Nonlinear Radiative Heat Research Articles

Predicting heat transfer Performance in transient flow of CNT nanomaterials with thermal radiation past a heated spinning sphere using an artificial neural network: A machine learning approach

An efficient heat transfer phenomenon using nanofluid have greater challenges in various industries, engineering application the recent trend. Keeping this in present scenario, this study aims to optimize the heat transmission rate in the magnetized flow of nanomaterials through a rotating, spinning sphere. The heat transfer phenomena in the time-dependent fluid are enhanced by the incorporation of nonlinear radiation and a variable heat source. Additionally, the free convective flow is influenced by the effects of thermal buoyancy and a transverse magnetic field. The proposed model along with several factors is standardized through adequate transformation rules. Further, shooting-based Runge-Kutta technique is adopted with the help of built-in MATLAB function bvp4c for the solution of the transformed system. The prime focus of the proposed work is the optimizing heat transfer rate combined with regression analysis using artificial neural network and then it uses Levenberg Marquardt algorithm with well-posed training, testing, and validation data. The error analysis also presented briefly and the variation of characterizing parameters is depicted via graphs. Further, the important outcomes are; the particle concentration of carbon nanotubes contributes to decelerating the velocity profiles, leading to an increase in boundary layer thickness. In contrast, increasing magnetization has the opposite effect. Both nonlinear radiative heat and an additional heat source enhance the heat transfer phenomenon.

Homogeneous–Heterogeneous reactions on Darcy–Forchheimer flow of SWCNTs/MWCNTs over a bidirectional Riga plate with nonlinear radiation and non-uniform heat source/sink

Homogeneous–Heterogeneous reactions on Darcy–Forchheimer flow of SWCNTs/MWCNTs over a bidirectional Riga plate with nonlinear radiation and non-uniform heat source/sink

3D-MHD mixed convection in a darcy-forchheimer maxwell fluid: Thermo diffusion, diffusion-thermo effects, and activation energy influence

In this article, the three-dimensional upper-convected Darcy-Forchheimer Maxwell (UCM) nanofluid flow over a stretching surface is analyzed to investigate the effects of activation energy, thermodiffusion, diffusion thermo, and magnetohydrodynamics (MHD) on heat and mass transfer. The energy equation incorporates a nonlinear radiative heat flux. Using similarity transformation, the nonlinear partial differential equations are reduced to ordinary differential equations, which are then solved using the well-known shooting technique via the fourth-order Runge-Kutta integration method. To validate our results, we also employ MATLAB's built-in function bvp4c. The impact of various parameters, such as activation energy, diffusion thermo, thermodiffusion, Brownian motion parameter, Prandtl number, thermophoresis parameter, and magnetic parameter, on velocity, temperature, and concentration is discussed both graphically and numerically. It is observed that the flow velocity decreases with an increasing magnetic field parameter. Additionally, higher values of the activation energy parameter reduce the nanoparticle concentration profile. The temperature and concentration exhibit opposite behaviors when thermodiffusion and diffusion thermo effects are enhanced.

Non-linear radiative second-grade nano fluid with sinusoidal magnetic force and arrhenius activation energy: A computational exploration

The goal of this work is to further improve our knowledge of the nonlinear radiative second-grade nano fluid flow boundary layer phenomena which is associated with an Arrhenius activation energy, a sinusoidal magnetic field, and a stretched peripheral with a heat source. The unsteady governing equations are transformed into a proper dimensionless arrangement, and then the explicit finite difference (EFD) method is applied to numerically calculate the equations. However, precise stability and convergence criteria have been developed to make the solution convergent. Along with the typical profile of other flow fields, the oscillatory forms of the velocity are shown. Tabular research has even demonstrated a relationship between the Nusselt number and other parameters, and graphical depiction has been used for regression and data prediction. The novel conclusions drawn from this research indicate that, in comparison to linear patterns, nonlinear radiative heat flux significantly raises (30.35 %) flow profiles with second-grade characteristics. Moreover, the heat transfer rates of second-grade Nano fluids are seen to be significantly influenced (35.14 %) by the sinusoidal magnetic component. When considering nonlinear thermal radiation, activation energy principles cause a major change (34.19 % more) in mass transmission, as high-temperature processes become an essential part of chemical reactions.

Flow of nanofluid past a radially stretching disk in an absorbent medium in company of multiple slips, nonlinear radiative heat flux and Arrhenius activation energy

AbstractAn investigation is carried out to analyze the flow, heat and mass transport phenomena of nanofluids over a disk stretched radially in a porous medium. Besides nonlinear radiative heat flux and Arrhenius activation energy, multiple slips are considered in this model. This ensures the novelty of the present research. The main goal of the current investigation is to explore the mutual impacts of nonlinear radiative heat flux, various slip factors and Arrhenius activation energy on flow, heat and mass transfers. The highly nonlinear central equations which are partial differential equations (PDEs) are transformed into nonlinear ordinary ones (ODEs) by employing suitable similarity alterations and then for finding the approximate numerical solutions, shooting technique with 4th order “Runge–Kutta method” are applied. The impact of a variety of parameters on “skin friction coefficient,” “Nusselt number,” “Sherwood number,” velocity of the fluid, heat and mass transfers are computed and presented graphically. It is interesting to observe that fluid velocity diminishes with the growing porosity, suction and velocity slip parameters. Nanofluid's temperature reduces for enhanced values of thermal slip parameter but for rising thermal radiation parameter, temperature is boosted up. Also, nanoparticle concentration diminishes for increasing values of mass slip parameter.

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.

Entropy optimization on magnetized radiative bioconvective flow of Carreau-Yasuda hybrid CNTs through a spherical surface in a non-Darcian porous medium with activation energy

This work inspects entropy generation and heat transfer induced by a bioconvection slip flow of nonlinear radiative Carreau-Yasuda hybrid nanofluid (NF) over a convectively heated sphere. Activation energy for microbes is contemplated in order to comprehend its contribution toward flow features. The original partial differential equations (PDEs) are rendered non-dimensional through appropriate conversions, and the resulting PDEs are solved using the overlapping grid spectral collocation algorithm. The impact of diverse flow factors on flow profiles, entropy generation, skin friction, heat, mass, and motile microbes transport rates is analyzed. Key outcomes reveal that hybrid NF flow demonstrates a supplementary indispensable feature in the operation of heat transport compared to mono NF flow. More entropy is generated in the system by using the hybrid NF model along with magnetic field, heat source, convective heating, nonlinear radiation, and viscous dissipation. Thermal fields and rate of heat transport are improved by including nonlinear radiative heat flux in the system. Mass and motile microbes transport rates are respectively enhanced by chemical and microbial reactions, but both quantities are reduced by activation energy. The effects of microbial reactions on flow quantities substantiate the significance of these features for the dynamics of microorganisms. The findings of this study can be useful in the upsurge of thermal performance of the working fluid and contribute toward the improvement of microbial fuel cell performance.

Second law analysis on magnetohydrodynamics flow of Eyring-Powell hybrid nanofluid over a cylinder/plate with non-linear thermal radiation and Cattaneo-Christov heat flux: Numerical and semi-analytical simulations

This study looks at the Powell-Eyring hybrid nanofluids and the magnetohydrodynamic boundary layer effect on a plate and cylinder that are stretching. In this model, we have taken copper-aluminum oxides as the nanoparticles and water as the base fluid. Many different theoretical models now exist to depict the effect of Powell-Eyring fluid flows through a cylinder on thermal transfer. Furthermore, external magnetic forces are perfect for addressing the fluid’s substantial characteristics and managing the system’s momentum and heat transmission. We investigate the heat transport activities of two separate geometries in magnetohydrodynamic fluids by stretching a plate and cylinder with heat production, using Christov-Cattaneo’s heat flux hypothesis to describe the heat transport activities. We convert the basic partial differential equations (PDEs) into ordinary differential equations (ODEs) through accurate correspondence transformations. We solve these ordinary differential equations using the fourth-order Runge-Kutta method. We make use of the HPM on behalf of the nonlinear system to facilitate such a comparison, and demonstrate that graphs and tables can visualize its more precise and consistent results. An increase in the magnetic parameter results in an increase in the Lorentz force, which results in resistance to the flow of fluid, and this is how velocity decreases. For fluid flow, stretched cylinders are better than plates. Higher values of the temperature ratio parameter enhance the temperature profile. Calculating the Brinkman number leads to a decrease in the Nusselt number. It is possible to improve industrial processes like metal extrusion, hot rolling, glass blowing, glass-fibre manufacture, wire drawing, etc. by using this kind of theoretical research.

MHD hybrid nanofluid and slip flow towards an exponentially stretching/shrinking sheet with nonlinear thermal radiation and nonuniform heat source/sink

The analysis of heat transfer of a hybrid nanofluid [Formula: see text] in the MHD stagnation point motion toward an exponentially expanding/shrinking sheet with a nonuniform heat source/sink, multiple slip conditions and nonlinear thermal radiation effects are carried out in this study. By applying the similarity transformation, the governing equations are transformed into Ordinary Differential Equations (ODEs). The Runge–Kutta method using bvp4c in MATLAB software is implemented to explain the ODEs. The results show that the local Nusselt number is decreased while the skin friction coefficient remains unaltered by the accumulation of thermal slip, space, and temperature-dependent parameters.

Three-dimensional MHD Mixed Convention Upper Convective Flow of Maxwell Fluid Throughout the Past in Thermophoresis and Brownian Motion with the Effects of Diffusion Thermo and Thermal Diffusion Utilizing Nonlinear Radiative Heat Flux

This article aims to investigate the impact of nanoparticles and magnetohydrodynamics (MHD) on the transfer of heat and mass using a three-dimensional upper-convected Maxwell (UCM) nanofluid flow across a stretched surface. A nonlinear radiative heat flow was included in formulating the equation that describes energy. The nonlinear partial differential equations of the issue are transformed into ordinary differential equations utilizing the similarity transformation. These equations are then solved using the well-known shooting approach in conjunction with the Runge-Kutta integration process of order four. To increase the dependability of our findings make use of the MATLAB. On the velocities, temperatures, and concentrations of the particles, the graphical and numerical representations of the effects of the main parameters, such as the Dufour parameter, the Brownian motion parameter, the Prandtl number, the thermophoresis parameter, and the magnetic parameter, are presented. It has been shown that the flow velocity decreases as a function of both the linear and nonlinear thermal radiation parameters. In addition, increasing values of the Brownian motion parameter have the effect of reducing the nanoparticle concentration profile, the same behavior has observed in the case of thermal diffusion and Diffusion thermo parameters.

Darcy-Forchheimer flow with viscoelastic Cattaneo-Christov heat flux model and nonlinear thermal radiation: A numerical investigation

Jeffrey fluids have found vast applications in industries and engineering along with their rheological properties. This article investigates the heat and fluid flow within the frame of the nonlinear thermal radiation and non-Fourier heat flux model on Jeffrey nanofluid over an inclined permeable stretched cylinder through saturated porous medium. In addition, non-uniform heat generation/absorption, nonlinear thermal radiation, thermal stratification, and homogeneous/heterogeneous reactions are accounted. Porous medium is characterized through nonlinear Darcy-Forchheimer relation. Shooting method is employed in conjunction with Runge-Kutta-Fehlberg method to solve nonlinear ODEs. The effects of flow variables involved in velocity, temperature and concentration profiles are deliberated through graphs. It is evident from obtained results that the temperature field rises with thermal radiation parameter and space dependent heat generation/absorption parameter. Local Nusselt number has same enhancing attitude towards the thermal relaxation time (0.7443≤−Nˆuz(Rez)−12≤0.7857 for0.2≤δe≤0.6) and thermal stratification parameter (0.7239≤−Nˆuz(Rez)−12≤0.7689for0.2≤S1≤0.6). The exactness of the solution and F′(ξ) variation is verified by comparison with already published literature. The computed results are of great interest in cooling of nuclear reactors. Viscoelastic stuff are generally employed in mats, car shields, computer hard drives and other protective paddings. Synthetic materials can work as the lubricant for an osteoarthritic joint.

Numerical Investigation of Diffusion Thermo, Hall Current, Activation Energy and Soret of MHD Darcy-Forchheimer Casson Fluid Flow with Inclined Plates

The present article is about the study of Darcy-Forchheimer flow of Casson fluid over a linear stretching surface. Effects like variable Hall current, Diffusion thermo, activation energy and Soret, is also incorporated for the analysis of heat and mass transfer. The governing nonlinear partial differential equations (PDEs) with convective boundary conditions are first converted into the nonlinear ordinary differential equations (ODEs) with the help of similarity transformation, and then the resulting nonlinear ODEs are solved with the help of shooting method. The impact of different physical parameters like Activation energy, Diffusion thermo, Brownian motion, thermophoresis parameter, hall current, magnetic parameter, nonlinear radiative heat flux, Prandtl number, Lewis number, reaction rate constant, on Nusselt number, velocity, temperature and concentration profile has been discussed. It is viewed that the fluid velocity and concentration profile enhance with increasing hall parameter and Activation energy respectively.

Effects of nonlinear thermal radiation on magnetized - nanofluid flow through an inclined microporous channel: An investigation of second law analysis.

This study aimed at studying the variational effect of nonlinear thermal radiation on the flow of Casson nanofluid ( ) through a porous microchannel with entropy generation. The novelty of this investigation includes the incorporation of porous media, nonlinear radiative heat flux, and convective heat transfer at the channel interface into the energy equation, which results in an enhanced analysis for the cooling design and heat transfer of microdevices that utilize nanofluid flow. Particularly, alumina ( ) is considered as the nanoparticles in this blood base fluid due to associated advanced pharmaceutical applications. With dimensionless variables being utilized, the governing equationsare minimized to their simplest form. The Chebysev-based collocation technique was employed to numerically solve the resultant ordinary differential equations with the associated boundary conditions and the impact of flow, thermal, and irreversibility distribution fields are determined through graphs. The findings identified that higher levels of Hartmann number produce the Lorentz force, which limits fluid flow and lowers velocity, the response of nonlinear thermal radiation diminishes the heat transfer rate, and a rise in the Casson parameter also reduces the Bejan number. The results of this research can be used to improve heat transfer performance in biomedical devices, design-efficient energy conversion cycles, optimize cooling systems, and cover a wide range of energy technologies from renewable energy to aerospacepropulsion.

Exploration of nonlinear radiative heat energy on Buongiorno modeled nano liquid toward an inclined porous plate with heat source and variable chemical reaction

Nanofluids are fluid suspensions of nanoparticles that exhibit a considerable improvement in their characteristics at low nanoparticle concentrations. Numerous research on nanofluids focuses on interpreting their behavior in order to use them in applications where improving straight heat transmission is crucial, such as in various industrial settings, nuclear reactors, transportation, biology, food, and electronics. Thus, this study examines the implementation of a novel numerical technique, namely the shooting method for nonlinear radiative heat energy study on Buongiorno modeled nano liquid confined by an inclined porous plate. The Brownian and thermophoresis diffusions impacts are also accounted. The transmission of thermal and solutal energy is regulated by the considerable influence of nonlinear thermal radiation, heat source, and variable chemical reactions. The dimensional modeled partial differential equations (PDEs), by using precise similarity functions, have been mutated into ordinary differential equations (ODEs). The outcomes for the flow field, thermal, and solutal outlines are captured graphically. The values of the dimensionless parameters are chosen from the literature in such a way that they have significantly affected the dimensionless boundary layer (BL) profiles. Also, the non-dimensional profiles of velocity, temperature, and concentration observe two different trends (increasing and decreasing) for diverse values of the dimensionless parameters.

Triple-Diffusive Bioconvection Flow of Sutterby Nanofluid Over an Oscillatory Stretchable Surface Immersed in a Darcy-Forchheimer Porous Medium

To respond to the demands of modern technological processes, the employment of nanofluids to maximize energy efficiency has been a topic of interest to many scientists. The stability of such nanofluids can be appropriately enhanced with the use of gyrotactic microorganisms. In the current framework, we inspect the triple-diffusive bioconvection flow of electro-magnetized Sutterby nanofluid via an oscillatory stretchable surface with Brownian diffusion of both nanoparticles and microorganisms, thermophoresis, buoyancy, and inertial forces. With the utilization of acceptable dimensionless variables, the governed flow equations are first metamorphosed into non-dimensional form, and solutions of the resulting equations are computed using the overlapping grid spectral collocation scheme. The rationale for choosing this numerical approach is provided by computing residual errors and condition numbers. The significance of physical parameters on the quantities of engineering interest and flow profiles is discussed. The main results include that reduced surface shear stress and minimal oscillatory nature of velocity are achieved with the inclusion of porous media, inertial forces, bioconvection, and nanofluid buoyancy forces. Temperature and rate of heat transfer are upsurged with the existence of variable thermal conductivity, nonlinear radiation, and convective heat conditions, which advocate that such features promote superior heat transport within the Sutterby working fluid. Growth in solutal Dufour Lewis number increases solutal concentration while reducing solutal-mass transfer rate. Improvement in microbial Brownian diffusion parameter causes enhancement in the rate of motile microorganisms transfer and reduction in the concentration of gyrotactic microorganisms. This implies that the random motion of motile microorganisms plays a prominent role in the dynamics of microorganisms.

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.

Nanofluid bioconvective transport for non-Newtonian material in bidirectional oscillating regime with nonlinear radiation and external heat source: Applications to storage and renewable energy

The enhanced thermal performances of nanofluids reports different applications in solar systems energy storage and renewable energy. The renewable enhancement in thermal management systems is predicted in recent years. Following such motivations of nanomaterials in the renewable systems, the objective of current wok is to present nanofluid flow with suspension of non-Newtonian material with additional impact of external heating source. The Williamson nanofluid is signifies to suggests the rheological impact of nonlinear material. The stability of nanofluid is reported with bioconvection assessment due to microorganisms. The thermal model is further modified in view of nonlinear radiative electromagnetic source and activation energy. Time dependent flow is induced due to bidirectional accelerating surface with uniform magnitude. The formulation of problem is based in partial differential systems. The solution procedure is based on analytical homotopy analysis technique. The thermal outcomes in variation of parameters are observed. It is claimed that external heat presentation can boosted the thermal profile more exclusively. With increasing the Williamson fluid parameter, the heat and mass transfer phenomenon can be improved.

Falkner-Skan aspects of a radiating (50% ethylene glycol + 50% water)-based hybrid nanofluid when Joule heating as well as Darcy-Forchheimer and Lorentz forces affect significantly

Falkner-Skan aspects are revealed numerically for a non-homogeneous hybrid mixture of 50% ethylene glycol-50% water, silver nanomaterials Ag, and molybdenum disulfide nanoparticles MoS2 during its motion over a static wedge surface in a Darcy-Forchheimer porous medium by employing the modified Buongiorno model. The Brownian and thermophoresis mechanisms are included implicitly along with the thermophysical properties of each phase via the mixture theory and some efficient phenomenological laws. The present simulation also accounts for the impacts of nonlinear radiative heat flux, magnetic forces, and Joule heating. Technically, the generalized differential quadrature method and Newton-Raphson technique are applied successfully for solving the resulting nonlinear boundary layer equations. In a limiting case, the obtained findings are validated accurately with the existing literature outcomes. The behaviors of velocity, temperature, and nanoparticles volume fraction are discussed comprehensively against various governing parameters. As crucial results, it is revealed that the temperature is enhanced due to magnetic field, linear porosity, radiative heat flux, Brownian motion, thermophoresis, and Joule heating effects. Also, it is depicted that the hybrid nanoliquids present a higher heat flux rate than the monotype nanoliquids and liquids cases. Moreover, the surface frictional impact is minimized via the linear porosity factor. Furthermore, the surface heat transfer rate receives a prominent improvement due to the radiative heat flux inclusion.

Exploration of diffusion-thermo and thermo-diffusion on the nonlinear radiative heat flow of a conducting fluid over a permeable surface

The featured problem explores the impact of cross-diffusion on the two-dimensional electrically conducting flow of a viscous liquid over a nonlinearly stretching sheet through a permeable medium. An inclusion of radiative heat energizes the heat transport phenomenon whereas the solutal transfer enriches by the conjunction of the chemical reaction. To justify the behavior of electromagnetic radiation, the Rosseland approximation is used by considering nonlinear thermal radiation. Further, the convective boundary conditions also affect the flow properties. The approachable transformations are employed to get a suitable non-dimensional form of the governing equations for the formulated problem. Due to the complex nature of the distorted equations, the system of equations is solved using an in-built code bvp5c predefined in MATLAB. The computation is carried out for the involvement of the suitable values of contributing parameters on the flow characteristics and along with the simulations of the rate coefficients. Further, the assigned particular parameters present an outcome that validates with a good correlation. Finally, the important outcomes are — enhanced suction due to the permeability of the surface augments the fluid velocity whereas the trend is reversed in the case of injection. The augmentation in the fluid temperature is exhibited for the radiating heat but the reacting species attenuates the fluid concentration.

MHD 3D Mixed Upper Convective Flow of Maxwell Nanofluid Flow Past in the Presence of Diffusion Thermo and Thermophoresis Effect using Nonlinear Radiative Heat Flux

This article aims to investigate the impact of nanoparticles and magnetohydrodynamics (MHD) on the transfer of heat and mass using a three-dimensional upper-convected Maxwell (UCM) nanofluid flow across a stretched surface. A nonlinear radiative heat flow was included in formulating the equation that describes energy. The nonlinear partial differential equations of the issue are transformed into ordinary differential equations utilizing the similarity transformation. These equations are then solved using the well-known shooting approach in conjunction with the Runge-Kutta integration process of order four. To increase the dependability of our findings, make use of the MATLAB. On the velocities, temperatures, and concentrations of the particles, the graphical and numerical representations of the effects of the main parameters, such as the Dufour parameter, the Brownian motion parameter, the Prandtl number, the thermophoresis parameter, and the magnetic parameter, are presented. It has been shown that the flow velocity decreases as a function of both the linear and nonlinear thermal radiation parameters. In addition, increasing values of the Brownian motion parameter have the effect of reducing the nanoparticle concentration profile