The research of non-Newtonian fluids has gained the attention of scientists because of its assorted uses in biological sciences, drug reduction, damping device production and industry. Second-grade nanofluid is one of the non-Newtonian fluids. This study includes the study of second-grade nanofluid flow passing through a stretchable vertical Riga surface of variable thickness. Thermal conductivity and viscosity are taken as variables, as the function of temperature. For heat transfer, this study includes the influences of thermophoresis and Brownian motion. The Cattaneo–Christov double diffusive (CCDD) model is considered and buoyancy forces’ effects are examined. The governing equations are converted to the nonlinear ordinary differential equations (ODEs) to solve these equations easily. The solution is obtained using the MATLAB package with its bvp4c technique. Consequences of different parameters like second-grade fluid parameter modified Hartmann number, thermal time relaxation parameter, concentration time parameter, variable thermal conductivity parameter, buoyancy forces, Brownian motion parameter, Schmidt number and thermophoresis parameter are interpreted through graphs and tables. This research exposes that Buoyancy forces’ parameters have antagonistic behavior on velocity curves. Depreciation in temperature and concentration is also noted with the rise in thermal time relaxation and concentration time relaxation.

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There are various implementations of common fluids in industrial and chemical processes. With the cooperation of the nanoparticles, the lower thermal properties of such fluids can be augmented. By using a new kind of nanofluid namely hybrid nanofluid, the heat transfer rate of such fluids can be boosted more quickly. The main intention of this research is on entropy analysis in the stagnant point flow of a hybrid nanofluid. The mixed convection nonlinear thermal radiative flow on a stretchable vertical sheet is examined under the influences of the induced magnetic field and chemical reactions. The impacts of Joule heating, partial slips and viscous dissipation are also involved. After the execution of the appropriate similarity transformations, the constituting equations of the flow problem emerge as the nonlinear dimensionless setup of ordinary differential equations. An amplification is examined in the velocity field, entropy generation, and induced magnetic field relative to the mixed convection parameter. With the improved Brinkman number, an augmentation is developed in the entropy of the system. Moreover, both the heat transfer rate and the surface drag force exhibit an accelerating behavior relative to the mixed convection parameter.

In many fields, there are various applications of non-Newtonian fluids. Various complicated fluids (polymer melts, clay coatings and oil) belong to the category of non-Newtonian fluids. The third-grade fluid is one of the most important non-Newtonian fluid models. This paper has the primary object of heat transfer mechanism and boundary layer third-grade fluid flow under the effects of thermal radiation. The time-dependent two-dimensional flow is considered to flow above a permeable stretchable vertical Riga plate. For numerical solutions, the setup of ordinary differential equations (ODEs) is acquired by converting nonlinear governing equations through relevant similarity transformations. The nonlinear setup of ODEs is numerically solved with the aid of a suitable software such as MATLAB via its bvp4c technology. Graphs are sketched to discuss the various flow parameters’ significance for the expression of velocity and temperature fields. Tabulated values of surface drag force and heat transfer rate corresponding to the numerous pertinent parameters are described. The current analysis of the concerned flow mechanism concludes that the fluid parameters descend the temperature distribution but amplify the profile of the fluid velocity. The radiation parameter escalates the temperature field.

The main purpose of this study is to scrutinize the axisymmetric flow of second-grade nanofluid with variable viscosity near a stagnation point under the influence of the Cattaneo–Christov double diffusion model. A Riga plate is assumed to be the source of the three-dimensional flow. The consequences of the anisotropic slip conditions and the Buongiorno model are included in the formulation of the constituting equations of the fluid flow. The highly nonlinear ordinary differential equations are developed with the executions of the relevant similarity transformations on the problem’s governing equations. For the asymptotic analysis, the appropriate expansions are implemented on the nonlinear system of ordinary differential equations. The bvp4c technique of the MATLAB package is implemented on the nonlinear ordinary equations for the numerical solutions. In order to explore the impact of the parameter slip factor on the pattern of velocities, temperature, and concentration profiles, several graphs are plotted. From this study, we conclude that the normalized velocities boost up with the amplification in the slip factor parameter but the temperature profile exhibits a declining behavior. The concentration field exhibits the accelerating behavior relative to the slip parameter.