The study highlights a rising number of fluids such as nanofluids and hybrid nanofluids encountered in daily life that exhibit non-Newtonian behavior and they are exploited in manufacturing due to their high heat transfer rate becoming more and more important as time goes on. The focus is on hybrid nanomaterials because they increase liquid alloys' and fluids' thermal conductivity. The various investigations on a thermal Marangoni convective flow of aluminium alloy and Boehmite alumina nanoparticles into gasoline oil in base fluid water on a steady Darcy-Forchheimer flow are covered. With the system's exponential heat generation and viscous dissipation, the thermal impact is more pronounced in the presence of Cattaneo-Christov heat flux. To simplify the highly coupled nonlinear governing equations (PDEs) and the boundary conditions (BCs), a suitable similarity conversion is being applied. The outcomes of the conversion equations and their BCs are evaluated by MATLAB bvp4c routine with the shooting techniques. Through the use of graphs and tables, it has been determined how different governing factors affect the velocity, temperature, skin friction, and Nusselt number. A quick comparison between a hybrid nanofluid and a nanofluid is displayed in each graph. We also discussed the system's Bejan numbers and entropy creation. It has been observed that the proportion of heat transmission increases with heat generation but decreases with the Marangoni number. A nonlinear increase in the permeability constant and Brinkman number results in a rise in entropy generation.

Nonlinear mixed convection in magnetohydrodynamic thermo-convection nanofluid flow is addressed. Flow is induced by a stretched surface. Chemical reaction effects on the activation energy of the species concentration of Arrhenius are considered. The nonlinear governing equations are converted to a dimensionless ordinary system through adequate transformations. The solutions of nonlinear dimensionless expressions are computed by employing the spectral quasilinearization method. A consequence of various parameters involved such as velocity, concentration, and thermal field has been reported graphically. Concentration has the reverse trend for both random motion and thermophoresis variables.

The analysis of impinging oblique nano-fluid past a stretching sheet is done in the current communication. The nanoparticles' behaviour in fluids for convective heat transfer has been extensively studied. We assume that the fluid and the stretching velocity change linearly. In this paper, we used a cutting-edge Genetic Algorithm technique to better understand how a nanofluid's thermal characteristics and heat transport vary over time. Additionally, the impact of a change in the fluid's impinging angle is investigated. The temperature and concentration curves, skin friction coefficient, and Nusselt number have all been observed and graphically displayed. 

An analysis was conducted to observe the collective consequence of the melting procedure across a stretching sheet in a Casson nanofluid with outer velocity. The outcomes of melting heat parameter (M) and Casson parameter (β) are shown in this analysis. The leading PDEs are moulded in ODE with similarity variables. The numerical results of moulded ODE are given by the RKF scheme with shooting procedures. Important parameters of the nanofluid are examined and graphically displayed. Tables are used to display the Sherwood number, Nusselt number, and skin friction coefficient based on different nanofluid characteristics. The development of cooling systems that raise the heat transmission belongings of nanofluids and increase engineering potential will be greatly aided by this research. 

The current study looks at the heat transfer of a magneto-radiative nanofluid over an exponentially contracting permeable sheet in the existence of heat generation with numerous slip boundary constraints. It also looks at the stability and duality of solutions. Here, a waterbased fluid with silver (Ag) nanoparticles is employed. Before being computed by bvp4c in the Matlab program, the governing nonlinear partial differential equations are converted into dimensionless nonlinear ODEs via a similarity transformation. Due to the contracting surface scenario, a dual-nature solution can only be found if a sufficient suction value is used. We may infer from stability investigation that the first one is stable while the second one is unstable. A stable solution makes sense with the least positive eigenvalues, but a lower unstable solution indicates negative eigenvalues. The Nusselt number and the skin-friction factor may be improved by increases in the silver nanoparticle’s solid volume percentage. The least eigenvalue converges to zero as the suction and contracting surface parameters reach their critical values. Nanofluids that are magnetic and radiative can be used to create beautiful and effective electromagnetic devices, including in the areas of clothing, paper, plastics, food colorants, cars, cancer therapy, medicines, ceramics, soaps, and paints.

The primary goal of the current investigation is to understand the thixotropic nanofluid’s magnetohydrodynamic (MHD) nonlinear convective flow. The implementation of appropriate transformations allows for the transition of sets of ordinary differential equations from partial differential systems. Spectral Quasi-Linearization Method (SQLM) is applied to solve these ODEs. Further study has been performed in order to establish a model for nanomaterials containing thermophoresis phenomena and Brownian motion. Graphs are used to depict and discuss the effects caused due to numerous quantities of fluid flow, temperature, environment, and nanoparticle concentration. In addition to this, the local Nusselt number, the skin friction coefficient, as well as the Sherwood number's numerical values, are determined and examined. Some interesting observations on velocity, heat, and concentration have been observed due to the variation made in thixotropic parameters and other allied parameters such as thermophoresis and Brownian motion. 

In this current study, we investigated the boundary layer steady nanofluid flow which is viscous. Utilizing the spectral quasi-linearization method (SQLM), the mathematical model has been solved. To analyze the convergence of the numerical method, we calculated the residual errors that are approximately less by [10-8 ]. The local Sherwood number, the coefficient of the rate of heat transfer, and the local drag force coefficient along with various flow parameters are analyzed numerically and graphically. The influence of thermophoresis and Brownian motion has also been discussed briefly.