Nonlinear Radiative Heat Transfer Research Articles

Impact of Arrhenius activation energy on magnetic nanofluid flow over a slendering stretchable sheet with nonlinear radiative heat transfer: A machine learning algorithm

Thermal systems in the contemporary world need effective cooling and heating methods. Heat transfer technology plays a vital role in various industries, including aerospace, electronic equipment, automobiles, and transportation. Considering the importance of effective cooling and heating processes, this framework explores the hydromagnetic stagnation point flow with binary chemical reactions, ohmic heating, Arrhenius activation energy, nonlinear thermal radiation, thermophoresis, and Brownian motion. At first, the flow equations are determined in a formal way as dimensional partial differential equations. Then, they are transformed into simpler, dimensionless ordinary differential equations using self-similar variables. The present study describes a novel approach to intelligent numerical computing, utilizing a Levenberg-Marquard algorithm-based MLP (Multi-Layer Perceptron) feed-forward back-propagation ANN (Artificial Neural Networks) implementation. The collection of data was conducted to facilitate the evaluation, validation, and instruction of the artificial neural network model. The utilization of appropriate self-similarity variables has facilitated the conversion of fluid transport equations into ordinary differential equations. The Runge–Kutta–Fehlberg (RKF) technique was used to solve these equations. The numerical results are presented visually for numerous constraints of the governing parameters. The increased values of the velocity ratio enhanced the fluid velocity. The nonlinear thermal radiation and temperature differential characteristics significantly raise the temperature of the fluid. Increasing the nonlinear radiation and magnetic field parameters improves the rate of heat transfer. The temperature of the fluid decreases as the size of stagnation increases. The skin friction coefficients decrease as the wall thickness and magnetic parameters increase.

Computational Assessment of ZrO2-Al2O3/EG and ZrO2-Al2O3-Cu/EG Nanomaterial on Blasius-Rayleigh-Stokes Flow Influenced by an Aligned Magnetic Field

In this work, the flow of a modified nanofluid is analysed as it passes over a moving surface to investigate the influence of nonlinear radiative heat transfer and the effects of magnetic fields that are aligned. In addition, ethylene glycol is used as the solvent while zirconium oxide and alumina are combined to generate a hybrid nanomaterial. Ternary nanomaterials consist of zirconium oxide, alumina, and copper dissolved in the ethylene glycol. For this mathematical model, Navier–Stokes equations were used to represent the assumed flow. The Navier–Stokes equations were approximated using the boundary layer method under the flow assumptions, yielding the PDE’s. Similarity transformations are used to translate this system into ODE’s. The bvp4c method is used to explain a dimensionless system. The impacts of the relevant physical parameters are elucidated quantitatively and visually. A greater temperature ratio parameter is observed to increase the temperature profile. In addition to this, when the magnetic field parameter is increased, the momentum layer becomes thicker.

A significant study on radioactive cross fluid model with melting boundary near stagnation region

The current research endows the mathematical modeling for the stagnation point flow along with melting nonlinear radiative heat transfer for cross fluid. It has many applications such as synthesis of polymer solutions, plastic manufacturing, food processing, preparation of synthesis, adhesives, etc. A radially stretching sheet has started the flow keeping the assumption of rotational symmetry. Transformation approach is adopted to attain the nonlinear ordinary differential equations based on standard conservation laws of mass, linear momentum and also energy. Numerical solutions of the governing problem are computed via the shooting technique. Characteristics of the parameters appearing in modeling like the melting parameter, power–law index, local Weissenberg number, nonlinear radiation parameter, temperature ratio parameter and Prandtl number are comprehensively analyzed through graphical behavior. In addition, comparative analysis is presented for the cases when the value of free stream velocity overtops the stretching velocity and vice versa. Results are authenticated by taking special cases and excellent compatibility is achieved with the existing literature. The detailed analysis anticipates that the boundary layer structures could be strengthened by growing the melting parameter. Elevation in Weissenberg number caused velocity along with temperature profiles to demonstrate for [Formula: see text]. Further, the temperature behaves oppositely analogous to development in nonlinear radiation parameter besides the temperature ratio parameter.

Study of nonlinear radiative heat transfer with magnetic field for non-Newtonian Casson fluid flow in a porous medium

This paper studies the effect of thermo-diffusion, electrical field, and nonlinear thermal radiation. Thermal radiant heat transfer has several industrial applications, and the analysis of radiation heat transfer in non-Newtonian fluids under different conditions has been widely studied. To better understand the problem of thermal nonlinear radiation heat transfer flow in non-Darcy Casson fluid on stretched surfaces, this research examines such a phenomenon. The Hybrid Analytical and Numerical Method (The HAN Method) is used to precisely analyze the steady flow of incompressible Newtonian electrically conducting non-Darcy Casson fluid on a vertical permeable stretchable plate with the presence of the magnetic field. The governing equations of this problem are reduced from the system of nonlinear partial differential equations (PDEs) into a system of nonlinear ordinary differential equations (ODEs) using similarity transformations. The results showed that Casson's parameter has a small and indirect effect on temperature and mass transfer, but it affects the velocity significantly and directly. Also, the magnetic field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. The electric field has a direct and significant effect on temperature and velocity but an indirect and significant effect on concentration. Also, the effects of parameters such as thermal buoyancy, inertial, porous permeability, Eckert number, Prandtl number, chemical reaction, Schmidt and Soret numbers, and porosity on velocity, temperature, and concentration have been studied.

Dynamics of tangent-hyperbolic nanoliquids configured by stratified extending surface: Effects of transpiration, Robin conditions and dual stratifications

A mathematical study is presented to evaluate double stratification effects on the dual convected flow of a non-Newtonian (tangent-hyperbolic) nanoliquid persuaded by porous stretching surface. Thermal radiation along with transpiration (wall suction/injection) and heat source/sink are included. Buongiorno's model is employed for nanoscale effects and a Rosseland diffusion approximation for nonlinear radiative heat transfer. Appropriate similarity transformations are deployed to alter the dimensional governing nonlinear PDEs (partial differential equations) to a nonlinear differential one with physically viable boundary conditions. The transformed dimensionless BVP (boundary value problem) is computed analytically by a HAM (homotopic analysis method) algorithm and a symbolic software. Validation with earlier studies employing the numerical method (Runge-Kutta-Fehlberg) is included. The evolution in velocity, thermal and solutal (nanoparticle) fields are interpreted through graphical outcomes for the impact of significant sundry parameters. Tabular outcomes are also presented for skin-friction, local Nusselt and Sherwood numbers. A rise in material variable (Weissenberg number), the flow is decelerated while it is accelerated with increasing nonlinear thermal convective parameter, mixed convection parameter and buoyancy ratio values. Temperatures are boosted with increment in radiative, thermophoresis, Brownian motion, thermal Biot number and heat generation parameters whereas they are reduced with increasing thermal stratification parameter. Nanoparticle concentration values are suppressed with higher Schmidt number, Brownian movement and solutal stratification variable however they are boosted with greater values of thermophoresis and concentration Biot number. Local Sherwood number is improved with Schmidt number, concentration stratification parameter and concentration Biot number. Local Nusselt number is strongly increased with greater Prandtl number, thermal stratification number, thermal Biot number and radiative parameter. The study finds applications in thermal nano-polymeric coating flows in materials processing operations.

On the Diffusive Limits of Radiative Heat Transfer System I: Well-Prepared Initial and Boundary Conditions

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling and greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions for the radiative intensity and with periodic, Dirichlet and Robin boundary conditions for the temperature. The global existence of weak solutions for this system is given by using a Galerkin method with a careful treatment of the boundary conditions. Using the compactness method, averaging lemma and Young measure theory, we prove our main result that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Moreover, under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial or boundary layer exists.

Effect of nonlinear thermal radiation and melting heat transfer assessment on magneto-nanofluid through a shrinking surface

ABSTRACT In this study, we have examined the stagnation point flow of MHD chemically reacting nanofluid along a stretching/shrinking sheet. The chemical reaction has vital applications in food preparation, the mechanism of water and oil emulsions, and chemical engineering. Therefore, this analysis is subjected to the effects of Joule heating, viscous dissipation, Brownian motion, chemical reaction, thermophoresis, and melting heat transfer. The governing transformed equations are solved numerically via shooting scheme together with Runge–Kutta–Fehlberg method. The impacts of various nanofluids and relevant regulating parameters such as chemical reaction parameter, magnetic parameter, radiation parameter, melting parameter, and Eckert number on dimensionless velocity, thermal, and concentration profiles as well as skin friction drag coefficient, Nusselt and Sherwood numbers are presented graphically. Although dual branch solutions are obtained in this investigation, only one solution is determined to be stable. It is seen that the coefficient of skin friction and mass transfer rate tend to be decreasing due to melting heat transfer. The results also revealed that higher estimations of magnetic parameter increase the heat transfer rate, but a reverse trend is noticed for surface drag coefficient and mass transfer rate in case of first solution.

Nonlinear radiative heat transfer of magnetohydrodynamic non-newtonian fluid flow past a shrinking sheet: Reiner–Philippoff model

This study aims to analyse the effect of MHD and nonlinear thermal radiation on heat transfer of Reiner–Philippoff fluid flow over a shrinking sheet. By adopting appropriate similarity transformations, the partial derivatives of multivariable differential equations are transformed into the similarity equations of a particular form. The resulting mathematical model is elucidated in MATLAB software using the bvp4c technique. The findings reveal the existence of dual solutions for a certain range of physical parameters. Since the dual solutions are established, stability analysis is employed to examine their stabilities. The outcomes show that the first solution is stable whereas the second solution is unstable. Moreover, the heat transfer rate reduces as the nonlinear thermal radiation is introduced in the operating fluid by increasing the temperature ratio parameter. However, increasing the magnetic parameter raises the friction factor which impulsively improves the heat transfer performance. The suction effect has a noticeable influence on the Reiner–Philippoff fluid, where increasing the suction strength enhances the skin friction coefficient and the heat transfer performance.

Comparative study for magnetized flow of nanofluids between two parallel permeable stretching/shrinking surfaces

The current study intended to discuss a comparative study on the three dimensional Casson nanofluid with nonlinear radiative MHD flow and heat transfer aspects between two parallel stretching/shrinking surfaces. The mathematical models for momentum and temperature are established by employing the boundary layer flow of fluids with spinel-type ferrite MnFe2O4 nanoparticles being distributed in Pure Water/ (H2O) as the base fluid. Remarkable models like Maxwell-Garnett and Patel models are inserted in view of thermal conductivity augmentation. The suitable similarity transformations are adopted for converting the governing non-linear partial differential equations into non-dimensional ODE's and obtaining the relevant parameters for discussion. The major outers of the present study are axial velocity {F′(η)} peters out with amplifying β subject to stretched and shrunk surfaces in relation to both Maxwell-Garnett and Patel models. Growing θw and n exhibits opposite effect on heat transfer rate.

On the magnetized 3D flow of hybrid nanofluids utilizing nonlinear radiative heat transfer

This article analyzes the heat transfer, non-linear thermal radiation, the Cattaneo-Christov heat flux model and velocity slip effects in hybrid nanofluid flow over a 3D moving sheet. The hybrid type nanoparticles like Ag-Cu and MoS2 and GO are suspended in working liquid. Hybrid nanoliquid is homogeneous-mixture with novel physical and chemical structures making it a promising option for improving thermal efficiency. Hybrid nanoliquids have high ability to absorb and preserve the hydrogen because of their very huge unique surface-area and distinctive and unusual nature of an each nanostructure. Nanostructure carbon atoms like graphite, graphene and few metals like molybdenum and magnesium have recently been found to store hydrogen due to their larger storage-capacity and the higher dehydrogenation and hydrogenation speeds. The system of the mathematical relation in PDEs form is converted to system of ODEs by employing suitable variables. The bvp4c tool available in computational software MATLAB is used for solving the dimensionless ordinary differential system. Furthermore, the flow expectations for each physical flow parameter like are discussed. The physical consequence of flow parameters against subjective flow fields are graphically highlighted with physical justifications. The vitality of prominent parameters against velocity field and temperature distribution is illustrated through graphs. The velocity field diminishes with a larger velocity slip parameter. The velocity field is enhanced by the higher estimations of the Grashof number. The consequence of temperature ratio parameter on thermal field is delineated. By enhancing the thermal relaxation parameter, the thermal field reduces.

Bioconvection transport of magnetized Walter's B nanofluid across a cylindrical disk with nonlinear radiative heat transfer

Nanotechnology plays a crucial role in the main innovation development of the modern age in the latest technology. In recent times, researchers are concentrated to build up various algorithms to increase their heat transfer rate. One of the approaches that have conquered this deficiency is to significantly raise the thermal properties of regular fluids by manifestation of nanoparticles in host fluids. In this article, a numerical study is developed to investigate the bio convective transport of Walter's B nanofluid past a cylindrical disk in the presence of thermophoretic and Brownian diffusions. Additionally, non-linear thermal radiation, variable thermal conductivity and motile microorganisms are also considered. The Buongiorno model is used to explore the nanofluid features with motile microorganisms. The constituted normalized system of modeled flow equations is condensed into dimensionless system of differential form by adopting appropriate similarity variables. The ordinary systems are elucidated through bvp4c technique in MATLAB software. Characteristics of flow parameters against velocity field, temperature distribution, volumetric concentration of species and microorganism's profile are discussed. From the results we observed that velocity field is reduced for larger magnetic parameter. It is noticed that developing values of mixed convection parameter raises the velocity field. It is analyzed that temperature distribution of Walter's B fluid upsurge for variable thermal conductivity parameter. Temperature field intensifies for thermal Biot number. It is perceived that solutal field of species diminishes for larger Brownian motion parameter. The microorganism field is found to decay with Peclet and bioconvective Lewis numbers. The current proposed model is more useful in the field of engineering. The improvement in heat transfer rate is current issue in the world. Nanofluids have high thermal efficiency therefore such fluids are more useful to improve the heat transfer rate.

Importance of bioconvection in 3D viscoelastic nanofluid flow due to exponentially stretching surface with nonlinear radiative heat transfer and variable thermal conductivity

Importance of bioconvection in 3D viscoelastic nanofluid flow due to exponentially stretching surface with nonlinear radiative heat transfer and variable thermal conductivity

Nonlinear Radiative Heat Transfer of Magnetite(Fe3O4)-Water Nanofluid over Unsteady Stretching Surface with Fluid Particle Suspension

The exploration of the magneto hydrodynamics(MHD) flow and nonlinear radiative heat transfer of magnetite Fe3O4 - H2O nanoparticle with fluid particle suspension over an unsteady stretching sheet is the central theme of the present work. The similarity transformations were employed to transfer the governing partial differential equations into ordinary ones prior to solve numerically using Runge - Kutta - Fehlberg-fourth and fifth order method with shooting technique. The variations of the temperature and velocity distribution and coefficients of heat transfer for magnetic parameter, temperature ratio parameter nanoparticle volume fraction, and thermal radiation parameter are discussed graphically. Comparative analysis of reported ones and present work results was presented and found to be in good agreement.

Numerical Treatments to Analyze the Nonlinear Radiative Heat Transfer in MHD Nanofluid Flow with Solar Energy

In the current study, the nonlinear radiative heat transfer effects due to solar radiation in magneto-hydrodynamic (MHD) nanofluidic problem are analyzed effectively by novel application of numerical computing by Adams predictor–corrector and explicit backward difference solvers. The governing relations of PDEs for the model are transformed into the system of ODEs, and numerical solvers are applied to the transformed system to study the effect of radiation parameter along with thermophoresis parameter, Brownian motion parameter, magnetic field parameter, Lewis number, Prandtl number, Eckert number and Biot number on velocity, temperature and nanoparticle concentration profiles. The comparative study of both solvers is provided in sufficient number of graphical and numerical illustrations to prove the worth in terms of accuracy, robustness and stability.

Cu–Al2O3–H2O hybrid nanofluid flow with melting heat transfer, irreversibility analysis and nonlinear thermal radiation

We have investigated the influence of hybrid nanoparticles on various physical quantities in a water-based hybrid nanofluid involved in a steady and fully developed forced convective flow generated over a stretched surface. Nonlinear thermal radiation and melting heat transfer analysis are featured in this work. To obtain the solution of the governing equations, a standard transformation and numerical procedure are implemented. Then, a comprehensive discussion of the effects of the flow regime on several governing parameters is presented. The results indicated that increasing magnetic strength $$M$$ and nanoparticle volume fraction $$\phi_{1}$$ lead to a thicker thermal boundary layer. A similar trend takes place with increasing nonlinear thermal radiation while the reverse is noticed for Eckert number. The entropy generation rate increases with the increase in Brinkman number and Bejan number reduces with increasing Eckert number. The obtained results of this model closely match with those available in the literature as a limiting situation. It is demonstrated that hybrid nanofluids exhibit lower entropy generation rates. The results of this study are of importance in the assessment of the effect of some essential design parameters on heat transfer and, consequently, in the optimization of industrial processes.

ENTROPY GENERATION AND IRREVERSIBILITY ANALYSIS ON FREE CONVECTIVE UNSTEADY MHD CASSON FLUID FLOW OVER A STRETCHING SHEET WITH SORET/DUFOUR IN POROUS MEDIA

The two-dimensional unsteady incompressible Casson fluid flow over a nonlinearly stretching sheet is studied here under the influence of an external magnetic field. The nonlinear thermal radiation heat transfer in the porous media is considered. The novelty of the present study is in the entropy generation and irreversibility analysis together with the Soret and Dufour effects for Casson fluid. The fluid velocity, temperature, concentration, friction factor, entropy generation rate, and Nusselt, Sherwood, and Bejan numbers are studied through solving the governing nonlinear equations in a transformed/converted system by a shooting method. It is found that the energy transport may be maximized by varying the magnetic field and unsteadiness factor. Moreover, an increase in the porosity parameter raises the temperature and concentration profiles, while it reduces the fluid's velocity. The Bejan number is augmented due to an increase in radiation, while it is reduced due to the increases in magnetic field and Casson fluid parameter. Finally, the irreversibility ratio is augmented as the magnetic field increases.

A Spectral Simulation of Magnetohydrodynamic Convective Nanofluid Slip Flow with Newtonian Heating and Radiative Heat Transfer

In this paper, we present a numerical analysis of natural convection boundary layer flow of a nanofluid over a stretching sheet under the influence of a variable magnetic field in the presence of nonlinear radiative heat transfer, hydrodynamic slip and Newtonian heating effects. The Brownian diffusion and thermophoresis effects are employed to describe the nanofluid flow model consisting of non-linear partial differential equations, which is transformed into a similarity form and then treated with the spectral local-linearization method (SLLM) to present an in-depth analysis of the flow and heat transfer characteristics of the fluid flow. The fluid flow problem finds applications in many engineering devices including geothermal heat source pump and in cooling of electronic devices and stretched wires.

Quadratic Convective Heat Transport of Casson Nanoliquid Over a Contract Cylinder: An Unsteady Case

An unsteady MHD flow of nonlinear radiative heat transfer of Casson liquid over a contract cylinder has been modeled. This is a theoretical study that involves mathematical approach to do the investigation. The nonlinear partial differential equations for heat transfer are solved numerically using the RKF-45 method. Effects of embedded kinetic parameters on the velocity and temperature of the system are depicted graphically and discussed accordingly. It is found that the rate of cooling is much faster for higher values of unsteadiness parameter. The higher value of unsteady parameter decreases the profiles of velocity and temperature. Further, thermal boundary layer thickness is decreased when the Prandtl number increases.

Correction to: Numerical study of non-linear thermal radiative heat transfer in a non-Darcy chemically reactive Casson fluid flow

The partial derivative DOW is missing in Eqs. (3–5) in the original publication. The corrected equations are shown below.

Time-Dependent Nonlinear Convective Flow and Radiative Heat Transfer of Cu-Al2O3-H2O Hybrid Nanoliquid with Polar Particles Suspension: a Statistical and Exact Analysis

The statistical and exact analysis of heat transfer rate and skin friction coefficient of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is performed. The heat transport phenomenon includes radiative heat effect. A micropolar fluid model is accounted. Exact solutions to the governing problem are found via Laplace transform method (LTM). The heat transfer rate and skin friction are analysed critically via statistical methods like probable error and regression models. The slope of linear regression of data points for skin friction and Nusselt number is estimated to quantify the increase/decrease. The Nusselt number and thermophysical properties for twenty-four different hybrid nanofluids are presented. A novel idea of a nonlinear convective flow of Cu − Al2O3 − H2O hybrid nanofluid with polar particle suspension is investigated for the first time. Opposite behaviour of velocity and microrotation profile are established when the physical parameters are varied.