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In this paper, we thoroughly examine the influences of slip effects and stagnation point flows in the context of an upper-convected non-Newtonian Maxwell nanofluid interacting with a stretching sheet. The existence of a heat generation, transverse magnetic field, and thermal radiation induces a flow resulting from a linearly stretched sheet. The application of the shooting method involves deriving nonlinear ordinary differential equations from the governing partial differential equations, followed by their solution. The effects of dimensionless governing parameters, including velocity ratio, Brownian motion parameter, thermophoresis parameter, velocity slip parameter, Lewis numbers, solutal slip parameter, Maxwell parameter, magnetic number, Eckert number, thermal slip parameter, chemical reactions parameter, and heat source parameter, are examined. The outcomes are illustrated and discussed through graphical representations, showcasing their impact on the velocity field, as well as heat and mass transfer characteristics. Tabular data are generated to display numerical values for physical parameters, including the skin-friction coefficient, local Sherwood number, and the reduced local Nusselt number. The findings suggest that an increase in the velocity slip parameter results in a reduction of both the local Sherwood number and the local Nusselt number. Furthermore, an increase in the strength of the magnetic field leads to a decrease in velocity profiles while simultaneously elevating temperature and concentration profiles.

Novel nanomaterial applications claim distinct uses in thermal engineering, cooling processes, heat transfer devices, and automobile industries, among others. Motivated research uses modified heat and mass flux theories to present thermal observations for the unsteady flow of magnetized Maxwell nanofluid, confined by porous bidirectionally stretched surfaces. The heat transfer model’s extension is based on Joule heating and heat source effects. The Cattaneo–Christov theories govern the expansion of mass and heat transfer. We analyze thermal problems under zero-mass diffusion constraints. The use of proper variables simplifies mathematical modeling into a dimensionless form. The Homotopy Analysis Method (HAM) solves the dimensionless system. The paper highlights the convergence criteria for the HAM procedure. Graphics underline the problem’s physical perspective. We observe that the Deborah number enhances heat and mass transfer. The temperature profile decreases when the parameter becomes unstable.

In this paper, the heat-transfer enhancement phenomena have been explored for non-axisymmetric Homann stagnation-point flow of Maxwell fluid. Furthermore, Buongiorno’s model for nanofluid is utilized to study remarkable impacts of random (Brownian) motion and thermophoresis of dispersed nanoparticle. The Maxwell nanofluid generates new class of asymmetric stagnation-point flows that depends on ratio $\gamma =b∕a$ ($b$ is shear and $a$ is strain rate) and Deborah number ${\beta }_1$. The numerical and asymptotic consequences of leading equations for current model are obtained using shooting technique. The solution is obtained for diverse values of involved parameters over $\gamma$. The wall shear stress, heat/mass transfer rate, velocities, temperature distributions and nanoparticle concentration compared to their large-$\gamma$ asymptotic behaviors were presented for different values of involved parameters. It is observed that the numerical outcomes of wall shear stress, heat-transfer rate and mass flux best agree with their perturbative solution for large-$\gamma$. Moreover, the wall shears $f^{\prime \prime }(0)$, $g^{\prime \prime }(0)$ grow as viscoelasticity raises. The reduction in heat flux and particles mass diffusion occurs near the wall boundary-layer due to clustering of nanoparticles. However, heated surface during thermophoresis is pushed nanoparticles into Brownian motion which constitute to enhance the heating process.

In this study, the numerous solutions to Falkner–Skan flow of a Maxwell fluid with nanoparticles are investigated, considering the nonlinear radiation and magnetic domain. The flow described above can be expressed in accordance with PDEs that are transformed into ODEs by choosing suitable variables of similarity. The fourth- and fifth-order Runge–Kutta–Fehlberg method can be utilized to solve these reduced ODEs by applying the shooting approach. The graphs were drawn to explain the effects of different parameters on different fluid profiles for both the lower- and upper-branch solutions. This study shows that the velocity outlines improve both solutions by increasing local Deborah numbers slightly. Besides, an increase in radiation reduces the thermal gradient for both solutions, thereby reducing the concentration gradient for both solutions contributing to raised Brownian motion and Lewis numbers.

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile.

The current paper focused on an unsteady bio-convective Maxwell nanofluid flow subject to convective boundary conditions through an exponentially stretching curved surface. The transportation of heat and mass are observed with thermophoresis and Brownian effect along with chemical reaction. The mathematical flow model is converted into a system of nonlinear system of ODEs via suitable transformation. The numerical solution of a nonlinear system of equations is established with the help of bvp4c MATLAB technique. It is deeply studied that in the curved surface, the pressure is never ignored. The graphical representation of several parameters along the temperature, concentration, microorganism density and velocity distribution is presented. It is examined that the greater estimation of curvature parameter boosts the temperature of fluid and concentration of nanoparticles, although a reverse trend is seen for the velocity profile. Further, it is examined from the numerical values that the heat and mass transfer rate reduce consequently with the enlargement of the curvature parameter.

This paper studies a chemical reactive Maxwell nanofluid flow in porous media with generalized Fourier and Fick laws in the presence of temperature-dependent thermal conductivity and robin conditions past a spinning cone. The characteristics of the fluid flow are examined using the Buongiorno nanofluid model. The equations that regulate the flow are highly nonlinear and are simplified using similarity transformations. Numerical solution is obtained by employing the bvp4c technique. The characteristics of various parameters on tangential and azimuthal velocities, heat, and mass transfers are depicted graphically. An opposing behavior on the tangential and azimuthal velocity fields is depicted in elevating the Deborah number. The solutal field upsurges on increasing the order of the reaction. The mass flux strengthens by augmenting the Schmidt number and solutal relaxation time. The validation of the proposed model in the limiting case is also given.

The heat conversation medium temperately regulates the heat exploitation effectiveness of solar energy. Nanofluids, a kind of functioning fluids with extraordinary thermal conductivity and strong light concentration, have been scrutinized and functionalized to progress the exploitation of solar energy. In recent times the current progress examines the nanofluids with the consideration of thermal sources as it can raise the heat transportation amount. Here, the purpose is to explore the thermal properties of Joule heating and thermal conductivity in magnetite Maxwell nanofluid. The concept of heat sink/source and chemical reaction are also studied. The achieved ordinary differential equations have been solved via homotopic algorithm. The enactment of functioning variables is examined. For Eckert number and variable conductivity factors, the Maxwell temperature field has analogous tendencies. The fluid concentration inflates for thermophoretic factor; however, slows down for the Brownian motion factor. The Brownian and thermophoretic factors decay for Nusselt number. Additionally, the excellent results have been achieved accompanied with possible existing prose precisely.

This study examines and analyzes the impact of MHD and bioconvection on Maxwell’s nanofluid flow in a porous medium that contains gyrotactic microorganisms. In addition, more study on chemically reactive activation energy and Cattaneo–Christov heat flux is conducted, and the conclusions from this research are presented. The bioconvection flow of Maxwell nanofluids over a stretched sheet is presented by highly nonlinear partial differential equations, which are reduced to ordinary differential equations using suitable similarity transformations. A shooting method based on the Runge–Kutta technique is used to overcome the issue. The outcomes are graphically represented and explored numerically in detail for the relevant parameters’ impact on the velocity, temperature, concentration, and motile microorganisms profiles. Results reveal that the velocity profile is decreased by increasing the magnetic parameter, while those enhanced by the mixed convection parameters. The thermal boundary thickness and temperature profile negatively correlate with the thermal relaxation time and Prandtl number and are proportional to the magnetic parameter. Boosting the Brownian motion parameter, Deborah number, and thermophoresis parameter improves heat transport. The activation energy and Prandtl parameters show an upward trend in concentration profiles. The density of the motile microorganisms is a decreasing function of Lewis and Peclet numbers.