Nonlinear Radiation Research Articles

Classical-quantum simulation of non-equilibrium Marshak waves

In the radiation hydrodynamic simulations used to design inertial confinement fusion (ICF) and pulsed power experiments, nonlinear radiation diffusion tends to dominate CPU time. This raises the interesting question of whether a quantum algorithm can be found for nonlinear radiation diffusion which provides a quantum speedup. Recently, such a quantum algorithm was introduced based on a quantum algorithm for solving systems of nonlinear partial differential equations (PDEs) which provides a quadratic quantum speedup. Here, we apply this quantum PDE (QPDE) algorithm to the problem of a non-equilibrium Marshak wave propagating through a cold, semi-infinite, optically thick target, where the radiation and matter fields are not assumed to be in local thermodynamic equilibrium. The dynamics is governed by a coupled pair of nonlinear PDEs which are solved using the QPDE algorithm, as well as two standard PDE solvers: (i) Python's py-pde solver; and (ii) the KULL ICF simulation code developed at Lawrence-Livermore National Laboratory. We compare the simulation results obtained using the QPDE algorithm and the standard PDE solvers and find excellent agreement.

Impact of Thermal Energy on Water and Ethylene Glycol (50:50)-Based Rotating Hybrid Nanofluid Past A Riga Surface with Radiation, Homogeneous and Heterogeneous Reactions

Hybrid nanofluid is crucial in improving the efficiency of heat transmission in thermal engineering applications, particularly the cooling of electrical equipment, heat exchangers, fuel cells, printing machines, etc. This study sought to investigate the augmentation of heat and mass transmission by the use of a rotating hybrid nanofluid consisting of a mixture of gold and silver nanoparticles suspended in water and ethylene glycol (50:50) past a heated Riga surface with velocity slip and suction. The energy equation is constructed using nonlinear radiation and heat consumption. The impact of both homogeneous and heterogeneous processes on the hybrid nanofluid is also explored. The governing mathematical model begins with partial differential equations that are converted into ordinary differential equations using a suitable conversion technique. The results of numerical computations are recorded as graphs and tables using the bvp4c scheme in MATLAB. It is noticed that both directional velocities undergo significant negative changes as a result of enhanced values of the rotational parameter. The higher levels of the radiation parameter resulted in significant enhancements in the thermal profile. The falling behavior of the nanoparticle concentration profile is recorded against a greater quantity of both chemical reaction parameters. Based on our analysis, when the Biot number changes from 0.4 to 0.8, the most significant heat transmission gradient occurs.

Robust Multimodal Image Matching Based on Radiation Invariant Phase Correlation

Abstract. Due to the influence of nonlinear radiation distortion and geometric deformation, achieving multimodal image matching remains a challenging task. To address these issues, this paper proposes a method called radiation invariant phase correlation (RIPC) to simultaneously estimate the rotation, scale, and displacement changes of multimodal image pairs. Firstly, based on the local structure characteristics of the image itself, we harness the nonlinear invariance of kernel canonical correlation analysis to devise the multimodal local self-correlation (MLSC) descriptor. This descriptor is resilient to nonlinear radiative differences, as well as local rotation and scale variations. Subsequently, we incorporate the log-polar coordinate transformation to capture the overall rotation and scale changes in the image, enabling independent representation of these factors on the Cartesian coordinate system. Finally, drawing upon the continuity of displacement estimation, as well as rotation and scale estimation, we construct a five-dimensional descriptor tailored for phase correlation. Extensive experiments conducted on five open-source datasets demonstrate that our proposed method surpasses state-of-the-art (SOTA) techniques in matching performance. Furthermore, our RIPC method achieves matching accuracy within 2-pixel threshold, which underscores its effectiveness in multimodal remote sensing image matching.

Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks

Abstract Hybrid nanofluids (HNFs) have outstanding energy transfer capabilities that are comparable to mono-nanofluids. Materials had appliances in obvious fields such as heat generation, micropower generation, and solar collectors. The objective of this study is to investigate the new aspects of convective heat transfer in an electrically conducting Carreau HNF situated between two parallel discs. In addition to the presumed stretchability and rotation of the discs, physical phenomena like nonlinear radiation, viscous dissipation, Joule dissipation, and heat generation and absorption are considered. The Cu and TiO2 nanoparticles dispersed in engine oil to understand the intricate phenomenon of hybridization. The Tiwari and Das nanofluid model is employed to model the governing partial differential equations (PDEs) and then simplified using boundary layer approximation. The suitable transformations of similarity variables are defined and implemented to change the set of formulated PDEs into ordinary differential equations. The reduced system is solved semi-analytically by the homotopy analysis method. The influences of involving physical parameters on the velocity and temperature are plotted with the help of graphical figures. This study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, our research provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers, and microelectronics.

Bioconvection across a revolving sphere under the influence of bilateral chemical reactions with temperature- and space- dependent heat generation

This paper discusses the time-dependent mixed convection flow of nanofluids (Al2O3-water) due to a stagnation-point over a rotating sphere in the presence of motile microorganisms. The suspension is considered to be electro-conducting and Joule heating impacts are not neglected. Exponential behaviors are considered for the included heat generation and chemical reaction influences. Besides, the non-linear radiation flux takes place in the flow area. Computational analyses are introduced for the problem formulations after converting them to similar forms. From the major results, the exponential heat generation enhances the temperature distributions while the exponential behaviors of the chemical reaction have negative influences on the nanoparticle concentration. Also, the skin friction coefficients in x− and z−directions get higher values when the rotational and the mixed convection parameters are rising. Further, the thermal scenario diminishes with increasing nanoparticle diameter, however the thermal radiation factor and the ratio between the liquid and the nanolayer conductivity significantly enhance the thermal characteristics of the water-based Al2O3 nanofluid. The findings offer practical information that might be applied to improve system performance in a number of fields, which could involve fluid mechanics, pharmaceutical technology, and thermal management, among others.

Nonlinear Radiative Response to Patterned Global Warming due to Convection Aggregation and Nonlinear Tropical Dynamics

Abstract Climate responses to global warming exhibit large dependence on the spatial pattern of sea surface temperature (SST) changes. A Green’s function (GF) approach—predicting the global climate response to a complex SST pattern change as the linear superposition of the response to finite-area SST perturbations evaluated in isolation—has been used to systematically evaluate and understand the top of atmosphere (TOA) radiation response to patterned warming. However, in general, the linear GF approach fails for TOA radiation reconstruction under future global warming scenarios in coupled models. Here, we show that the linear superposition of global mean TOA radiation responses to large SST warming perturbations at multiple patches (the GF approach prediction) overestimates the actual response to simultaneous multipatch perturbation. This is because the linear superposition overestimates tropical large-scale convection aggregation strengthening upon localized heating that enhances longwave radiative cooling, which is further explained by the overestimation of circulation response and associated horizontal water vapor transport. The nonadditivity of TOA radiation response is caused by the nonadditivity of convection aggregation, ultimately rooted in nonlinear tropical dynamics. We also demonstrate that the prediction error of the GF approach grows with decreasing patch size (equivalently, increasing patch number). We conclude that using the GF approach to predict future climate change could overestimate longwave radiative cooling and underestimate (effective) climate sensitivity. Numerical experiments may be used to identify specific perturbation patterns where the errors are smaller than the signal. Our research also highlights that an increase in the degree of large-scale convection aggregation has a nonlinear and negative feedback for mean warming.

Three-dimensional bioconvection in a nanofluid film over a wedge surface with entropy generation and nonlinear radiation: A revised Buongiorno model

ABSTRACT The advances in the field of nanotechnology tends to improve the rate of heat extraction and transmission from foreseeable causes and has fascinated researchers and scientists. Furthermore, nanofluids are having a useful impact on various fields such as nuclear industries, powered lasers, chilling of microelectronic devices, solar energy capture, transformers oil cooling, and in cancer diagnosis. Hence, magnetohydrodynamic (MHD) three-dimensional bioconvective flow of nanofluid accommodating gyrotactic microorganisms over a wedge surface with zero nanoparticles mass flux boundary conditions is studied, using large Reynolds number approximation. The additional novelty of the study is the implementation of the revised Buongiorno model, which deliberates the effects of thermo-migration and Brownian diffusion of nanoparticles, together with passive control of nanoparticles fraction on the wedge surface. The self-similar form of conservation equations of energy, nanoparticle fraction, gyrotactic microorganisms, and momentum are handled numerically. T The results of the Blasius and the Hiemenz flows are retrieved as special cases of the model. It was found that the temperature of the nanofluid increases considerably when considering the nonlinear thermal radiation compared to the linear radiant heat. Increasing the strength of the Brownian diffusion increases the heat transport but reduces the mass transport.

Impact of non-linear radiation on magneto - Casson fluid suspended hybrid nanomaterials in sodium alginate: Smarter textiles

BackgroundThe combination of sodium alginate (SA) and nanoparticles in Casson nanofluids can have several advantages in textile applications such as to enhance the dye absorption and finishing properties and uniform and controlled coatings on complex shapes of the fabric and garments with intricate designs or three-dimensional textile structures etc. These fascinating properties attracted us to work on this article, a Casson hybrid nanoflow under the influence of magnetic effects past a curved stretching surface. Key terms & problem definitionThis study examines the heat transfer characteristics of Casson nanofluid flow over a stretching sheet with nonlinear thermal radiation and convective boundary conditions. A Casson fluid is a non-Newtonian fluid that exhibits a yield stress, meaning it behaves like a solid below a certain shear stress. Nonlinear thermal radiation accounts for the effects of temperature-dependent radiative heat transfer. Convective boundary conditions simulate the heat exchange between the fluid and a surrounding environment. The nanoflow has its base fluid as Sodium Alginate (SA) and a mixture of Silver (Ag) and Titanium oxide (TiO2) is suspended in the fluid. MethodologyThe nanoflow model is cracked numerically employing Runge-Kutta Fehlberg technique along with shooting method. Results of flow affecting parameters on the flow characteristic quantities and engineering quantities are portrayed and presented through graphs and tables. Key findingsHybrid Nanoflow momentum decreases with an increase in the Casson parameter due to the yield stress which quite helps in the controlled and complex shape printing on the garments. The temperature of the nanofluid increases with an increase in nonlinear radiation parameter. In the presence of Ag and TiO2 nanoparticles, the non-linear radiation parameter becomes essential for managing their intricate impact on heat transfer within the fabric. Practical relevanceImproved heat transfer can significantly reduce drying times, leading to increased productivity. More efficient heat transfer can reduce energy consumption. Reduced viscosity can allow for better penetration of fluids into fabrics, leading to more uniform dyeing and finishing. Casson hybrid nanofluids can accelerate the dyeing process and improve colour uniformity. Casson hybrid nanofluids can be used in finishing processes to enhance wrinkle resistance and improve fabric appearance.

Unified analytical theory of nonlinear optical diffraction by nonlinear gratings

When a pump laser shines upon a periodically poled lithium niobate (LN) thin plate nonlinear grating, second-harmonic generation (SHG) and its nonlinear diffraction occurs, with the nonlinear Raman–Nath diffraction (NRND), nonlinear Bragg diffraction (NBD), and nonlinear Cerenkov radiation (NCR) being several prominent examples. In this work we build and present a unified analytical theory to solve SHG for the NRND, NCR, and NBD processes from LN domains, domain walls, and defects. We find that the critical physical entity that governs the nonlinear diffraction is the effective nonlinear coefficient for each Fourier wave component. The analytical theory has a great generality and applicability scope. It allows us to retrieve and analyze everything about the dependence of SHG nonlinear diffraction on a series of physical and geometrical parameters such as the pump laser intensity, polarization, incidence polar and azimuthal angles, the LN thin plate thickness and its crystalline orientation, LN domain size and pitch, domain wall thickness and crystalline configuration, defect size and crystalline configuration, and the SHG diffraction beam angle and polarization. The analytical theory also enables us to analyze deeply the similarities and differences of the three nonlinear diffraction processes NRND, NCR, and NBD, build a smooth and broad connection bridge among these three processes, and construct a unified physical picture to understand, describe, and exploit these three processes of seemingly big difference. Besides, the analytical theory can be applicable to handle nonlinear diffraction by domains, domain walls, and defects in other more complicated 2D and 3D nonlinear gratings made from LN and other nonlinear crystals. Finally, the analytical theory can help to build a bridge connecting the extrinsic SHG nonlinear diffraction properties with the intrinsic domain poling and inversion material and physical properties of LN and other nonlinear crystals and explore novel nonlinear optical devices and technologies.

First principles investigations of linear and nonlinear optical, radiation shielding and thermoelectric properties of the non-centrosymmetric Ba-based chalcogenides Ba2In2X5 (X=S, Te)

We explore the structural, elastic, optoelectronic, Radiation Shielding, and thermoelectric properties of Ba2In2X5 (X = S, Te) using first-principles computations and semi-classical Boltzmann Transport equations. These materials are classified as semiconductors exhibiting band gaps of 2.0 eV and 3.0 eV for both investigated NLO compounds that have more significant direct band gaps of superior optical birefringence and second-order NLO coefficients. The bonding properties have been investigated by analyzing the electron charge density (ECD) contour of the (1 0 1) crystallographic plane. It is clear from the reflectivity spectra that both compounds have a high degree of reflectivity, which could make them useful as UV and visible light shields. From 0 to 14.0 eV, the approximated reflectivity values, R (ω), are displayed against the incident photon energy. Therefore, the reflectivity is around 30 % before E ≈ 12.0 eV and 40 % reflection at ∼13.0 eV. Phase matching is possible for both compounds detected, as shown by the birefringence computations. Furthermore, the radiation shielding properties of Ba2In2S5 and Ba2In2Te5 have been evaluated using Phy-X software, demonstrating their potential effectiveness in medical and nuclear energy applications. The thermoelectric properties display N-type nature at low temperatures when the Seebeck coefficient changes from N to P-type at higher temperature ranges. These compounds have remarkable optical and thermal properties, rendering them highly attractive materials for thermoelectric and optoelectronic devices.

Simulating Nonlinear Radiation Diffusion Through Quantum Computing

The recent success of the fusion ignition experiment at Lawrence-Livermore National Laboratory has renewed excitement for inertial confinement fusion. Designing such experiments relies on computational modeling using radiation hydrodynamic codes run on massively parallel supercomputers which simulate hydrodynamic flows, radiation diffusion, and thermonuclear burn. Constructing a quantum algorithm for radiation hydrodynamics that provides a quantum speedup is of great interest. A recent quantum algorithm that solves the Navier-Stokes equations of hydrodynamics with a quadratic speedup marks a first step towards this goal. Here we take the next step and present a quantum algorithm for nonlinear radiation diffusion that also has a quadratic speedup. To verify the algorithm we consider radiation striking a cold, optically thick target that generates a Marshak wave in the target. Results of numerical simulation of the quantum algorithm are compared with those of a standard partial differential equation solver and excellent agreement is found.

Fast low-temperature irradiation creep driven by athermal defect dynamics

The occurrence of high stress concentrations in reactor components is a still intractable phenomenon encountered in fusion reactor design. Here, we observe and quantitatively model a non-linear high-dose radiation mediated microstructure evolution effect that facilitates fast stress relaxation in the most challenging low-temperature limit. In situ observations of a tensioned tungsten wire exposed to a high-energy ion beam show that internal stress of up to 2 GPa relaxes within minutes, with the extent and time-scale of relaxation accurately predicted by a parameter-free multiscale model informed by atomistic simulations. As opposed to conventional notions of radiation creep, the effect arises from the self-organisation of nanoscale crystal defects, athermally coalescing into extended polarized dislocation networks that compensate and alleviate the external stress.

Entropy generation of Williamson hydromagnetic non-linear radiative nanofluid flow near a stagnation point over a porous stretching sheet

Purpose This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous stretched sheet near a stagnation point. Also, the qualities of viscous dissipation, Cattaneo–Christove heat flux and Arrhenius activation energy are taken into account. Thermophoresis, Brownian motion and Joule heating are also considered. Design/methodology/approach The Navier–Stokes equation, the thermal energy equation and the Solutal concentration equations are the governing mathematical equations that describe the flow and heat and mass transfer phenomena for fluid domains. By using the proper similarity transformations, a set of ordinary differential equationss are retrieved from boundary flow equations. The classical Runge–Kutta fifth-order algorithm along with the shooting technique is implemented to solve the obtained first order differential equations. Findings The study concludes that the temperature distribution boosting for thermal radiation, magnetic field and Eckert number where as the velocity and entropy generation escalate for the Williamson parameter, diffusion parameter and Brinkman number. The skin-friction and heat and mass transfer rate increases with the fluid injection. In addition, tabulated values of friction drag and rate of heat and mass transfer for various values of constraints are provided. Originality/value The comparison of the present results is carried out with the published results and noted a good agreement.

Exploring swirling flow dynamics: Unsupervised machine learning in Maxwell hybrid nanofluid convection over an exponentially stretching cylinder with non-linear radiation effects

This article analyses the flow of Maxwell hybrid nanofluid induced by an exponentially stretching and rotating cylinder. The presence of non-linear convection, non-linear radiation, and magnetic field is also assumed. The factors covered in the study has a wide spectrum of application in various disciplines, and therefore we analyse the influence of different flow parameters after numerically solving the set of modelled differential equations. A data-free physics-informed neural network using a wavelet activation function is used to approximate the numerical solution. The reliability of the used methodology is validated by comparing the results of the limiting case with the available results. The paper demonstrates the effectiveness of using PINN in an unsupervised fashion to tackle fluid flow problems, showcasing their ability to provide reliable and accurate solutions without the need for extensive datasets. This approach highlights the potential of PINN to address complex fluid dynamics problems by utilizing physical laws within the neural network framework. From the numerical study, it is observed that hybrid nanofluid has a better rate of heat transfer compared to the nanofluid. Furthermore, radiation parameter and maxwell flow parameter is seen to exhibit significant impact of the flow profiles.

Thermo-physical properties of non-linear radiative flow of magnetized Ellis fluid comprising analysis of oxytactic microorganisms and nano-enhanced phase materials

The basic aim of existing analysis is to scrutinize the two-dimensional flow regime of Ellis model under the consideration of magnetic field. The effect of thermophoresis as well as Brownian motion for Ellis model with the impacts of parameters like thermal radiation, bioconvection of microorganisms and viscous dissipation are also deliberated. On the other hand, the features of bioconvection have been systematically examined for its extensive uses in microbial developed oil recovery, gas-bearing alluvial basin, bio-microsystems and oil modeling. Under the effects of tension force, viscoelastic materials change according to viscoelastic and elastic illustration. Here we considered it due to hydro-dynamics unevenness and designs within suspension of subjective spinning microbes. Therefore, this paper presents a theoretical and computational evaluation of the unsteady 2D Bioconvection flow of Ellis fluid, which has non-linear radiation features as well as gyro-tactic microorganisms, illuminating the novelty of the work. Here, convective B. Cs are used for the current study, coupled PDEs are changed into coupled ODEs by using some suitable B. Cs and similarity conditions. The acquired ODEs are numerically solved by using bvp4c scheme. Here Physical effects concerning all such parameters are studied in detail and represented graphically. We found that increasing behavior of temperature for higher value of Brownian movement and thermophoresis parameter whereas fall in Prandtl number. The gyrotactic microbes result in reduction for rising values of Peclet number.

Magnetohydrodynamic alumina–silver viscoelastic hybrid nanofluid flow over a circular stretched cylinder with nonlinear heat radiation and Arrhenius energy

Magnetohydrodynamic alumina–silver viscoelastic hybrid nanofluid flow over a circular stretched cylinder with nonlinear heat radiation and Arrhenius energy

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.

Stability analysis of dual solutions for nonlinear radiative magnetohydrodynamic flow of [formula omitted] hybrid nanofluid over a nonlinearly shrinking surface

The present work explores the existence and temporal stability of dual solutions with the consequence of nonlinear thermal radiation on hybrid nanofluid flow (including Silver and Titanium dioxide nanoparticles in water) past a permeable shrinking sheet. The analysis also considers the united outcomes of suction/injection, Joule heating, viscous dissipation, and magnetohydrodynamics. Employing realistic assumptions and suitable similarity transformations, the governing nonlinear partial differential equations are formulated and altered into a nonlinear ordinary differential equations system. These equations are then solved numerically using the Lobatto IIIA technique. It is observed that dual solutions can occur within a precise range of the shrinking surface parameter. Analyzing the temporal stability of these dual solutions under small disturbances shows that the upper solution branch is stable and represents a physically realistic solution to the problem. In contrast, the lower solution branch is unstable and not physically realizable. No solution exists beyond the critical λc=−1.3915 for the shrinking parameter. The critical values of shrinking parameter λc=−1.2565,−1.3188, and −1.4161 correspond to volume fractions of hybrid nanofluid with φAg−TiO2 of 2%,4%, and 8%, respectively. No solution exists beyond this critical point. The graphical representation and quantitative explanation demonstrate how various emergent characteristics affect momentum and thermal boundary layer profiles, Nusselt number, and skin friction. The velocity and temperature profile of hybrid nanofluid can be improved by adding a small volume of nanoparticle volume fraction. Thermal boundary layer thickness is amplified by an accumulation in the shrinking parameter, power index of velocity component, thermal radiation parameter, and temperature difference ratio. Sheering stress and heat transfer coefficient improve with adding more nanoparticles in the base fluid for the first solution braches, but opposite effects are found in the second solutions. The contributions of this research are significant both theoretically, in terms of advancing the mathematical modeling of hybrid nanofluid flow with heat transfer in engineering systems, and practically, in terms of applications to engineering cooling systems.

Non-similar solution of Casson fluid flow over a curved stretching surface with viscous dissipation; Artificial neural network analysis

PurposeThe main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.Design/methodology/approachThe non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.FindingsThe results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.Originality/valueAI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

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