Curved veins and arteries make up the human cardiovascular system, and the peristalsis process underlies the blood flowing in these ducts. The blood flow in the presence of hybrid nanoparticles through a tapered complex wavy curved channel is numerically investigated. The behavior of the blood is characterized by the Casson fluid model while the physical properties of iron (Fe₃O₄) and copper (Cu) are used in the analysis. The fundamental laws of mass, momentum and energy give rise the system of nonlinear coupled partial differential equations which are normalized using the variables, and the resulting set of governing relations are simplified in view of a smaller Reynolds model approach. The numerical simulations are performed using the computational software Mathematica’s built-in ND scheme. It is noted that the velocity of the blood is abated by the nanoparticles’ concentration and assisted in the non-uniform channel core. Furthermore, the nanoparticles’ volume fraction and the dimensionless curvature of the channel reduce the temperature profile.

In order to meet the current challenges in the fabrication of nanobiomaterials and enhancement of thermal extrusion systems, current theoretical continuation is targeted at the rheology of couple stress nanofluid by exploiting activation energy, porous media, thermal radiation, gyrotactic micro-organisms, and convective Nield boundary conditions. The heat and mass performances of nanofluid are captured with an evaluation of the famous Buongiorno model, which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The couple stress fluid is beneficial to examine multiple kinds of physical problems because this fluid model has the capability to describe the rheology of various complex fluids, e. g., fluids having long-chain molecules as a polymeric suspension, liquid crystals, lubricants, and human and animal blood. Simultaneous behavior of the magnetic field and porosity are studied with thermal radiation effects. The distribution of velocity has been conducted by using second-order velocity slip (Wu’s slip) and activation energy features. For the dimensionless purpose, the similarity variable has been initiated, and the modeled equations are renovated sufficiently. A famous shooting method is used to determine the numerical solutions, and accurate results have been obtained. A variety of critical flow parameters is graphically illustrated with physical significance.

Background: The improvement of the thermal conductivity of nanofluids is practical for different processes such as drug delivery, manufacturing of crystals, polymer processing, food and drink, cancer treatment, oil and gas, paper making and for many more. The bioconvection phenomenon has engrossed the attention of numerous researchers for its many applications in biotechnology, mechanical and electrical engineering. Bioconvection nanofluids are more prominent in the fields of biomedicine, pharmacy, nanodrug delivery, biomedical, automotive cooling and the military. Purpose: The major purpose of the current work was to determine the numerical and statistical analysis of a novel thermal radiation and exponential space-based heat source on the bioconvective flow of a pseudoplastic 3D nanofluid past a bidirectional stretched Riga surface. The behavior of the Arrhenius activation energy (AAE) and thermal radiation are also disclosed. Methodology: Suitable similarity transformations were used to transmute the partial differential equations of the flow-modeled phenomena into the structure of ordinary differential ones. The numerical solutions for the renewed set of ODEs were tackled by the bvp4c shooting algorithm built-in MATLAB software. Furthermore, the statistical analysis was computed by applying response surface methodology (RSM). Research implications: The numerical analysis is valid for the incompressible three-dimensional, magnetized flow of a pseudoplastic bioconvection nanofluid through a bidirectional surface with Riga plate aspects in the occurrence of activation energy. Social implications: The flow across three dimensions has quite important implementations in various fields, for example, polymer production, material production technology, the manufacturing of nano-biopolymer computer graphics, industry, powered engineering, aeroplane configurations, etc. The current analysis is more applicable in nanotechnology. Results: The consequences of flow control parameters over flow profiles were studied and explained under the graphic structures. Numerical outcomes were computed and discussed in detail. From the results, it was noted that the velocity field was increased via a larger mixed convection parameter. The temperature distribution was boosted via the thermal Biot number. The concentration of nanoparticles declined via the greater Lewis number. Furthermore, the motile microorganisms field was reduced via the Peclet number. Originality: Until now, no investigation has been recognized to examine the consequences of the bioconvection flow of three-dimensional pseudoplastic nanofluids past a Riga plate containing motile microorganisms utilizing the shooting method called bvp4c. Conclusions: From the results, it was concluded that nanofluids are more helpful for heat transfer increments. Furthermore, from the experimental design observed, the response declined via the thermophoresis parameter, which was significant from the ANOVA observed model.

The current continuation aim is to explore the rheological consequences of Eyring Powell nanofluid over a moving surface in the presence of activation energy and thermal radiation. The bioconvection of magnetized nanoparticles is executed with the evaluation of motile microorganism. The most interesting Wu’s slip effects are also assumed near the surface. The evaluation of nanoparticles for current flow problems has been examined by using Buongiorno’s model. The governing equations for the assumed flow problem are constituted under the boundary layer assumptions. After converting these equations in dimensionless form, the famous shooting technique is executed. A detailed physical significance is searched out in the presence of slip features. The variation of physical quantities, namely velocity, nanoparticles temperature, nano particles concentration, motile microorganism density, skin friction coefficient, local Nusselt number and motile organism density number are observed with detailed physical aspects for various flow controlling parameters.

The thermal performances based on the interaction of nanoparticles are the topic of great interest in recent years. In the current continuation, we have utilized the activation energy and thermal radiation consequences in the bioconvection flow of magnetized Oldroyd-B nanoparticles over a stretching cylinder. As a novelty, the second order slip features (Wu’s slip) and convective Nield boundary assumptions are also introduced for the flow situation. The heat performances of nanofluids are captured with an evaluation of the famous Buongiorno’s model which enables us to determine the attractive features of Brownian motion and thermophoretic diffusion. The suggested thermal system is based on the flow velocity, nanoparticles temperature, nanoparticles volume fraction and motile microorganisms. The governing flow equations for the flow problem are constituted with relevant references for which numerically solution is developed via shooting algorithm. A detailed graphically analysis for the assisted flow problem is performed in view of the involved parameters. Although some studies are available in the literature which deals with the flow of various fluids over-stretching cylinder, the phenomenon of bioconvection and other interesting features are not reported yet. Therefore, present scientific computations are performed to fill this gap and the reported results can be more useful for the enhancement of thermal extrusion processes, solar energy systems, and biofuels.

The appropriate utilization of entropy generation may provoke dipping losses in the available energy of nanofluid flow. The effects of chemical entropy generation in axisymmetric flow of Casson nanofluid between radiative stretching disks in the presence of thermal radiation, chemical reaction, and heat absorption/generation features have been mathematically modeled and simulated via interaction of slip boundary conditions. Shooting method has been employed to numerically solve dimensionless form of the governing equations, including expressions referring to entropy generation. The impacts of the physical parameters on fluid velocity components, temperature and concentration profiles, and entropy generation number are presented. Simulation results revealed that axial component of velocity decreases with variation of Casson fluid parameter. A declining variation in Bejan number was noticed with increment of Casson fluid constant. Moreover, a progressive variation in Bejan number resulted due to the impact of Prandtl number and stretching ratio constant.