Nonlinear Radiation Research Articles

Formation Mechanism of Laser-driven Magnetized “Pillars of Creation”

The Pillars of Creation, one of the most recognized objects in the sky, are believed to be associated with the formation of young stars. However, so far, the formation and maintenance mechanism of the pillars are still not fully understood due to the complexity of the nonlinear radiation magnetohydrodynamics (RMHD). Here, assuming laboratory laser-driven conditions, we studied the self-consistent dynamics of pillar structures in magnetic fields by means of two-dimensional and three-dimensional (3D) RMHD simulations, and the results support our proposed experimental scheme. We find that only when the magnetic pressure and ablation pressure are comparable, the magnetic field can significantly alter the plasma hydrodynamics. For medium-magnetized cases (β initial ≈ 3.5), the initial magnetic fields undergo compression and amplification. This amplification results in the magnetic pressure inside the pillar becoming large enough to support the sides of the pillar against radial collapse due to pressure from the surrounding hot plasma. This effect is particularly pronounced for the parallel component (B y ), which is consistent with observational results. In contrast, a strong perpendicular (B x , B z ) magnetic field (β initial < 1) almost retains its initial distribution and significantly suppresses the expansion of blown-off gas plasma, leading to the inability to form pillar-like structures. The 3D simulations suggest that the bending at the head of “Column I” in the Pillars of Creation may be due to nonparallel magnetic fields. After similarity scaling transformation, our results can be applied to explain the formation and maintenance mechanism of the pillars, and can also provide useful information for future experimental designs.

Framing the features of nanolayer and diameter of carbon nanotubes in the flow of blood over a stretching cylinder in presence of magnetic induction

This study explores the slip boundary layer electrically conducting flow of nanofluid over a stretching cylinder. Flow type in present study is considered to be steady and incompressible flow with mixture of SWCNTs/MWCNTs and human blood. Thermal conductivity of present flow model is measured by merging the consequence of diameter of SWCNTs/MWCNTs nanoparticles and solid–liquid interfacial-layer. Velocity slip, non-linear radiation, and induced magnetic-flux are considered in flow. The mode of heat transmission in flow is presented in appearance of dual heat flux, that is, Cattaneo-Christov heat flux and prescribed heat flux. By executing similarity exploration, we modernize the leading PDEs of the acknowledged flow model into ODEs. The consequential equations are solved numerically by recalling Runge–Kutta–Fehlberg fourth-fifth order scheme through shooting system. Deliberations on consequence of flow features on flow specific are organized accurately via graphs and charts. The professed numerical consequences are novel and distinctive. These consequences can contribute to other scholars on electing the suitable factors to enlarge the heat conduction technique in medical science, society, and the industry.

Transient Thermoelastic Analysis of Rectangular Plates with Time-Dependent Convection and Radiation Boundaries

Approximate analytical solutions are presented for the transient thermoelastic problem of rectangular plates with time-dependent convection and radiation boundaries. To include the nonlinear radiation boundary, the whole heating process is divided into several time steps, and a linearized approximation is used to simplify the radiation term for each step. The one-dimensional transient temperature along the thickness direction is solved using the technique of the separation of variables. The displacement and stress solutions are obtained by applying the state-space method to the three-dimensional thermoelasticity equations. The accuracy of the present solutions is demonstrated by comparison with the reported results in the open literature and the finite element solutions. In the numerical examples, two kinds of thermal boundaries, namely, time-independent convection boundaries and time-dependent convection and radiation boundaries, are considered to show the availability of the present solutions.

Nonlinear analytical solution for radiation stress of higher-order Stokes waves on a flat bottom

The radiation stress of water surface waves plays an important role in many aspects of marine hydrodynamics. The nonlinear effects of highly nonlinear waves on the radiation stress were investigated on a flat bottom under finite water depth and deep water conditions. Analytical solutions for radiation stress were derived based on different order nonlinear Stokes wave theory, respectively. The results indicate that the nonlinear radiation stresses are significantly greater than those based on the linear wave, and they increase as the nonlinearity strengthens. Through an inter-comparison of the expressions of nonlinear radiation stress of various orders of Stokes waves, it turned out that the results based on the second-order Stokes wave overestimated the radiation stress, while the expressions based on Fenton's fifth-order Stokes wave were more reasonable in reflecting the nonlinear effect of waves. In the case of extreme wave steepness, the fifth-order Stokes wave radiation stresses Sxx5 was approximately 17% larger than that of the linear wave. Finally, using the expressions of the fifth-order Stokes wave radiation stress, bound infragravity waves excited by the bichromatic wave groups formed by the superposition of two fifth-order Stokes waves were obtained.

Soret and Dufour effects on dissipative Jeffrey nanofluid flow over a curved surface with nonlinear slip, activation energy and entropy generation

Nanofluids have potential abilities and thermal features and provide more efficient results of heat transfer when compared with common liquid. Therefore, the major novel aspect of the current analysis is to analyze the entropy production and thermal feature of the system in the presence of cross-diffusion, nonlinear radiation, endothermic/exothermic reaction, activation energy and dissipation effects. Slip factor is additionally considered to slowing down the nanomaterial velocity. Furthermore, the effects of Lorentz force and nonlinear mixed convection are accounted. The governing differential equations for considered nanofluids are first converted into dimensionless ODEs utilizing proper variables. The obtained system is then computed using NDsolve technique. The approximated results for different distributions are shown through curves and tables. The impact of dimensionless parameters is visualized on fluid velocity, temperature, concentration, Nusselt number, skin friction and entropy generation. It has been observed that velocity steps up with curvature, ratio of buoyancy, solutal mixed convection and thermal convection parameters but declines for upgrading slip parameter. The temperature step down by upgrading exothermic/endothermic parameter, Dufour number and Brownian diffusion parameter, thermophoretic parameter and radiation parameter. It is also noticed that the concentration of the nanofluid upsurges for increasing activation energy and soret number, but concentration minimizes for growing the temperature difference parameter. Numerical results show that the Nusselt number decays for rising Soret number, Dufour number, thermophoretic parameter and Brownian diffusion parameter but a reverse trend is seen for radiation parameter and activation energy. Also, skin friction coefficient declines by enhancing thermal convection parameter, solutal mixed convection parameter and slip parameter but upgrades for boosting buoyancy parameter.

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.

SAR and Optical Image Registration Based on Deep Learning with Co-Attention Matching Module

Image registration is the basis for the joint interpretation of synthetic aperture radar (SAR) and optical images. However, the significant nonlinear radiation difference (NRD) and the geometric imaging model difference render the registration quite challenging. To solve this problem, both traditional and deep learning methods are used to extract structural information with dense descriptions of the images, but they ignore that structural information of the image pair is coupled and often process images separately. In this paper, a deep learning-based registration method with a co-attention matching module (CAMM) for SAR and optical images is proposed, which integrates structural feature maps of the image pair to extract keypoints of a single image. First, joint feature detection and description are carried out densely in both images, for which the features are robust to radiation and geometric variation. Then, a CAMM is used to integrate both images’ structural features and generate the final keypoint feature maps so that the extracted keypoints are more distinctive and repeatable, which is beneficial to global registration. Finally, considering the difference in the imaging mechanism between SAR and optical images, this paper proposes a new sampling strategy that selects positive samples from the ground-truth position’s neighborhood and augments negative samples by randomly sampling distractors in the corresponding image, which makes positive samples more accurate and negative samples more abundant. The experimental results show that the proposed method can significantly improve the accuracy of SAR–optical image registration. Compared to the existing conventional and deep learning methods, the proposed method yields a detector with better repeatability and a descriptor with stronger modality-invariant feature representation.

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

A thin layer lubricant surface applications due to nonlinear radiated hybrid nanoparticles with orthogonal stagnation point flow

ABSTRACT The improved thermal association of heat transfer is considerably observed due to hybrid nanoparticles. Being to suspension of base fluids with two distinct nanoparticles, the stable properties of hybrid nanofluids are measured. Current contribution reports the enhancement in thermal impact of water (base liquid) uniformly decomposed with hybrid nanoparticles theoretically. The hybrid nanofluid properties are justified with copper and aluminum oxide nanoparticles. With improved heat transfer mechanism, the motivations for observing the aspect of lubrication phenomenon in the vicinity of stagnation points are associated to the manufacturing systems and chemical processes ample applications in fluid bearing, assembling of thin films, coating and printing. Moreover, the treatment of heat transfer is further influenced by nonlinear radiation and mixed convection applications. The dimensionless variables successfully transformed the system into a dimensionless form, which is further solved using the Keller box method. The comparative heating transfer onsets are predicted for the traditional nanofluid with suspension and hybrid nanofluid with decomposition. The results show that the lubrication phenomenon controls the wall shear force while enhancement in Nusselt number is noticed. Increasing observations for skin friction and Nusselt number are resulted for hybrid nanofluid as compared to simple nanofluid.

Thermal Diffusion and Diffusion Thermo Effects on MHD 3D Mixed Upper Convective Flow of Maxwell Nanofluid Flow Past using Nonlinear Radiative Heat Flux

This article aims to investigate the effect 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 in the presence of diffusion thermo and thermal diffusion. 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, we additionally make use of the bvp4c built-in function that is available in 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

MHD slip effects on (50:50) hybrid nanofluid flow over a moving thin inclined needle with consequences of non-linear thermal radiation, viscous dissipation, and inclined Lorentz force

Due to their enormous implementation in engineering scrupulous, hybrid nanofluids have become a prevailing substance of consideration in mathematical and physical research. The augmentation of thermal conductivity is an exclusive emphasis of hybrid nanofluids. The fluid prototype substance probing in the existing study is the Ethylene Glycol–water (50:50) as base fluid and a mixture of nanoparticles are magnetic (Fe3O4) and non-magnetic (Al2O3) hybrid nanofluid. It is found in heat transfer and cooling in electronic devices, engines, refrigerants, energy storage and the automotive industry. To obtain solutions, the Partial Differential Equations with slip boundary conditions that describe the flow are converted into Ordinary Differential Equations with appropriate transformations using a numerically based technique known as the fourth-order Runge–Kutta method with shooting techniques. The illustration diagram of the gained outcomes accentuates the consequence of numerous physical variables on the flow dynamics in relation to fluid momentum, and thermal silhouette. Also, the consequence of heat transfer rate and surface drag force in multiple variables like Eckert number, magnetic variable, and radiation constant, are tabulated. These studies explain the decline in the thermal outline of hybrid nanofluid under slip situations when upsurges the non-linear radiation parameter. By analyzing these studies of hybrid nanofluids, it is possible to improve heat transfer efficiency and control temperature gradients in systems where nonlinear thermal radiation and viscous dissipation are important factors.

Investigation of Oldroyd‐B fluid flow and heat transfer over a stretching sheet with nonlinear radiation and heat source

AbstractThe given investigation concerns the study of non‐Newtonian Oldroyd‐B fluid flow across a permeable surface along with nonlinear thermal radiation, chemical reactions, and heat sources. Equations modified are thus numerically evaluated by employing bvp4c‐technique. Obtained outcomes are exhibited graphically. Pictorial notations are used to investigate the consequences of necessary parameters of velocity, energy, and mass. Acquired outcomes provide promising agreement with already established consequences provided in the open literature. The obtained results guided that magnetic field parameter (), porosity parameter (), Deborah number reduce momentum boundary layer thickness, furthermore, growth in the relevant Deborah number improves the corresponding momentum boundary layer.

Bioconvection transport of upper convected Maxwell nanoliquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction

Abstract The microorganisms’ concept has appealed substantial consideration of modern researchers because of its utilization in commercial and industrial products, for illustration, biofuel (prepared from the waste), drug delivery, and fertilizers. Keeping such utilizations of microorganisms in mind, an analysis based on gyrotactic microorganisms featuring the mixed convective nonlinear radiative Maxwell nanoliquid stagnation point flow configured by permeable stretching surface is presented. Boundary layer stretching flow subjected to transpiration effects is formulated. Modeling is based on Buongiorno’s nanoliquid model. This model captures Brownian diffusion along with thermophoresis aspects. Energy expression is formulated under nonlinear version of radiative heat-flux, heat source, thermal Robin conditions, and heat sink. Mass transport analysis is presented considering solutal Robin conditions and chemical reaction. In addition, the Robin conditions for motile microorganisms are also considered. The complex mathematical expressions of Maxwell liquid are simplified utilizing the Boundary layer concept and then suitable transformations assist to obtain the mathematical problems in ordinary differential forms. The analytical approach (that is homotopy analysis methodology) is utilized for computational analysis. The outcomes obtained are presented graphically and numerically. The detailed description of emerging physical non-dimensional parameters is included. Our findings indicate that the motile density field strongly boosted with the increment in Peclet number and microorganisms Biot number; however, they are suppressed with the increase in the values of bioconvection Schmidt number and motile microorganism concentration difference parameter.

Unsteady non-axisymmetric MHD Homann stagnation point flow of CNTs-suspended nanofluid over convective surface with radiation using Yamada–Ota model

The increasing number of ways in which carbon nanotubes (CNTs) may be used in business and technology has led to an explosion of interest in these tiny tubes. As a result, the Yamada–Ota model is used to investigate the unsteady, non-axisymmetric MHD Homann stagnation point of carbon nanotubes passing over a convective surface with nonlinear radiation. Consisting of single-walled and multi-walled carbon nanotubes that are suspended in water (H2O). The length of the nanomaterial is between [Formula: see text] nanometers, while its radius is between [Formula: see text]. The method of similarity transformation is altered so that it may be used to get the dimensionless system of differential equations from the mathematical model that is envisioned for PDEs. After that, approximate solutions are obtained using MATHEMATICA and the Shooting with RK-IV technique. In this paper, we provide a graphical discussion and a physical interpretation of the results of measures of practical significance as a function of key factors. The results indicated that an increase in the volume fraction led to a corresponding rise in the heat transfer rate. However, it is reduced by the magnetic energy that is supplied to it. Carbon nanoliquids with a single wall have a greater melting point than nanoliquids with multiple walls. Industrial and technological uses of the issue under examination span several fields, including aviation and health. The results of the interface velocity and heat transfer rate at the surface, as well as the solution of each profile, are shown graphically, along with an analysis of the effects of MHD on the flow and heat transfer characteristics of the fluid under the influence of radiation.

Nonlinear radiation effects on water-based nanofluid containing CNTs subject to heat source/ sink past a wedge

In this paper, a two-dimensional and incompressible laminar flow comprised of water-based carbon nanotubes over convectively heated moving wedge under the magnetic field and nonlinear radiation and heat production/ absorption is investigated. The base nanofluid (water) contains single wall carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs). In order to convert the dimensional nonlinear partial differential equations in nondimensional nonlinear ordinary differential form, an adequate set of similarity variables had been used. These set of equations and boundary conditions are evaluated by the implementation of RKF-45 (Runge–Kutta–Fehlberg fourth-fifth) order scheme. The influence of several physical parameters on particular nanoparticle’s volume friction, temperature and velocity ratio parameter, heat source/ sink parameter, nonlinear radiative constraint, exponent constant, magnetic factor, Eckert and Biot numbers is studied. An opposite behavior of volume fraction and velocity ratio parameters on velocity and energy profiles is achieved.

Impacts of thermal radiation with nanoparticle aggregation and variable viscosity on unsteady bidirectional rotating stagnation point flow of nanofluid

Interest in nanofluids with nanoparticle-induced aggregation effects like solar-powered energy and crossflow heat transfer is growing in the modern industrial sector. The main goal of this research is to find out how nonlinear radiation, changes in viscosity, and aggregation affect the flow of ethylene glycol-based nanofluids in three dimensions. It is concerned with stagnation point flows that are not axisymmetric and that take place on stretching sheets. In accordance with the imposed hypotheses, the governing equations will be modelled. With the help of a similarity transformation, a complicated set of nonlinear partial differential equations can be turned into a simpler set of ordinary differential equations. This simplification facilitates the process of solving the equations. The algorithm will then be used to perform a numerical solution of the simplified set of equations. Runge-Kutta (RK-IV) and the shooting method are used to derive the numerical results. Different parameters and their effects are graphically displayed. As the concentration of nanoparticles in the skin increases, it appears that both the rate of heat transmission and the coefficient of friction increase. The heat transfer rate and the skin coefficient of friction inclination both increase as the instability parameter is increased. To the contrary, it was found that delaying boundary layer's separation by increasing stress rate of surrounding fluid was effective. Tables also compare the nanoparticles aggregation effects with and without radiation and show the variation in Nusselt numbers. High levels of agreement were found between the findings of the current study and those of a previous publication for the same instance, lending further support to the findings.

Dynamical phenomena developed by a spiralling stretchable sheet in magnetized Casson-spinel ferrite nanofluid

Nanofluid research has sparked widespread attention due to its immense implementations in various courses, including chemical engineering, microelectronics, solar energy, cooling systems, electronics, power-saving, etc. This research offers modelling and numerical simulation for the magnetized Casson-based spinel ferrite (MnFe2O4) nanofluid stream owing to a spiralling stretchable sheet placed in a Darcy permeable medium. Diverse impacts like nonlinear heat radiation, viscous and Joule warms, and heat generation/absorption are considered in stimulating heat exchange. Under the imposed physical assumptions, equations governing the flow and heat flow are modelled. The partial derivative model is transferred to the ordinary derivative model by utilising compatible similarity variables. The resulting nonlinear linked ordinary derivative model is tackled computationally by the 4th-order Runge-Kutta integration procedure, accomplishing the best strategy shooting algorithm based on the built-in function of the bvp4c solver in MATLAB. Different attributes of the considered flow phenomenon corresponding to the pertinent model parameters are disclosed effectively via graphs and tables. Some leading outcomes are that amplification is examined in the thermal field and allied zone thickness responding to the radiation parameter and Biot number. With the upgraded rotation parameter, an augmentation is developed in the absolute value of the local skin friction coefficients. Moreover, amplifying the rotation parameter enfeebles the local Nassault number. This modelling could be effective in manufacturing and technological processes like polymeric material extrusion, stretchable/shrinkable packaging, and designing magnetic storage devices.

Simulation of entropy and heat and mass transfer in Water-EG based hybrid nanoliquid flow with MHD and nonlinear radiation

The essence of heat transfer has always been a major aspect in the evolution of modern day industrialization. In order to enhance the heat transfer rate the fluids have also evolved from traditional fluids to more complex hybrid nanofluids. Here in this scenario a hybrid nanofluid flow consisting of Co and Ti nanoparticles have been considered. The flow is drawn over a pervious stretchable cylinder concealed by the impacts of nonlinear radiation and magnetic field. The rate of heat transfer and entropy accumulated during the mechanism has also been evaluated for the system. This study of entropy provides a broader area of development for industrial organizations. The governing equations were solved by using the BVP4C tool of MATLAB. For this applicable similarity transformations were used to non dimensionalize the equations and then converted to IVP for obtaining the solutions. Both graphical and tabular form of the solutions were provided for better understanding of the situation. The novel results gained from the analysis concluded that the efficiency of heat transfer was more in case of hybrid nanofluid than that of nanofluid and the base fluid. The magnetic field inversely affected the velocity profile of the fluid whereas the nonlinear radiation directly affected the temperature distribution of the fluid. These results offer a variety of information for many large scale industries like food processing industries, plastic industries etc., to improvise their system.

Computation of stagnation coating flow of electro-conductive ternary Williamson hybrid mathrm{GO}-mathrm{AU}-{mathrm{Co}}_{3}{mathrm{O}}_{4}/mathrm{EO} nanofluid with a Cattaneo–Christov heat flux model and magnetic induction

Modern smart coating systems are increasingly exploiting functional materials which combine multiple features including rheology, electromagnetic properties and nanotechnological capabilities and provide a range of advantages in diverse operations including medical, energy and transport designs (aerospace, marine, automotive). The simulation of the industrial synthesis of these multi-faceted coatings (including stagnation flow deposition processes) requires advanced mathematical models which can address multiple effects simultaneously. Inspired by these requests, this study investigates the interconnected magnetohydrodynamic non-Newtonian movement and thermal transfer in the Hiemenz plane's stagnation flow. Additionally, it explores the application of a transverse static magnetic field to a ternary hybrid nanofluid coating through theoretical and numerical analysis. The base fluid (polymeric) considered is engine-oil (EO) doped with graphene left(GOright), gold left(Auright) and Cobalt oxide left(C{o}_{3}{O}_{4}right) nanoparticles. The model includes the integration of non-linear radiation, heat source, convective wall heating, and magnetic induction effects. For non-Newtonian characteristics, the Williamson model is utilized, while the Rosseland diffusion flux model is used for radiative transfer. Additionally, a non-Fourier Cattaneo–Christov heat flux model is utilized to include thermal relaxation effects. The governing partial differential conservation equations for mass, momentum, energy and magnetic induction are rendered into a system of coupled self-similar and non-linear ordinary differential equations (ODEs) with boundary restrictions using appropriate scaling transformations. The dimensionless boundary value problem that arises is solved using the bvp4c built-in function in MATLAB software, which employs the fourth-order Runge–Kutta (RK-4) method. An extensive examination is conducted to evaluate the impact of essential control parameters on the velocity f{^{prime}}left(zeta right), induced magnetic field stream function gradient g{^{prime}}left(zeta right) and temperature theta left(zeta right) is conducted. The relative performance of ternary, hybrid binary and unitary nanofluids for all transport characteristics is evaluated. The inclusion of verification of the MATLAB solutions with prior studies is incorporated. Fluid velocity is observed to be minimized for the ternary mathrm{GO}–mathrm{Au}–{mathrm{Co}}_{3}{mathrm{O}}_{4} nanofluid whereas the velocity is maximized for the unitary cobalt oxide left({mathrm{Co}}_{3}{mathrm{O}}_{4}right) nanofluid with increasing magnetic parameter (beta ). Temperatures are elevated with increment in thermal radiation parameter (Rd). Streamlines are strongly modified in local regions with greater viscoelasticity i.e. higher Weissenberg number (We). Dimensionless skin friction is significantly greater for the ternary hybrid GO–Au–C{o}_{3}{O}_{4}/EO nanofluid compared with binary hybrid or unitary nanofluid cases.

Bioconvective nonlinear radiative flow of cross nanofluid due to porous oscillating surface with variable thermal conductivity and Cattaneo–Christov model

Present exploration elucidates the bio-convective time-dependent flow of Cross nanoparticles across periodically stretched surface immersed in porous space. Modified diffusion theories are employed to evaluate mass and thermic transference attributes effectively. Aspects of thermic transformation are additionally inspected with nonlinear radiation, variable thermic conductivity and heat generation characteristics. Magnetic consequences are deployed for physical importance. Dimensionless expressions are accomplished with pertinent transformations, and then analytically elucidated by homotopic technique. Physical importance of leading variables on curves of skin friction, temperature, microorganisms and concertation are premediated graphically. Numerical computations are executed to briefly notice the significance of relative variables on local Sherwood, motile density and Nusselt numbers and organized in respective tables. It is acknowledged that velocity curves display declining tendencies for enlarging buoyancy ratio, bio-convective Rayleigh and Weissenberg numbers. The present study accentuated that temperature boosted prominently for heat generation and variable thermic conductivity. The attained outcomes further divulge that concentration display diminishing results for solutal relaxation variable while such declining outcomes ensued in temperature for thermic relaxation variable. Furthermore, microorganism’s curves display declining responses for bio-convective Lewis and Peclet variables. Finally, shear wall force improved for magneto-porous variable but lessened for Weissenberg number.