Nonlinear ODEs Research Articles

Zeta potential and activation energy effects in an EMHD non-Newtonian nanofluid flow over a wedge with Darcy-Forchheimer porous medium

The transmission of mass and heat alters the distinctive of non-Newtonian nanoliquid, which have several applications including extrusion, cooling of metallic plates, transport of biological fluids, coating, heat exchanger technology, and feed roll material movement. Mass and heat transfers in tangential hyperbolic nanoliquid streams via a wedge were analyzed, along with the roles played by Arrhenius activation and electro-magneto-hydrodynamics. Additionally, the impact of Darcy-Forchheimer flow and magnetic fields are considered in this simulation. By choosing suitable similarity variables, the necessary nonlinear partial differential formulation is transformed into nonlinear ODE’s (ordinary differential equations). After that, the equations are solved in Matlab through BVP4c solver. Flow fields, heat and mass transfer primary affecting factors were shown in graphically and discussed. Also, the coefficient of skin friction, Nusselt and Sherwood numbers are also presented graphically in the primary influenced parameters. An escalation in the Weissenberg number causes a decrease in the values of nanoliquids velocity, but an escalation in the power law index parameter causes an enhancement in nanoliquids velocity. If the suction and injection fluid have a zeta potential opposite that of the surface, it may improve interaction and change the boundary layer, thereby decreasing the coefficient of skin friction.

Significance of Variability in Liquid Properties on 3D MHD Maxwell Nanofluid Flows Over a Stretching Surface with Heat Generation/Absorption and Chemical Reaction

Objective of the current research investigation is linked with advancement in nanotechnology and fluids flow phenomena subject to various fluid models. The model adopted over here is Maxwell–nanofluid model subject to magnetohydrodynamics impact confined within the dimensions of a bi-directional stretching surface. The boundary is assumed to be convective in the context of thermal state and zero mass flux in the context of nanoparticles. Furthermore, slip condition on velocity and a source of heat generation/absorption is also considered in the flow model. It is pertinent to mention that base fluid is assumed to be chemically reactive by involving first order chemical reaction term in the governing equation of concentration of nanoparticles. So formulated, highly nonlinear set of governing equations is converted into nonlinear ODEs involving various parameters including Brownian diffusion, Deborah number, magnetic parameter, Prandtl and Schmidt number, heat generation/absorption and the first order chemical reaction. The ODEs are solved by a semi-analytic technique of OHAM (Optimal Homotopy Analysis Method). The results are plotted graphically. The obtained findings are compared without available literature in the same direction by assuming special cases on various parameters.

A swarm-intelligence based formulation for solving nonlinear ODEs: γβII-(2+3)P method

A reverse engineering approach is taken to develop efficient numerical techniques for solving nonlinear ODEs through the numerical solution of a particular problem in engineering. The problem is the dynamic analysis of a mechanical system under a severely irregular seismic signal or earthquake load. It is a challenging problem which requires strong formulation to be tackled. Its solution is a rich source of information that could be exploited through artificial intelligence (AI) and statistical computation. This work devises a new strategy to conduct such a task and construct a series of 3∼5 points high-precision time integrators. The integrators belong to single-step two-derivative class of methods. The interconnectivity relationships between the weights of the integrators are formulated by linear regression and heuristics. These relationships make it possible to generate a wide spectrum of ODE-solving techniques in a continuous weighting space. In an innovative attempt, strong Hermite interpolators are constructed to couple with the integrators and improve the accuracy of the presented algorithms. They precisely evaluate the instep points of the integrator. All these issues are appropriately collected in the presented methodology. Four classes of weighting rules are presented for the integrators: 1) Symmetry weighting rule (SWR) 2) Consistency weighting rule (CWR), 3) Fundamental weighting rule (FWR), and 4) Auxiliary weighting rule (AWR). The first two rules are adopted from outward form of the well-configured quadratures available in literature. The third and the most important one, the so-called FWR, is disclosed here for the given integrator. It formulates the correlation between the weights of an optimal integrator. Finding the min-error solution of the vibration equation guides us to the FWR. Evolutionary grey wolf optimizer (GWO), accompanied with a statistical multilinear regression, extracts the FWR. This research pioneers the application of swarm-intelligence in formulation of the FWRs for the given two-derivative integrator. Finally, all the weighting rules and Hermite interpolators are combined into some unified algorithms so-called γβII−q+rP algorithms to efficiently cope with initial value ODEs. Great performance of the presented methods is demonstrated through the numerical examples.

Darcy-Forchheimer chemically reactive bidirectional flow of nanofluid with magneto-bioconvection and Cattaneo-Christov properties

Since the last two decades, researchers have paid significant attention to nanofluid because of their high rates of thermal conduction. Due to the widespread usage of these materials in several types of thermal transport devices, including nuclear reactor cooling, car generators, petrochemicals, industrial heating and cooling needs, as well as heat transfer technology. Applications for non-Newtonian liquid can be found in a wide range of fields, notably chemical nuclear reactor, paper manufacturing, petroleum engineering, processes, food processing, geophysics, biological sciences and many others. To determine the properties at different shear rates When the shear rate is significantly increased, a cross fluid model was developed to help with the difficulty. Main theme of existing work is to scrutinize the magneto-bioconvection aspects for 3D nonlinear material with triple stratification phenomenon. Additionally, we have examined heat-mass efficacy utilizing time-dependent thermal relaxation phenomenon and Buongiorno nanofluid model. It has been proposed that the horizontal stretching sheet has been inserted in Darcy-Forchheimer porous medium. Features of magnetohydrodynamics and activation energy are considered in cross fluid model. Furthermore, to improving the fluid's thermal properties, the combination of microorganisms (microbes) in nanofluids also causes the flow to be stable. With the implantation of similarity variables, we have transformed non-linear PDEs into non-linear ODEs. Utilizing bvp4c scheme (MATLAB pregame), the governing system of ODEs are solved. The tabular and graphical representations are used to illustrate the results. By raising the concentration relaxation and Brownian motion parameters, a considerable decrease in concentration profile is seen. The development of thermal Biot number and Forchheimer number approximations has advanced the temperature field, which is an interesting observation. The fluid's microorganism profile is assumed to be deteriorating based on Lb and δ1.

Abaqus implementation of a large family of finite viscoelasticity models

In this paper, we introduce an Abaqus UMAT subroutine for a family of constitutive models for the viscoelastic response of isotropic elastomers of any compressibility – including fully incompressible elastomers – undergoing finite deformations. The models can be chosen to account for a wide range of non-Gaussian elasticities, as well as for a wide range of nonlinear viscosities. From a mathematical point of view, the structure of the models is such that the viscous dissipation is characterized by an internal variable Cv, subject to the physically-based constraint detCv=1, that is solution of a nonlinear first-order ODE in time. This ODE is solved by means of an explicit Runge–Kutta scheme of high order capable of preserving the constraint detCv=1 identically. The accuracy and convergence of the code is demonstrated numerically by comparison with an exact solution for several of the Abaqus built-in hybrid finite elements, including the simplicial elements C3D4H and C3D10H and the hexahedral elements C3D8H and C3D20H. The last part of this paper is devoted to showcasing the capabilities of the code by deploying it to compute the homogenized response of a bicontinuous rubber blend.

Extending nonstandard finite difference scheme rules to systems of nonlinear ODEs with constant coefficients

In this paper, we present a reformulation of Mickens' rules for nonstandard finite difference (NSFD) schemes to adapt them to systems of ODEs. We want to compare several methods within the class of NSFD schemes. These methods are expressed as exponential integrators which treat exactly the linear part of the equations. While the classical methods address each equation of a system separately, we propose here to address them as a whole, which involves a reformulation of Mickens' rules. This leads to enhance the results compared to the classical case, even if approximations of the matrix exponentials are used. Precisely, using Cayley–Hamilton theorem we obtain two correction factors, one of which is linked to the size of the system and the other to the nonlinear term, we are thus able to use test cases which show the impact of one or another corrector. We prove the consistency and the zero-stability of the method in the nonlinear case to conclude to the convergence of the method.

Significance of mixed convective double diffusive MHD stagnation point flow of nanofluid over a vertical surface with heat generation

The mixed convection double-diffusive MHD flow of boundary layer nanofluids above vertical region is designed. This flow is explained near stagnation point along with heat generation. Using Buongiorno’s model, the properties of Brownian motion, thermophoresis, and diffusion of regular and cross type are included. Using appropriate similarity transformations of the local similarity technique, non-linear unstable PDEs in governing model converted to non-linear ODEs, which were then evaluated numerically by the Keller-box method (KBM) using the computational software MATLAB 2021a. Graphical analysis of possessions of parameters on the boundary layers in profiles of velocity, solute concentration, temperature and nanoparticle concentration is illustrated. The statistics of the reduced Sherwood number and the reduced Nusselt number for solute and nanoparticles in cases of assisting flow and opposing flow are added as well to the results. The fastest rate of heat transfer is achieved in a scenario with a negligible thermophoresis effect. The thermophoresis parameter and the buoyancy parameter of the regular double diffusive appear to rise rather than decrease in the nanoparticles lowered Sherwood number, while the Brownian motion parameter rises. The temperature and layer thickness for heat generation have a quite opposite effect. When the computed numerical findings are compared to earlier published work, it is discovered to be in good percentage. The need for numerous industrial applications and improvements in the efficiency and energy consumption of systems, such as cooling and heating transportation, in water heaters, nuclear reactors, optical devices, turbines, aerodynamics, and electronics, have led to the establishment of this investigation.

Scrutinization using both numerical and analytical techniques for Darcy Forchheimer flow in the gyrotactic microorganism of nanofluid over a rotating disk

The current investigation explores the impact of Darcy Forchheimer’s flow of nanofluid due to a spinning disk with slip conditions and microorganisms. The mechanism of fluid flow over a rotating disk incorporates the theoretical as well as the practical interest of it in applied sciences and engineering. Energy and mass transport equations are produced with thermal radiation and chemical reactions. The modeled couple of nonlinear PDEs are simplified to the system of ODEs using the self-similar solution. Analytical solutions are found for the resulting nonlinear ODEs using the homotopy analysis method (HAM) technique, while numerical solutions are found using ND-solve and bvp4c. The convergent of the series solution is investigated. The graphical evaluation of prospective parameters encompasses the examination of their consequences on several factors, including the velocity profile, temperature profile, volume percentage of nanoparticles, and profile of microorganisms. The occurrence of radiation parameter, thermophoresis, and Brownian motion effects is commonly observed to contribute to the augmentation of heat transfer. We computed the percentage result in numerical as well as analytical study. The utilization of the provided observations can effectively contribute to the enhancement of heat transfer devices, centrifugal compressors, internal combustion engines, and microbial fuel cells.

Inclined Magnetic Field on Mixed Convection Darcy–Forchheimer Maxwell Nanofluid Flow Over a Permeable Stretching Sheet With Variable Thermal Conductivity: The Numerical Approach

The behavior of a Maxwell nanofluid in mixed convection Darcy–Forchheimer inclined MHD flow across a stretched sheet is investigated in this research study. In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. These ODEs are then solved using the shooting method and a fourth‐order Runge‐Kutta methodology. The study explores how fluid flow velocity is affected by magnetic field inclination and suction/injection effects. This is attributed to the strengthening of the magnetic field with an increase in the inclination angle α. Additionally, the imposed magnetic field generates an opposing force, known as the Lorentz force, which contributes to a reduction in the velocity curve. Furthermore, various parameters affect the profiles of concentration, temperature, velocity, and Nusselt number. A number of parameters are looked at, such as the response rate constant, mixed convection, buoyancy ratio, suction/injection, Brownian motion, Lewis number, and thermophoresis. Interestingly, the results show that activation energy and mixed convection parameters, respectively, have an increasing effect on concentration and velocity curves.

The mixed convection thermally radiated hybrid nanofluid flow through an inclined permeable shrinking plate with slip condition and inclined magnetic effect

In this paper, we consider the slip boundary condition to analyze the radiative inclined magnetohydrodynamics mixed convection hybrid nanofluid (Al2O3–Cu/H2O) flow across an inclined shrinking permeable plate. The following model’s governing PDEs are transformed into nonlinear ODEs with the help of similarity transformations. To achieve the numerical solution of ODEs, the boundary-value problem of 4th order accuracy (bvp4c) is applied. With appropriate values for the copper volume fraction, magnetic parameter, slip parameter, and radiation parameter, the numerical results are described and graphically represented in velocity and temperature profiles. Due to the shrinking plate, the dual solutions are to be observed. For higher values of copper volume fraction, slip parameter, and magnetic parameter the first solution in the velocity profile increases and the second solution in the velocity profile decreases by increasing the value of copper volume fraction and magnetic parameter. By increasing the magnetic parameter, and slip parameter first solution of the temperature profile decreases while both the solution increases by increasing the copper volume fraction and radiation parameter.

Spatial dynamics in the family of sixth-order differential equations from the theory of partial formation

Topic of the paper. Bounded stationary (i.e. independent in time) spatially one-dimensional solutions of a quasilinear parabolic PDE are studied on the whole real line. Its stationary solutions are described by a nonlinear ODE of the sixth order of the Euler–Lagrange–Poisson type and therefore can be transformed to the Hamiltonian system with three degrees of freedom being in addition reversible with respect two linear involutions. The system has three symmetric equilibria, two of them are hyperbolic in some region of the parameter plane. Goal of the paper. In this paper we, combining methods of dynamical systems theory and numerical simulations, investigate the orbit behavior near the symmetric heteroclinic connection based on these equilibria. It was found both simple (periodic) and complicated orbit behavior. To this end we use the theorem on a global center manifold near the heteroclinic connection. For the third symmetric equilibrium at the origin we found the region in the parameter plane where this equilibrium is of the saddle-focus-center type and found the existence of its homoclinic orbits, long-periodic orbits near homoclinic orbits and orbits with complicated structure.

Unsteady magneto porous convective transport by micropolar binary fluid due to inclined plate: An inclusive analogy

In this investigation, the consequence of viscous dissipation on the unstable magneto porous convective transport by a micropolar binary fluid due to an inclined surface with viscous dissipation and thermal radiation is examined. Viscous dissipation plays a noteworthy role in industrial applications. The governing PDEs are converted to combined ODEs with the Boussinesq approximation using a similarity analysis. The obtained non-linear ODEs are resolved using the shooting method with “ODE45 MATLAB” coding assistance. The numerical outcomes are revealed graphically for various dimensionless parameters and numbers, including temperature, concentration, velocity, and micro-rotation. The temperature, micro-rotation, and velocity fields escalate with increasing Eckert numbers. The radiation parameter and variable viscosity parameter increase the flow rate of the fluid. Increasing radiation parameters, suction parameters, and Prandtl numbers lessen the fluid temperature. The buoyancy parameters have symmetrical impacts on the velocity and microrotation of fluid particles in the cooling and heating modes. Improving Eckert number, inclined angle, Schmidt number, Prandtl number, and magnetic parameter reduces skin friction. The heat transmission rate escalates in quantity due to larger Prandtl number values. Rising Prandtl, Eckert, and Schmidt numbers accelerate the mass transfer rate. The current research result is compared to previously published article's result with good agreement.

The existence of multiple topologically distinct solutions to $\sigma_{2,p}$-energy

Let ${\An} \subset \R^n$ be a bounded Lipschitz domain and consider the $\sigmap$-energy functional \begin{equation*} {{\mathbb F}_{\sigmap}}[u; {\An}] := \int_{\An} \big|{\wedge}^2 \nabla u\big|^p dx, \end{equation*} with $p\in\mathopen]1, \infty]$ over the space of measure preserving maps \begin{equation*} {\mathcal A}_p(\An) =\big\{u \in W^{1,2p}\big(\An, \R^n\big) : u|_{\partial \An} = {x},\ \det \nabla u =1 \mbox{ for ${\mathcal L}^n$-a.e.\ in $\An$} \big\}. \end{equation*} In this article we address the question of multiplicity {\it versus} uniqueness for {\it extremals} and {\it strong} local minimizers of the $\sigmap$-energy funcional $\mathbb F_{\sigmap}[\cdot; {\An}]$ in ${\mathcal A}_p({\An})$. We use a topological class of maps referred to as {\it generalised} twists and examine them in connection with the Euler-Lagrange equations associated with $\sigmap$-energy functional over ${\mathcal A}_p({\An})$. Most notably, we prove the existence of a countably infinite of topologically distinct twisting solutions to the later system in all {\it even} dimensions by linking the system to a set of nonlinear isotropic ODEs on the Lie group ${\rm SO}(n)$. In sharp contrast in {\it odd} dimensions the only solution is the map $u\equiv x$. The result relies on a careful analysis of the {\it full} versus the {\it restricted} Euler-Lagrange equations. Indeed, an analysis of curl-free vector fields generated by symmetric matrix fields plays a pivotal role.

Influence of Thermophoresis and Brownian Motion on MHD Hybrid Nanofluid MgO - Ag/H2O Flow along Moving Slim Needle

The objective of this paper is to analyze the impact of thermophoresis parameter, Brownian motion, velocity ratio parameter, similarity radius of the slim needle, magnetic parameter, Prandtl number and thermal radiation on the steady state, laminar, MHD hybrid nanofluid composed of MgO-Ag/H2O flowing along a horizontal hot thin needle. To achieve this, the BVP-5C shooting technique is employed through MATLAB to solve the transformed nonlinear ODEs governing the fluid flow. This study investigates the impact of non-dimensional parameters on the flow velocity, temperature and concentration profiles within the hybrid nanofluid. The effects of skin friction, local Nusselt number and Sherwood number are demonstrated through the use of tables. The observation reveals that elevating the thermophoresis parameter results in a simultaneous reduction in the temperature and concentration profiles, while an opposite behavior is observed for Brownian motion. The magnetic parameter and thermal radiation values result in a rising temperature profile, while the trend is reversed for the velocity ratio parameter, Prandtl number and Schmidt number. The Nusselt number demonstrates an upward trend with higher values of thermophoresis parameter, velocity ratio parameter and thermal radiation. Further, Sherwood number experiences an increase with greater values of Brownian motion and magnetic parameter but it displays a contrasting pattern for thermophoresis, velocity ratio parameter and thermal radiation parameter. Validation of this model with existing data has been excellent.

Impact of activation energy on carreau nanofluid flow over non-linear stretching surface

- The main goal of this article is to outline the key elements of activation energy that govern the slip flow of Carreau fluid over a non-linear stretched surface with heat transfer. By using the Arrhenius relation, activation energy aspects are included. Brownian diffusion and thermophoretic effects are shown through the study of nanoparticle dispersion using the Buongiorno model. The governing issue was first formulated as PDEs with appropriate boundary conditions, which were then converted into non-linear ODEs by applying a comparable transformation. Then, using Runge-Kutta integration and shooting techniques, the solution to the obtained complex differential system is discovered. Graphs reveal the effect of flow on linked profiles with respect to parameters. A published study that compares the current result describes the accuracy and reliability of the work. Through graphs and tables, the amount of engineering interest for shear thinning and thickening aspects of Carreau fluid is assessed. This includes wall drag coefficient, heat, and mass flux at the surface in comparison. It is calculated that by increasing non-linearity index velocity field depreciates for n = 0.5 and n = 1.5. Additionally, opposite behavior in momentum distribution is found against power law index (n) by fixing (m). Temperature of fluid decreases against power law index for m = 1.0 and m = 0.5.

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

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

Biomagnetic Fluid Flow on a Nonlinearly Stretching Sheet with Variable Thickness in a Magnetic Environment

The main contribution of the current work is a numerical and mathematical investigation of the effects of magnetic dipole and electrical conductivity on the heat and flow transfer of biomagnetic fluid over a non-linear stretched sheet with variable thickness. Static magnetic fields are produced by magnetic dipoles, which are used in medical a pplications such as MRI, drug administration, and cancer therapy. Additionally, the impact of non-linear heat source/sink features was examined in the study, leading to an interesting phenomenon. The PDEs are attenuated to nonlinear ODEs with dealing appropriate similarity variables. These resultant ODEs are computed by developing an effective method emerged on the application of the finite differences technique. In the end, this section offers a summary of the implications resulting from different physical limitations on blood flow, including variable thickness and power index effects. It was discovered that the rise in Kelvin and Lorentz forces in the boundary layer significantly affected blood flow. The current findings for the biomagnetic fluid model are novel and inventive since they effectively expand upon the issues previously addressed by previously published scientific documentation.

Nanoparticle aggregation effect over MHD oblique stagnation point flow of the convective surface of nanoliquids

This research could be useful in the construction of heavy power engines and the cooling of nuclear reactors, as well as in the insulation of buildings, the management of petroleum reservoirs, and the production of solar energy collectors. In this study, a numerical model is used to look at the steady, laminar, and incompressible MHD oblique stagnation point flow of nanofluids over a stretched convective surface. It is possible to evaluate nanoparticle aggregation with modified versions of the Krieger-Dougherty and Maxwell-Bruggeman models. Transforming the governing nonlinear PDEs into connected nonlinear ODEs through similarity transformations is necessary. We use a very efficient and precise numerical method to solve these equations. Mathematical implementation of the shooting technique using the Runge-Kutta-IV algorithm. Annotations on graphs illustrate how major physical factors affect the velocity, Nusselt number, streamlines, and temperature profiles. The local skin friction coefficient is tabulated. Velocity and temperature profiles increase with increasing values of stagnation parameters. The rate of heat transfer increases noticeably after incorporating the parameters [Formula: see text] and [Formula: see text]. When using the aggregation model, the heat transfer rate is increased by around 0.89%, compared to an increase of about 0.59% when not using the model. These enhancements manifest themselves at a 1% concentration of [Formula: see text] when the parameter [Formula: see text] is set to 0.5. With aggregation effects, ethylene glycol-based fluids performed better than without aggregation in terms of heat transfer rate. Consequently, we are confident in our numerical findings, which match earlier material for the limiting condition.

Significance of Melting Heat Transfer, Inclined Magnetic Field, and Thermal Radiation on the Dynamics of Williamson Nanofluid Above a Stretching Sheet

This study investigates the melting heat transfer in MHD flow that occurs when the flow is past a stretched sheet. With the use of the boundary layer concept, a set of non-linear ODEs is derived from a system of PDEs of motion and energy. After transforming the non-linear ODEs and their boundary conditions into dimensionless form with the use of appropriate similarity conversions, the equations are then numerically solved by employing the MATLAB inbuilt solver bvp4c method in conjunction with the shooting methodology. Through the use of a variety of charts and tables, the authors analyze and describe in depth the effects that relevant factors have on a variety of flow fields. As melting factor (Me) increases, it is discovered that the effect of Me on fluid temperature and velocity distributions decreases. Williamson parameter and inclined magnetic profile are shown to have decreasing impact on velocity and momentum parameter. After that, the findings are compared with the earlier published findings in limited situations of the issue, and it is discovered that they are in exceptional specify with those findings.

Heat transfer analysis of Carreau–Yasuda nanofluid flow with variable thermal conductivity and quadratic convection

Abstract Brownian motions and Thermophoresis are primary sources of nanoparticle diffusion in nanofluids, having substantial implications for the thermo-physical characteristics of nanofluids. With such a high need, the 2D, laminar MHD (Magnetohydrodynamic) quadratic convective stream of Carreau–Yasuda nano liquid across the stretchy sheet has been reported. The flow is caused by surface stretching. The principal purpose of this extensive study is to enhance thermal transmission. The effects of variable thermal conductivity and heat source are considered as well. The governing boundary layer equations are transmuted using similarity parameters into a series of non-linear ODEs (ordinary differential equations). The bvp4c algorithm is adopted to fix the translated system numerically. The effects of prominent similarity variables over the temperature, velocity and concentration field are graphically visualized and verified via tables. It explored that fluid’s speed diminishes for the more significant inputs of the magnetic coefficient, Brownian motion coefficient and Prandtl number. The thermal efficiency is improved for larger values of thermophoretic constant, varying thermal conductance and heat-generating parameters. The concentration field has proved to be a decreasing function of nanofluid constants.