid past an inclined stretching sheet by considering temperature-dependent viscosity and thermal conductivity

ABSTRACT In this paper, an unsteady magneto-bioconvection flow of Powell Eyring nanofluid over an inclined stretching sheet in the presence of variable viscosity and thermal conductivity with multiple slip effects has been investigated numerically. The binary chemical reaction with activation energy, viscous dissipation and nonlinear thermal radiation effects are included in this study. The fluid viscosity and the thermal conductivity are assumed to be a linear function of temperature. The basic governing equations are solved numerically by the Runge-Kutta Felhberg method after using similarity transformation. The impact of bioconvection and important physical parameters on profiles of velocity and temperature of nanofluid and nanoparticles concentration, the density of motile microorganisms are analyzed graphically. Findings reveal that the velocity profile decreased by increasing the Powell Eyring fluid parameter values, whereas the temperature distribution depicts the opposite trend. The temperature profile increased with an increment of thermal conductivity parameter, whereas the opposite trends are found for Eckert number. The trend of the graph of temperature profile and nanoparticle concentration profile declined with an increment of the temperature slip parameter. Also, the nanoparticle concentration profile and density of microorganism profile decreased with an increment of activation energy parameter and chemical reaction parameter. The scope of the present investigation can be related to the advanced nanomechanical bioconvection energy conversion devices and bio-nanocoolant systems, among other relevant things.

Theoretical analysis of Arrhenius activation energy on 3D MHD nanofluid flow with convective boundary condition

Industry and space technology have significant issues managing heat energy and controlling mass dispersion. The purpose of this study is to develop motion caused by boundary layer thickness sheets that are increasingly being used in various engineering fields (civil engineering, mechanical, aeronautical, maritime processes and constructions). The activation energy is a critical factor in chemical reactions due to the existence of many applications in gas-cooled reactors, nuclear thermal rockets and liquid-fluoride reactors. This study presents the numerical analysis of activation energy on three dimensional (3D) nanofluid (NFs) motion via Stretching Surface (SS) with nonlinear thermal radiation effect. This is in contrast to the conventional slip condition, convective condition applied at surface. The governing basic equations are translated into nonlinear ODEs by suitable similarity transformations. The relevant boundary value problem was explored for a numerical solution for applying the MATLAB based on Runge–Kutta–Fehlberg (RKF) scheme via shooting technique. The major outcomes of current work have more concentration ([Formula: see text]) and Mass Transfer Rate ([Formula: see text]) for various numerical values of Activation Energy ([Formula: see text]). The present solutions determine very good correlation with the previously studied ones in a special case as predicted in the tables.

Nonlinear thermal radiation effect on magnetohydrodynamics flow of Cu−H2O and TiO2−H2O of Casson nanofluids over stretching wall through porous channel

This paper presents a numerical solution for the nonlinear thermal radiation effect of magnetohydrodynamic flow of Casson nanofluid over a stretching wall through a porous channel. As the linear thermal radiation leads to a significant difference between the highest and lowest possible temperatures, the nonlinear thermal radiation is used in this work. The governing partial differential equations are changed into nonlinear ordinary differential equations using similarity transformation and then solved using the Runge–Kutta method together with the shooting technique. The graphical representation of the temperature and the velocity profiles is presented for different values of the parameters involved in the problem. The obtained results of the skin friction and the heat transfer are compared with the results in the literature and achieved an excellent agreement.

Numerical study on magnetohydrodynamics micropolar Carreau nanofluid with Brownian motion and thermophoresis effect

ABSTRACT The current work explores the investigation of the influence of nonlinear thermal radiation on unsteady, magnetohydrodynamics boundary layer flow of micropolar Carreau nanofluid past a stretching sheet. Viscous dissipation, internal heating, Brownian motion, heat source/sink, thermophoresis, chemical reaction, and Joule heating effects are considered in the study. To analyze the model, the governing partial differential equations are rephrased and written in the non-dimensional form with the relevant dimensionless quantities. To obtain the solutions, the nonlinear non-dimensional governing equations are numerically solved using finite difference approximation. The impact of every significant flow parameter on fluid motion, micro-rotation, temperature, concentration, surface drag, heat, and mass transfer rates are presented through plotted graphs and tables. It is noted from the study that the fluid flow and angular motion increase, whereas the temperature declines with higher values of the micropolar constant. Further, it is noticed that thermal distribution is a rising function of radiation parameter, and due to the nonlinear thermal radiation effect, there is an increase of 4.903% in temperature distribution when compared to linear thermal radiation. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study.

Effect of nonlinear thermal radiation on second order slip flow and heat transfer of Jeffrey nanofluid over a stretching sheet with non-uniform heat source/sink

The flow and heat transfer of Jeffrey nanofluid over a stretching sheet with non-uniform heat source/sink is considered in the present analysis. Effects of nonlinear thermal radiation and second order slip are taken along with uniform magnetic field. System of partial differential equations governing the described problem is reduced to nonlinear ordinary differential equations with aid of similarity transformations. Further, reduced equations are solved numerically using Runge-Kutta-Fehlberg 45 order method with shooting technique. Effects all flow pertinent parameters are recorded in terms of tables and graphs. The results are studied with help of plotted graphs, tables. Results are compared with existing one for some limiting cases and are found to be excellent agreement. It is found that both first, second order velocity slip parameters reduces the thickness of momentum boundary layer and hence decrease the velocity as a result of this one can find the increase in thermal boundary layer.

Numerical analysis of heat transfer in Ellis hybrid nanofluid flow subject to a stretching cylinder

This work covers the theoretical and computational examination of the Ellis hybrid nanofluid flow model with magnetic, Darcy-Forchheimer, and non-linear thermal radiation effects across the stretching cylinder. The convective slip boundary condition is imposed on the surface of the cylinder. Hybrid nanoparticles (AA7072 and AA7075) are scattered in base fluid (water) to create a hybrid nanofluid. The phenomenon of fluid flow has been analytically developed for energy and fluid velocity as a non-linear partial differential equation (PDE)-based system. Through appropriate similarity replacements, the design of PDEs is further streamlined to the set of ordinary differential equations (ODEs). Utilizing a built-in MATLAB (R2020b) algorithm called bvp4c, numerical solutions are found for the obtained dimensionless equations. Graphical discussions are used to illustrate the outcomes of velocity and temperature profiles. The velocity profile of mono and hybrid nanofluids declined for higher inputs of Darcy–Forchheimer and magnetic parameters. Additionally, it has been observed that the energy contour is improved caused of thermal radiation and thermal Biot number. Moreover, our results are consistent with the existing literature.

Powell-Eyring Fluid Flow Over a Stretching Surface with Variable Properties

The objective of this study is to investigate the effect of temperature dependent viscosity and thermal conductivity on the stretching surface and heat transfer of a Powell-Eyring fluid with the effect of nonlinear thermal radiation. The Prandtl number is also considered to be varying within the boundary layer. The governing model which consists of a set of coupled non-linear partial differential equations is converted into a system of ordinary differential equations via suitable similarity transformations and then solved by a recent and reliable numerical method called the spectral quasi-linearization method is used in the computational analysis. The result shows that there is large variation in the value of the Nusselt number and skin friction co-efficient.

Numerical simulation of MHD two‐dimensional flow incorporated with joule heating and nonlinear thermal radiation

AbstractThe current investigation presents a numerical simulation of boundary layer flow with heat transfer. The study primarily emphasizes heat generation due to the influence of nonlinear thermal radiation. Moreover, the simultaneous effects of Joule heating and viscous dissipation have been incorporated for the thermal enhancement of the magnetohydrodynamics (MHD) on the convective boundary layer flow over a flat plate. Dimensional analysis is brought into use to determine the hydro and thermal boundary layer thickness for the two‐dimensional flow. Subsequently, the application of the suitable similarity transformation yields a nonlinear coupled flow problem with is solved numerically with the help of the Runge–Kutta Fehlberg (RKF) method incorporated with the Shooting technique. Moreover, this theoretical study highlights the immense mechanical and aeronautical applications of thermal radiation. In view of computational findings and simulating results, linear and nonlinear thermal radiation effects can also be investigated on fluids passing through a cylinder and channels. Finally, computational data tabulated against some pertinent parameters and parametric study reveal that non‐linear thermal radiation is more effective for highly viscous fluids.

Activation energy on three-dimensional Casson nanofluid motion via stretching sheet: Implementation of Buongiorno’s model

In this work, the statistical (“Numerical”) modelling of activation energy and chemical reaction on non-Newtonian liquid motion via stretching sheet (SS) were performed, analysed statistically, employing the shooting technique. The convective boundary conditions are considered on Casson liquid (“non-Newtonian”) motion with couple stress SS. The behaviour of thermophoresis diffusion and Brownian motion via a special effect of non-linear thermal radiation are assuming in temperature equation for liquid motion. This analysis highly governing nonlinear system of D. Es of velocity, temperature, concentration and activation are simulated via iterative scheme encoded with MATLAB programming language. The geometric model is described bvp 4th order of R-K-F (“Range-Kutta-Fehlberg”) scheme. We found that, 35% of heat transfer rate produces in motion of couple stress Casson nanofluid and the activation energy released 28% of mass transfer rate at stretching surface. A comparative result of linear and nonlinear SS presented via various dimensionless parameters on graphs and tables.

Cattaneo – Christov heat and mass flux model for Electromagnetohydrodynamic (EMHD) non-Newtonian flow of Jeffrey nanofluid with nonlinear thermal radiation and stratified boundary conditions

Our intention in this article is to analyze the enhancement of heat and mass transfer of an electromagnetohydrodynamic incompressible flow through a stretching sheet. An electrically conducting non-Newtonian Jeffrey nanofluid is considered. The Cattaneo–Christov model of heat and mass flux is engaged to scrutinize the thermal relaxation properties. The basic Buongiorno nanoparticle model is taken under Brownian motion, thermophoresis, and nonlinear thermal radiation effects with stratified boundary conditions. The Joule current is incorporated in the energy equation. The total entropy generation is also discussed by implementing the second law of thermodynamics. The nonlinear systems are computationally solved by the optimal homotopy analysis method. The influences of embedded factors on skin friction, Nusselt number, and Sherwood number are accessible through tables. It is been witnessed that for advancing values of thermal relaxation parameter the temperature profiles decrease, but increases for thermophoresis and thermal radiation parameter. Entropy rates are enhanced for radiation parameter and Reynold’s number. This is also observed that for advancing values of Deborah number from 0.4 to 0.8, the skin friction coefficient increases by 40%, and the Nusselt number is increased by 23% for advancing values of thermal radiation parameter ranging from 0.3 to 0.7.

MHD Micropolar Fluid in a Porous Channel Provoked by Viscous Dissipation and Non-Linear Thermal Radiation: An Analytical Approach

The present exploration discusses the combined effect of non-linear thermal radiation along with viscous dissipation and magnetic field through a porous medium. A distinctive aspect of our work is the simultaneous use of porous wall and a porous material. The impact of thermal rays is essential in space technology and high temperature processes. At the point when the temperature variation is very high, the linear thermal radiation causes a noticeable error. To overcome such errors, nonlinear thermal radiation is taken into account. The coupled system of ordinary differential equations are derived from the partial differential equation. The dimensional model equations are transformed into non-dimensional forms using some appropriate non-dimensional transformation and the resulting nonlinear equations are solved numerically by executing persuasive numerical technique R-K integration procedure with the shooting method. Graphical analysis were used to assess the consequences of engineering factors for the momentum, angular velocity, concentration and temperature profiles. The skin friction values, local Sherwood and Nusselt number are the fascinating physical quantities whose numerical data are computed and validated against different parametric values. The vortex viscosity parameter and spin gradient viscosity parameter shows the reverse phenomenon on micro-rotation profile. The thermal radiation phenomena flattens the temperature and speeds up the heat transfer rate in the lower wall and a peak in the concentration is observed for the Pem>>1 due to the inertial force. The Variational Iteration Method (VIM) and Adomian Decomposition Method (ADM) are the two analytical approach which have been incorporated here to decipher the non linear equations for showing better approximity. Comparisons with existing studies are scrutinized very closely and they are determined to be in good accord.

MHD natural convection heat and mass transfer flow over an inclined porous plate with thermophoresis and nonlinear thermal radiation effects

AbstractThis study examined magnetohydrodynamic natural convection mass and heat transfer flow of an electrically conducting and viscous incompressible fluid over an inclined porous plate with thermophoresis, suction/injection, and uniform magnetic field. The mathematical model governing the fluid behavior surrounding an inclined plate is solved through the Runge–Kutta–Fehlberg fourth–fifth order after utilizing the shooting method. The implication of active dimensionless parameters in the governing equations is fully discussed in detail. The results obtained show that, in the existence of nonlinear thermal radiation and suction/injection, the heat transfer rises with the increase in the angle of inclination but it decreases with the mass transfer and plate shear stress. Furthermore, the heat transfer rate experiences a serious setback due to the increase in the buoyancy force but improves the plate shear stress. The mass transfer is directly proportional to the thermophoresis effect. In addition, Particle suction increases the velocity and temperature curves while it declines the concentration profile, but the opposite is valid for injection. Nonlinear thermal radiation positively affects the temperature, velocity, and concentration profiles. The Lorentz force suppresses the fluid transport and retard the rate of particle concentration, but promotes the fluid temperature distribution. It is also deduced that increasing the rate of particle suction from 0 to 1, accounts for over 76% increase in the particle deposition at the plate surface. However, increasing the rate of particle injection from 0.004 to 0.250 accounts for an over 83% decrease in the particle deposition at the plate surface.

Effects of Nonlinear Thermal Radiation and Heat Generation/Absorption on Magnetohydrodynamic (MHD) Carreau Nanofluid Flow on a Nonlinear Stretching Surface Through a Porous Medium

The present paper introduces a numerical study on the electromagnetic flow of Carreau nanofluid on a nonlinearly surface that stretches in a porous medium under the influence of heat absorption/generation and nonlinear thermal radiation besides the effects of thermophoresis and Brownian motion on the distributions of velocity, temperature, and nanoparticle concentration. The similarity transformations were used in converting the structure of governing partial differential equations into a structure of an ordinary differential equations that subsequently answered numerically by the Runge-Kutta fourth order technique with shooting technique. Also, graphical forms and numerical tables were used to show the results of all effects of physical coefficients that will be presented later in detail. Finally, some results of the study showed a decline in distributing the concentration and temperature of nanoparticles when reinforcing the values of the Lewis number and Prandtl number.

Entropy Optimization and Heat Transfer Analysis of Magneto-Bioconvective Powell Eyring Nanofluid with Nonlinear Thermal Radiation and Chemical Reaction Over a Stretching Sheet

This paper investigates the entropy generation in the bioconvection of Powell Eyring nanofluid containing motile gyrotactic microorganisms over a convectively stretching sheet. The influences of magnetohydrodynamic forces, nonlinear thermal radiation effects, chemical reactions of species in a Powell Eyring nanofluid flow are analyzed. Motile microorganisms are added along with nanoparticles in the Powell Eyring base fluid for the prevention of nanoparticles agglomeration and to stabilize the nanoparticles in the suspension. The governing nonlinear partial differential equations along with boundary conditions are solved numerically after these equations are transformed into a system of nonlinear ordinary differential equations by using the similarity transformation. The results are compared with previously published research papers. The impact of significant physical and bioconvection parameters on the profile of nanofluid velocity, temperature, nanoparticles concentration, the density of motile microorganisms, and entropy generation are analyzed graphically. It is noticed that the velocity profile increases by increasing the values of the Powell Eyring fluid parameter. The incidence of nanoparticles in Powell Eyring nanofluid decreases the nanoparticle concentration due to an increase in the value of the chemical reaction parameter and Lewis number. Also, the profile of entropy generation increases as the values of Br, γ1, and γ2 are increased.

Combined effect of induced magnetic field and thermal radiation on ternary hybrid nanofluid flow through an inclined catheterized artery with multiple stenosis

The present article introduces a theoretical study of ternary hybrid nanoparticle (Cu–Ag–Au) on a two-dimensional blood flow through an inclined catheterized artery with multiple stenoses in the presence of wall slip. The combined effect of Non-linear thermal radiation and external induced magnetic field gives rise to innovative results in the current study. Further, the purpose of this study is to graphically observe the flow characteristics of tri-hybrid (Cu–Ag–Au), hybrid (Cu–Au), and single (Au) nanofluid flow through arteries with composite stenosis. This model involves tri-hybrid nanoparticles as part of the heat transfer process, as well as thermal radiation to further enhance the temperature rate. In the mathematical model, continuity, linear momentum, thermal energy, and Maxwell’s equations are simplified under the assumption of mild stenosis. The homotopy perturbation method is used for finding the analytical solution of non-linear PDE. With the help of contours, the flow pattern is also presented. This study indicates that magnetic force significantly controls the flow velocity and the expansion of the magnetic field, whereas the increase of radiation parameter does the opposite. Moreover, magnetic force and radiative heat reduces the pressure gradient and temperature in the blood flow, respectively, as well as thermal slip enhances the temperature distribution. These graphical outcomes instigate that the tri-hybrid nanoparticles are more helpful in attenuating the hemodynamics factors (such as blood velocity and temperature) as compared to the hybrid and single nanoparticles.

Graphene-gold/PDMS Maxwell hybrid nanofluidic flow in a squeezed channel with linear and irregular radiations

The hydrothermal performance of a hybrid nanofluid made of graphene, gold/polydimethylsiloxane between two squeezing plates is discussed in this study. In the investigation of thermal transport of the flow, both linear and nonlinear thermal radiation's effects are taken into account. Bejan numbers are used to determine the system's energy efficiency. Viscous and thermal radiation effects on Maxwell hybrid nanofluid flow in a squeezing channel are incorporated to explore the outcomes. By applying similarity transformations, the set of ordinary differential equations in this case is transformed into the governing equations. With the use of the Runge–Kutta–Fehlberg technique converted system is solved numerically. Skin friction and heat transfer rates under the influence of certain oriented parameters are numerically analysed and presented in tabular form. The impacts of different factors on the temperature and velocity profiles are illustrated graphically and briefly described. Important findings include that the Bejan number raises as the radiation parameter Rd rises, but that it falls with respect to the Eckert number effect. Additionally, the skin friction values and Nusselt number in the hybrid nanofluid case are larger than in the nanofluid case. Furthermore, it has been found that the Deborah number-described stress relaxation phenomenon causes the flow field and thermal energy transfer to be less efficient when fluids are moving. There is surprisingly little research on the hybrid fluid integrated into their issues.

Couple stress Darcy–Forchheimer nanofluid flow by a stretchable surface with nonuniform heat source and suction/injection effects

The thermal enhancement of industrial and engineering processes with interaction of nanofluids is exclusively important and presents applications in extrusion systems, heat transfer devices, electronic chips, chemical reactions, nuclear processes, etc. Owing to such motivated significance of nanofluids, the aim of this investigation is to present the heat and mass transfer phenomenon in the Couple stress nanofluid flow containing the microorganism due to oscillatory stretched surface. Additionally, the Darcy–Forchheimer applications, nonuniform heat source and nonlinear thermal radiation effects are considered. The modification in the concentration equation is done by activation energy. The independent variables in the defined flow system are decreased via suitable variables. The computation is simulated using the homotopy analysis method. It is noticed that the magnitude of velocity periodically decreases for larger values of suction parameter and inertia coefficient. The presence of an external heat source parameter enhanced the temperature profile. Moreover, the increment in the suction parameter improves the heat and mass transfer rate.

Effect of non-linear thermal radiation on MHD Casson fluid flow past a stretching surface with chemical reaction

The analysis is accomplished to discover the innovation of an incompressible magnetohydrodynamic Casson liquid flow driven by a stretchable sheet with convective boundary conditions. The variations of non-linear thermic heat, chemical response and unequal heat absorption/generation are reserved into account. The flow reckonings are mutated into a scheme of dimensionless non-linear ODEs with appropriate similarity variables. The elucidation of the problem is attained by captivating the help of the fourth-order RK-based shooting procedure. The bearings of influential parameters on velocity, thermal and solutal fields are revealed with the assistance of diagrams and also the physical measures skin friction, local solutal and thermic heat transport are revealed in a distinct chart. Escalating the non-linear thermal radiation parameter as well as the temperature ratio restriction escalates the fluid temperature. The rate of mass transport is extraordinary for the increase of chemical response parameter and Schmidt number.

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 of λ p, δ m and δ q, and as a result, F′(ξ) accelerates while the opposite trend is observed for M and ϕ. The drag friction is boosted by the augmentation M, λ p and ϕ, 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) and ϕ(ξ) profiles. The HAM and the numerical technique (shooting method) were found to be in good agreement.