Nonlinear Thermal Radiation Research Articles

A numerical investigation of the chemically reactive maxwell nanofluid flow over a convectively heated rotating disk using Darcy–Forchheimer porous medium

This study investigates the convective heat transfer characteristics in the vicinity of a stagnation point for the flow of Maxwell nanofluid over a porous rotating disk. The analysis takes into account the complex inert-active effects arising from nonlinear thermal radiation, activation energy, and the presence of a Darcy–Forchheimer medium. Through numerical simulations, the enhancement of heat transfer due to the addition of nanoparticles is explored, considering their impact on heat transport. The rotational and porous characteristics of the disk, coupled with nonlinear thermal radiation and activation energy effects, are crucial factors in shaping the overall heat transfer behavior. The study aims to provide valuable insights into the complicated interactions of these phenomena, contributing to the understanding of advanced heat transfer processes and their potential applications in various engineering systems. Using suitable variables to convert the system of leading equations to dimensionless form has then been evaluated by employing the bvp4c approach. It has been revealed that Radial flow has retarded with an upsurge in Deborah number, inertial factor, and porous factor while has upsurge with growth in rotational factor. Angular velocity has declined with higher values of Deborah number, and porous factor and has upsurged with escalation in inertial and rotational factors. Azimuthal flow has weakened with an upsurge in porous factor and has augmented with growth in Deborah number, inertial factor, and rotational factor. Thermal profiles have augmented with an upsurge in rotational, porous, inertial, thermophoresis, Brownian, and radiation factors, and Deborah number has declined with growth in the Prandtl number. Concentration distribution has declined with an upsurge in Schmidt number, Brownian motion factor, rotation factor, and porous factor, while has grown with the escalation in chemically reactive, thermophoresis, inertial factors, and Deborah number.

The significance of quadratic thermal radiative scrutinization of a nanofluid flow across a microchannel with thermophoretic particle deposition effects

Abstract The investigation of thermal radiation and thermophoretic impacts on nano-based liquid circulation in a microchannel has a significant impact on the cooling of microscale equipment, microliquid devices, and many more. These miniature systems can benefit from the improved heat transfer efficiency made possible by the use of nanofluids, which are designed to consist of colloidal dispersion of nanoparticles in a carrier liquid. Understanding and precisely modeling the thermophoretic deposition (TPD) of nanoparticles on the channel surfaces is of utmost importance since it can greatly affect the heat transmission properties. This work examines the complex interaction between quadratic thermal radiation, magnetohydrodynamics, and TPD in a permeable microchannel. It aims to solve a significant knowledge gap in microfluidics and thermal and mass transport. The governing equations are simplified by applying suitable similarity restrictions, and computing solutions to the resulting equations is done using the Runge‒Kutta Fehlberg fourth‒fifth-order scheme. The results are shown using graphs, and significant engineering metrics are analyzed. The outcomes show that increased Eckert number, magnetic, and porous factors will improve the thermal distribution. Quadratic thermal radiation shows the greater thermal distribution in the presence of these parameters, while Linear thermal radiation shows the least thermal distribution. The rate of thermal distribution is higher in the linear thermal distribution case and least in the nonlinear thermal radiation case in the presence of radiation and solid fraction factors. The outcomes of the present research are helpful in improving the thermal performance in microscale devices, electronic devices cooling, health care equipment, and other microfluidic applications.

Stagnation point slip flow of Al2O3/γ-Al2O3 nanofluids subject to Lorentz force and nonlinear thermal radiation over a stretching sheet

The flow analysis of Al 2 O 3 and γ ‐Al 2 O 3 nanofluids near a stagnating point over a stretching sheet having velocity slip at the solid–liquid interface is presented. There is a quadratic surface temperature and a linear deformation acting on the wall boundary. Due to the uniformly applied transverse magnetic flux, the Lorentz force has an impact on the flow. The effect of nonlinear TR is integrated into the heat equation. Further, water H2O and EG C2H6O2 are base fluids. The governing boundary equations are translated into dimensionless ODEs using relevant similarity variables and solved numerically using the Runge-Kutta algorithm scheme (fourth-order) and the shooting algorithm. The impacts of the parameters, that is, velocity ratio ε , velocity slip δ , nonlinear TR Rd, the temperature ratio parameter θ w , and magnetohydrodynamics M are observed for the velocity h 2 ≤ y ≤ 0 and temperature θ ( η ) fields graphically. The results of local skin friction and local Nusselt number are shown in the table. A comparative analysis of the present results and the results of previous studies has also been made in tabular form. The research indicates that water as a base fluid gives better thermal conductivity than ethylene glycol. The consequence of TR enhances the heat transfer rate of both Al 2 O 3 / γ ‐Al 2 O 3 with H2O and C2H6O2.

Application of Artificial Neural Networks Modelling for Analyzing Non-Newtonian Fluid Flow Over Porous Media with an Induced Magnetic Field

The goal of this work is to better comprehend how enhanced thermal transfer, which really increased the induced magnetic field of hybrid nanofluid, may alleviate the growing heat density of tiny and other technological processes. Non-Newtonian fluid, like Oldroyd-B fluid is encrypted for a given physical model. Furthermore, copper and alumina hybridize in sodium alginate to produce a homogeneous, very diluted combination. The non-linear PDE system of equations is transformed into an ordinary differential system by applying the appropriate self-similarity variables. For this stage of the work, we built a mid-rich integrated ANN-LMBP that is envisioned with non-linear thermal radiation and heat production. Graphical depictions are used to demonstrate the interplay between various skewing. The entropy production of the Oldroyd-B fluid slopes with temperature ratio for all comparing scenarios, while Bejan number exhibits a declination with increase in Brinkman number. For uses including thickening, gelling, emulsifying, stabilizing, and texturizing, the predictions come true. Since sodium alginate is a standard component that is utilized in many cuisines today, including ice cream, jelly, acidic milk drinks, sauces, fast noodles and beer.

Numerical Computational of Chemically Reactive Hybrid Nanofluids with Melting Phenomena Passing Through a Disk: Comparative Study

This paper aims to investigate the solutions for the axisymmetric flow and heat transfer coming from a permeable disk in hybrid nanofluids. The nanofluids are under the influence of thermal radiation and contain magnetohydrodynamics and melting phenomena. For this, the momentum and temperature mathematical model is developed to investigate the axisymmetric flow of two-dimensional hybrid nanofluids, containing nanoparticles and a base fluid. Using appropriate similarity variables, nonlinear partial differential equations have been transformed into ordinary differential equations. These are further solved using the function bvp4c, which is built into MATLAB software. The physical behavior of parameters is discussed for the values on the basis of visuals and tables. The analysis further shows an increase in the local Nusselt number and skin frictional coefficient due to nonlinear thermal radiation and magnetic parameters. The results may be promising for the applications of hybrid nanofluids in heat transfer and cooling systems of all modern industries. The authors have confidence in their study due to the novelty of the results and underline the numerous practical utilities of hybrid nanofluids.

Artificial Neural Network and Numerical Simulation for Magneto Hydrodynamics Hybrid Nanofluid Flow Towards a Stretching Cylinder

The present study focuses on influence of boundary layer flow of heat transfer analysis on hybrid nanofluid through a stretching cylinder. Moreover, the impressions of porous medium, heat generation/absorption are discussed. Further, the stimulus of non-linear thermal radiation and MHD are part of this investigation. For motivation, the Artificial Neural Networks also deliberated. Arrogate similarity variables are employed to transform the governing modelled PDEs into a couple of highly nonlinear ODEs. A numerical approach based on the shooting approach with MATLAB bvp5c built in function is employed for solution of the set of resulting ODEs and acquired outcomes are compared with existing literature, obtained results an exceptional agreement. Artificial nerve cells or node locations form a network of nerves, a contemporary name for a chain composed of human brain cells. The impact of physical parameters like Magnetic Field, Eckert number, Porosity, Prandtl number, Heat generation, thermal radiation, parameters on dimensionless velocity and energy fields are discussed through graphs and tables. The velocity profile decreased by about 42% when the magnetic field parameter values increases from 0.5 to 1.5. On the other hand increased by 78% on energy profile. The energy profile improved by about 97% when the Eckert number values increases from 1.0 < Ec < 3.0. The current model may be applicable in real life practical implications of employing Water–Cu/Ag/Al2O3 nanofluids on cylinders encompass enhanced heat transfer efficiency, and extended component lifespan, energy savings, and environmental benefits. This kind of theoretical analysis may be used in daily life applications, such as industrial and biomedical industries.

Influence of quadratic thermal radiation and activation energy impacts over oblique stagnation point hybrid nanofluid flow across a cylinder

Quadratic thermal radiation is a fundamental term within the field of radiative heat transfer, which pertains to the interaction of thermal radiation. It encompasses a quadratic correlation between temperature and radiative qualities. Although linear thermal radiation is more prevalent in numerous everyday applications, non-linear thermal radiation is important in some situations, particularly where a more precise representation of the radiative transfer of heat is required. The phenomenon assumes a crucial function in some contexts that need enhanced accuracy in modeling radiative heat transfer. In view of this, the present investigation is carried out to examine the hybrid nanofluid flow across a cylinder under the influence of quadratic, nonlinear and linear thermal radiation and activation energy. The governing system of nonlinear differential equations is transformed into a system of ordinary differential equations via similarity transformations. The current study presents the results utilizing the shooting and Runge-Kutta Fehlberg 45 numerical scheme. The outcomes show that the curvature constraint will improve all three profiles while solid fraction decreases velocity and raises the other two profiles. Quadratic thermal radiation shows less temperature distribution, followed by linear and non-linear thermal radiation cases. The rate of thermal distribution improves 0.60 % for linear thermal radiation case, 0.52 % for nonlinear thermal radiation case and 0.656 % for quadratic thermal radiation case from hybrid nanofluid to nanofluid. Further, the rate of mass transfer shows 0.068 % improvement for from hybrid nanofluid to nanofluid. The results provide useful insights that may be used to enhance system efficiency across various applications, including but not limited to the mechanics of fluids, chemical technology, and thermal administration.

Lie group analysis and SQLM of entropy generation of MHD nonlinear radiative micropolar nanofluid flow with thermophoresis and Brownian motion

This study investigates the entropy generation in hydromagnetic mixed convection of a micropolar fluid flowing over a stretchable sheet, taking into account various influential factors such as nonlinear thermal radiation, Ohmic dissipation, uniform heat source/sink effects, chemical reaction, thermophoresis, and Brownian motion. The Spectral Quasilinearization Method (SQLM) is employed, which transforms nonlinear equations into a series of linearized ones, streamlining the solving process. Additionally, Lie group analysis is utilized to identify symmetries and derive similarity transformations crucial for converting partial differential equations into coupled ordinary differential equations, which are then solved numerically. A comprehensive sensitivity analysis is conducted on critical parameters, including the Darcy parameter, Biot number, Brinkman number, nonlinear convection parameter, and chemical reaction parameter. This analysis explores the impacts of these parameters on various flow profiles, such as velocity, temperature, microrotation, concentration, and entropy generation, enriching the depth and practical relevance of the findings. The results reveal that increasing the Brinkman and Reynolds numbers enhances entropy generation profiles while increasing the coupling parameter reduces them. The focus on entropy generation analysis provides valuable insights into energy utilization and system efficiency, particularly in micropolar fluid dynamics. Furthermore, the study underscores the practical implications of its findings by highlighting their relevance in evaluating the effectiveness of industrial processes, especially those related to energy conversion and heat transfer phenomena.

Feasibility of integrated numerical and Adaptive Neuro-Fuzzy Inference System models in predicting the thermophysical properties of unsteady coupled micropolar–Casson hybrid nanofluids

This article aims to probe postulated phenomena using a paired micropolar and Casson hybrid fluid over a rotating disk. The intension to design a numerical technique (Runge–Kutta fourth-order along with shooting technique) integrated Adaptive Neuro-Fuzzy Inference System (ANFIS) envisioned with a thermal and exponentially space-dependent heat source, nonlinear thermal radiation and entropy production is developed in this phase of work. To ensure that, a nonlinear partial differential equation set of equations has been transformed into an ordinary differential equation by using the proper self-similarity variables. The model's research results, with a few notable outliers, are mostly consistent with those from prior research that was merged into the dataset used to train the ANFIS model. With the impact of active factors, the results are esthetically exhibited for numerous profiles. This displays that with the rise in magnetic field and radiation, the velocity and temperature profiles increase sharply, resulting in a contradiction phenomenon with the decreasing electric field inputs. Also, tilting of vortex viscosity, spin gradient viscosity and microinertia density on the various microrotation components displays inclination. Moreover, ANFIS training was exploited to analyze the approximate solutions for specific scenarios, and the developed ANFIS was evaluated against a testing dataset to emphasize its performance. Due to their longer render, the nanoparticles exploited here are deemed suitable for use in bone implants, iodinated agents for blood imaging and red blood cell stimulation. Thus, the results of this study may be applied to therapeutic anemia therapies.

Local non-similar solution for MHD mixed convection flow of a power law fluid along a permeable wedge with non-linear radiation

In this study, a novel investigation for the effects of non-linear thermal radiation and magnetic field is conducted on mixed convection flow of non-Newtonian fluid along a permeable wedge. Power-law model is used as a non-Newtonian fluid model that predicts shear thinning/thickening effects. For theoretical analysis, a mathematical model in terms of nonlinear PDEs are transformed into a dimensionless non-similar model which is treated as a non-linear ODE when streamwise coordinate is assumed as a constant. The obtained system is solved numerically using the built-in ‘bvp4c’ technique, and the effects of the pertinent parameters is examined through plots illustrating the velocity profiles, temperature distributions, Nusselt number, and skin friction coefficients. From the results, it is revealed that heat transfer rate accelerates in occurrence of assisting flow as compared to opposing flow and further in the existence of thermal radiation, heat transfer rate becomes higher which is crucial in industry because more enhancement in heat transfer rate is required. Skin friction coefficient reduces in the occurrence of opposing flow as compared to assisting flow and further reduction is noted by taking thermal radiation.

Nanoparticle aggregation kinematics and nanofluid flow in convectively heated outer stationary and inner stretched coaxial cylinders: Influenced by linear, nonlinear, and quadratic thermal radiation

The consequence of nanoparticle aggregation and convective boundary condition on the nanofluid stream past the co-axial cylinder with radiation impact is investigated in the present examination. The influence of linear, nonlinear, and quadratic thermal radiation on the nanofluid flow is analyzed. The outer cylinder stays stable, while the inner cylinder deforms horizontally in the axial direction, allowing fluid to flow. By using similarity variables, the governing equations are transformed into ordinary differential equations (ODEs). Subsequently, the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method is employed to solve the reduced ODEs. The upshot of several nondimensional terms on the temperature and velocity profiles is displayed with graphical representation. The comparison of linear, quadratic, and nonlinear thermal radiation on the thermal profile is illustrated. The upsurge in curvature parameter increases velocity and thermal profile. The increase in radiation parameter intensifies the temperature profile. The thermal profile improves with a rise in the values of radiation parameter. The radiation parameter generates thermal energy in the flow zone, which is why the temperature field has improved. The thermal Biot number exhibits an increasing response with temperature and thermal boundary layer thickness. The linear thermal radiation shows better heat transfer compared to quadratic and nonlinear thermal radiation.

Stochastic supervised networks for numerical treatment of Eyring–Powell nanofluid model with Darcy Forchheimer slip flow involving bioconvection and nonlinear thermal radiation

The aim of this study is to estimate the solution of Eyring–Powell nanofluid model (EPNFM) with Darcy Forchheimer slip flow involving bioconvection and nonlinear thermal radiation by employing stupendous knacks of neural networks-based Bayesian computational intelligence (NNBCI). A dataset for the designed NNBCI is generated with Adam numerical procedure for sundry variations of EPNFM by use of several variants including slip constant, Schmidt number, mixed convection parameter, Prandtl number, and bioconvection Lewis parameter. Numerical computations of various physical parameters of interest on EPNFM are estimated with artificial intelligence-based NNBCI and compared with reference data values generated with Adam’s numerical procedure. The accuracy, efficacy, and convergence of the proposed NNBCI to successfully solve the EPNFM are endorsed through M.S.E, statistical instance distribution studies of error-histograms, and assessment of regression metric. The proposed dataset exhibits a close alignment with the reference dataset based on error analysis from level E[Formula: see text] to E[Formula: see text] authenticates the precision of the designed procedure NNBCI for solving EPNFMs. The executive and novel physical importance of parameters governing the flow, such as nanofluid velocity, temperature, and concentration profiles, are discussed. The observations imply that the presence of the slip constant, mixed convection parameter and Lewis number influences the velocity of the nanofluid. However, it is observed that temperature of the nanofluid declines for higher values of Prandl number while the concentration of nanofluid improves with increasing values of Schmidt number.

Numerical analysis of multiple slip effects on CuO /MgO/TiO2-water ternary hybrid nanofluid with thermal and exponential space-based heat source

In contemporary science, the efficiency of heat transfer holds paramount importance across various engineering applications, where nanofluids play a significantly influential role. Therefore the present study focuses on the significance of multiple slip in heat transfer of3-Dnatural convectional ternary hybrid nanofluid flow across a stretching sheet. The study investigates the implications of a temperature-dependent and exponentially space-based heat source, coupled with non-linear thermal radiation effects. Impact of magnetic field is further considered for the present investigation. The three dissimilar nanoparticles (CuO,MgO&TiO2) are dispersed in water as base fluid to improve the heat transfer. The system of partial differential equations is developed under considered assumptions. The Partial differential equations (PDEs) are transmuted into nonlinear coupled dimensionless system of ordinary differential equations (ODEs) by applying similarity transformations. The reduced dimensionless nonlinear equations are numerically solved by employing shooting scheme via bvp4c built-in function MATLAB. The properties of flow controlling parameters via velocity and thermal profiles are elaborated through graphs. The results designated that the x-direction velocity slip declines the velocity. The momentum profile (velocity profile) is declined for greater stretching ratio parameter. Furthermore, it is analyzed that the thermal field is boosted up for larger amounts of temperature base and exponential space-based heat source. It is concluded that heat conduction capacity is higher in ternary hybrid nanofluid than hybrid and mono nanofluids. Additionally, Prandtl number serves to enhance the Nusselt number with augmentation in Thermal radiation parameter. The physical applications of the considered model in solar energy, heat pumps, heat exchangers, air purifiers, the automotive industry, electrical chillers, turbines, nuclear networks, broadcasters, ships, and biotechnology.

Entropy generation and activation energy on nonlinearly thermo-radiative and magnetohydrodynamic heat transfer of Jeffrey nanofluid with non-uniform heat source/sink using SQLM

ABSTRACT Entropy generation and activation energy analysis on MHD heat and mass transfer of Jeffrey nanofluid under the impact of nonlinear thermal radiation and heat source/sink (non-uniform) over a linearly stretching sheet has been investigated numerically using Spectral Quasilinearization Method (SQLM). The Brownian motion with thermophoretic effects has been utilized. The basic equations concerned with the problem are solved numerically. The impacts of different governing physical parameters are analyzed on the velocity, temperature, and concentration fields, along with entropy generation, and Bejan number profiles are analyzed graphically. It is found that the concentration profiles have a mixed tendency with magnetic parameters. In addition, the temperature profiles increase in the presence of Brownian motion with thermophoresis effects, whereas the composite behavior is noticed on the entropy generation profiles. It is also found that both the temperature and concentration profiles diminish for various values of Deborah number while the velocity profile increases. Also, it is noticed that both the temperature profiles increase for enhanced values of the space-dependent and time-dependent parameters. Due to activation energy, the Bejan number profiles decrease, whereas the entropy generation profiles increase far away from the expandable sheet but decrease closer to the sheet.

Enhanced transport phenomena in Casson fluid flow over radiative moving surface: Influence of velocity and thermal slip conditions with mixed convection and chemical reaction

Researchers are interested in the non-Newtonian fluid flow with mixed convection because of its extensive use in industry and manufacturing. Additionally, thermal radiation in convective heat transfer is critical for thermal transmission regulation. As a result, the authors provide an in-depth study of how mixed convective effects on concentration and temperature impact mass, heat, and non-Newtonian Casson fluid flow. A transverse magnetic field and vertical permeable stretched sheet affect the fluid. Nonlinear thermal radiation, Brownian motion, thermophoresis, velocity slip, and temperature slip are all examined. The governing nonlinear partial differential equations (PDEs) can be changed into especially nonlinear coupled ordinary differential equations (ODEs) with the right similarity transformation. We use the RK-45 technique in Mathematica to solve the system to accommodate different physical attributes. The data are analyzed graphically. This study shows that increasing the free convection parameters [Formula: see text] and [Formula: see text] improves the velocity profile. However, the Casson parameter, magnetic field, velocity slip, and mass suction parameter lower it. Increasing [Formula: see text], and [Formula: see text] parameters lead to a higher temperature profile, whereas [Formula: see text], and [Formula: see text] parameters have the opposite. Increased concentration is shown with [Formula: see text] and [Formula: see text] parameters, whereas [Formula: see text] and [Formula: see text] have the opposite impact. Skin friction increases against [Formula: see text] and [Formula: see text] and reduces for S and M Heat transfer increases for [Formula: see text] and S whereas reduces for [Formula: see text] and [Formula: see text] Mass transfer increases for [Formula: see text] and [Formula: see text] and reduces for [Formula: see text] and [Formula: see text].

Numerical analysis of the heat transfer application on a convective tangent hyperbolic nanofluid flow over a porous stretching cylinder with stratification effects

The nanofluids has attractive applications in the industrials and engineering field because nanofluids offer the improvement in the thermal efficiencies of flow, which is very fruitful in the energy sector. This study emphases on the numerical exploration of heat and mass transfer efficiencies on a mixed convective flow of tangent hyperbolic nanofluid under the consideration of gyrotactic microorganisms. To analyze the magnetized boundary layer flow, the stratification boundary conditions are considered on the surface of the stretching cylinder. The thermal analysis involves the important features such as activation energy, nonuniform heat source/sink, and nonlinear thermal radiation. The flow model is altered into system of nonlinear ordinary differential equations by utilization of suitable similarity variables and Bvp4c solver on the MATLAB to find numerical solutions. The graphical and tabulated investigation is presented for various developing parameters thoroughly. The results indicate that by the increment of mixed convection parameters the fluid velocity accelerate consequently, whereas raising values of the Weissenberg number reduce the fluid velocity. TThe greater values of the Prandtl number lead to a decrease in fluid temperature, while the concentration of nanoparticles rises with the increase in activation energy parameters. Additionally, the heat transfer rate reduces due to stronger values of thermophoresis parameter, although reverse tendency is observed for the greater values of Brownian motion parameter.

Unsteady MHD flow analysis of hybrid nanofluid over a shrinking surface with porous media and heat generation: Computational study on entropy generation and Bejan number

The use of hybrid nanofluids in real-world situations is essential for enhancing the efficiency of heat transmission, especially in cooling semiconductor technology and industrial processes. The entropy generation on unsteady Al2O3-Cu/H2O hybrid nanofluid flow over a three-dimensional shrinking sheet is addressed numerically in this study, taking into account the effects of magnetohydrodynamic (MHD), nonlinear thermal radiation, porous media, heat generation, viscous dissipation, joule heating, and convective conditions. Using well-known non-similarity transformations, the model is carefully converted from partial differential equations (PDEs) to ordinary differential equations (ODEs). Afterwards, the behaviors of critical physical characteristics are uncovered across different parameter configurations by a numerical solution using the finite difference technique in bvp4c MATLAB. The velocity profiles of hybrid nanofluid grow proportionately with increases in the values of ϕ2,M,A,K and λ parameters. As Rd,θw,Ec,Bi,H and ϕ2 increase, the temperature of the hybrid nanofluid rises, but as M and A increase, the temperature falls. The local skin friction in both the x and y- directions is increased by enhancing the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, porous media K, and the ratio of strain rate λ parameter on the shrinking surface. The local Nusselt number is improved by cumulative the unsteadiness A, nanoparticle volume fraction ϕ2, magnetic M, and Biot number Bi parameter in the direction of a shrinking surface, while the Nusselt number decreases when Eckert number Ec, thermal radiation Rd, heat production H, and temperature ratio θw are improved. An upsurge in the magnetic parameter leads to the development of entropy generation. Increasing levels of the magnetic parameters led to a reduction in the Bejan number. At a nanoparticle volume fraction of 1 % and a nonlinearity radiation scenario, where the unsteadiness values are 0.5, the Nusselt number for hybrid nanofluid shows an estimated improvement of 10.55 % compared to regular nanofluid.

Advanced Computational Framework to Analyze the Stability of Non-Newtonian Fluid Flow through a Wedge with Non-Linear Thermal Radiation and Chemical Reactions

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation (Rd). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index (R), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f′(η), θ(η), and ϕ(η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (Cfx, Nux, and Shx) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase (M=0.01, 0.05, 0.1), then the solution bifurcates at different critical values, i.e., λc=−1.06329,−1.097,−1.17694. The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement.

Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate

Abstract Casson fluids containing carbon nanotubes of various lengths and radii on a moving permeable plate reduce friction and improve equipment efficiency. They improve plate flow dynamics to improve heat transfer, particularly in electronic cooling and heat exchangers. The core objective of this study is to investigate the heat transmission mechanism and identify the prerequisites for achieving high cooling speeds within a two-dimensional, stable, axisymmetric boundary layer. This study considers a sodium alginate-based nanofluid containing single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) and Casson nanofluid flow on a permeable moving plate with varying length, radius, and nonlinear thermal radiation effects. The plate has the capacity to move either parallel to or perpendicular to the free stream. The governing partial differential equations for the boundary layer, which are interconnected, are transformed into standard differential equations. These equations are then numerically solved using the Runge–Kutta fourth-order scheme incorporated in the shooting method. This research analyses and graphically displays the effects of factors including mass suction, nanoparticle volume fraction, Casson parameter, thermal radiation, and temperature ratio. Additionally, a comparison is made between the present result and the previous finding, which presented in a tabular format. The coefficient of skin friction decreases in correlation with an increase in Casson fluid parameters and Prandtl number. Heat transfer rate decreases with a variation in viscosity parameter, while it is increasing with an increase in Prandtl number. In addition, this study demonstrates that heat transfer rate for MWCNT is significantly higher than that of SWCNT nanoparticles. Thermal radiation and temperature ratio reduce the heat transfer rate, whereas nanoparticle volume fraction and Casson parameter enhance it over a shrinking surface.

Nonlinear heat radiation and mass transfer characteristics on MHD Walters’ B fluid flow through a porous medium over a stretching sheet

To handle the continuous thermal power supply is very important in thermal systems and industries, so magnetized heat transport with non-Newtonian fluid is an appropriate platform for thermal power energy. In view of this usefulness, this paper provides a numerical assessment of electrically conducting Walter's B fluid flow through nonlinear permeable stretching sheet subject to mixed convective, porous medium, and Newtonian heating phenomena. Thermophoresis and Brownian motion effects have been included in energy and species diffusion equations to account for the impacts of nonlinear thermal radiation, joule heating, heat source and chemical reaction. The system of governing equations has been reduced to dimensionless nonlinear coupled equations using similarity transformations. The bvp4c technique has been used to obtain the solution for velocity, temperature, and concentration distributions. We consider both regions of assisting and opposing flow and provide various tables and graphs to examine the impact of varying values of emerging factors. Heat source and thermal radiation characteristics are found to enhance the thermal boundary layer thickness, which may be used to dissipate heat. The magnetic parameter augmented the fluid temperature and decelerated the velocity field. The chemical reaction parameter accelerated the concentration distribution. Further, the Sherwood number, Nusselt number, and skin friction coefficient have been determined and compared well to prior research that has been published.