A mathematical model is created to analyze the impact of Thompson and Troian slip boundaries over a contracting/expanding surface sustaining nanofluid-containing carbon nanotubes along a stagnation point flow. Both multi-wall (MWCNTs) and single-wall (SWCNTs) carbon nanotubes are taken into consideration, with water serving as the base liquid. The flow is obtained due to the stretching or contracting of the surface. The thermal radiation, activation energy, buoyancy impacts, and chemical processes called quartic autocatalysis are additionally added to the original mathematical model. The MATLAB-constructed bvp4c function involving the three-stage Lobatto IIIa formula for the numerical results of dimensionless velocity, concentration, and temperature profiles are used. By contrasting it against a published paper in this limited instance, it is determined whether the suggested mathematical model is legitimate. In this sense, a remarkable consensus is achieved. Graphical representations are used to depict the behavior of many non-dimensional flow variables, such as the slip velocity parameter, the inertia coefficient, the porosity parameter, and the solid volume fraction. Surface drag force computations are reported to examine the effects at the permeable stretching surface. It has been shown that increasing the slip velocity factor increases the fluid streaming velocity while decreasing the surface drag force. If the endothermic/exothermic coefficient increases, the local thermal transfer efficiency falls. For nanofluids, the changing viscosity factor increases axial velocity while decreasing temperature distribution. Additionally, the solid volumetric fraction improves the temperature distributions by lowering the concentration profile and speed.

This article presents an analysis of the radiative flow of nanofluid past a convected vertical Riga plate with activation energy and nonlinear heat generation. A Riga plate is a surface-mounted electromagnetic actuator with a spanwise aligned array of alternating electrodes and permanent magnets. The aforementioned rheological model is formulated in the way of the nonlinear partial differential equations (PDEs). The system of nonlinear coupled ordinary differential equations (ODEs) is obtained from the modeled nonlinear PDEs by incorporating valid similarity transformations. The system of ODEs is then figured out by the reliable shooting method. The effects of mixed convection, modified Hartmann number, Biot number, thermophoresis, Eckert number, reaction rate, the width of magnets and electrodes, and Lewis and Prandtl numbers on the velocity, temperature, and concentration profiles are investigated graphically and numerically. It is found that the speed of the fluid can be managed with the separation of magnets and electrodes. Further, the concentration of nanofluid is significantly enhanced in the presence of activation energy. Also, the nonlinear exponential index parameter of heat generation declines the temperature of the fluid. Further, it is found that in the presence of thermal radiation, viscous dissipation, and nonlinear heat generation, the Nusselt number increases averagely by about 11.3%.

This research paper focuses on investigating the phenomenon of entropy generation, specifically within the context of blood flow. Blood is modeled as a three‐layered liquid model, with micropolar and Newtonian fluids occupying the center and periphery sections of the tube, respectively. A narrow glycocalyx layer adjacent to the wall is regarded as indicating a permeable area caused by the accumulation of carbohydrates and fibrous tissues within the tube wall. Further, the walls of the cylinder are taken as permeable. The objectives of this study include understanding the mechanisms and factors contributing to entropy generation in blood patterns, exploring the relationship between entropy generation and flow characteristics, and analyzing the impact of entropy generation on the overall energy efficiency of the system. The transformation of ordinary differential equations (ODEs) from partial differential equations (PDEs) can be accomplished by employing a similarity approach that combines shooting methods with the inculcation of the RK‐4 method. This integrated technique facilitates the transformation process effectively. Then, MATLAB software is used to plot graphs for accuracy purposes. Under various physical limitations, the comparison study demonstrates that trihybrid nanoliquids exhibit ultrahigh thermal efficiency compared to ordinary nanoliquids, and incorporating these nanofluids enhances entropy generation, temperature, and Bejan profiles, improving thermal conductivity and energy transfer. This integration ensures sustained performance over time, benefiting from carefully selected nanoparticles for stability optimization. As a result, these fluids are extremely useful for industrial applications, particularly filtration and ultrahigh heat.

This study examines the flow and heat transfer of a finite thin layer of a hybrid nanofluid across an unstable stretching surface with varying thermal conductivity and viscous dissipation effects. A hybrid nanofluid model is considered to comprise two different types of nanoparticles, and , with kerosene oil used as a base fluid. To study the phenomenon of thermal conduction, a modified version of Fourier’s law model is adopted because in the power-law model, the thermal conductivity depends on the velocity gradient. A system of nonlinear ordinary differential equations is obtained by considering the similarity transformations over the obtained rheological system of partial differential equations which is then tackled by a well-known numerical approach, i.e., the bvp4c MATLAB technique. The rheological impacts of the power-law index, solid volume fraction, film thickness, Eckert number, and modified Prandtl number on temperature and velocity fields are graphically discussed and illustrated. In the presence of nanoparticles, the temperature of the working fluid is enhanced and the power-law index has an inverse relation with the velocity of the hybrid nanofluid.

The goal of the basic work is to, better understand how a Maxwell nanofluid flows in the stretching cylinder with active and passive controlled nanoparticles and study about oblique stagnation point blood flow of Maxwell nanomaterials over a stretching cylinder. Three different types of nanoparticles Cu + Al2O3 + TiO2 are considered with blood used as base fluid. This is accomplished by deriving the fluid flow and heat transfer governing equations from the conservation laws of mass, momentum, concentration and energy. Following that, the resulting partial differential equations are numerically solved using the proper techniques and boundary conditions. Similarity, transformation are applied to reduce the governing partial differential equations into a system of nonlinear ordinary differential equations, which are solved by numerically by shooting method coupled with Runge-Kutta method BVP4C. The effects of Prandtl number, Schmidt number, Thermophoresis parameter, Velocity ratio parameter, types of nanoparticles, nanoparticles concentration at the surface of cylinder, radius of cylinder and length of cylinder, effect flow behavior with active and passive nanoparticles on stretching cylinder are graphically illustrated and discussed. The main objective is to examined the oblique stagnation point flow of incompressible Maxwell nanofluid past a stretching cylinder with regulated active and passive nanoparticle concentration conditions.