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Non-Newtonian fluids display fascinating and versatile flow behavior, enabling applications in fields where precise control and manipulation of viscosity are required. This paper presents the rheology of Homann stagnation point flow for a Jeffrey fluid containing gyrotactic microorganisms over a biaxially stretching surface. The system of equations is solved numerically using appropriate similarity transformations and conditions. The boundary conditions are set to maintain a fixed physical environment, and the far field values are defined accordingly. The dual solutions are found and expressed in terms of relevant quantities, and their behavior is analyzed using graphical representations via bvp5c. Stability analysis is conducted as well. The model is extended to study the behavior of Jeffrey nanofluids under the influence of various physical phenomena such as thermophoresis, Brownian motion, Ohmic heating, heat source/sink, radiation, and chemical reaction. The model presented in this paper can help researchers predict and optimize the behavior of such systems for a range of industrial and biomedical applications. It is observed that when the smallest eigenvalue is positive, the disturbance initially decreases, and the flow is stable, otherwise unstable. The stretching/shrinking parameters affect the flow field and boundary layer characteristics, leading to changes in the skin friction forces and an increase in the skin friction coefficient. Moreover, the Peclet number augmented the concentration of microorganisms due to gyrotactic bioconvection for first and second solutions, whereas bioconvective Lewis number shows an opposite trend. The comparison of the present results, as a simplified case, with existing literature demonstrates good agreement.

In this paper, the self-propelled movement on gyrotactic swimming microorganisms into this generalized slip flow by nanoliquid over the stretching cylinder with strong magnetic field is discussed. Constant wall temperature was pretended as well as the Nield conditions of boundary. The intuitive non-Newtonian particulate suspension was included into applying Casson fluid by the base liquid and nanoparticles. This formation on the bio-mathematical model gives the boundary value problem by the nonlinear partial differential equations. Primly, modeled numerical system was converted to nondimensional against this help on acceptable scaling variables and the bvp4c technique was used to acquire the mathematical outcomes on the governing system. This graphical description by significant parameters and their physical performance was widely studied. The Prandtl number has the maximum contribution (112.595%) along the selected physical parameters, whereas the Brownian motion has the least (0.00165%) heat transfer rate. Anyhow, Casson fluid was established for much helpful suspension of this method on fabrication and coatings, etc. Therefore, this magnetic field performs like the resistive force of that fluid motion, and higher energy was enlarged into the structure exhibiting strong thermal radiation.

The suspension nanoparticles in non-Newtonian materials convey different applications in the thermal systems, engineering processes, industrial energy developments, extrusion systems, solar system, etc. It is commonly observed that the thermal properties in the various base materials fluctuated and cannot be assumed to be constants. A decomposition of nanofluids is fluctuated and cannot considered as a constant. The objective of this communication is to inspect the thermal mechanism of non-Newtonian nanofluids due to accelerated frame in view of variable thermal conductivity. The modified mathematical relations for Fourier and Fick theories are utilized to model the problem. The nanofluids contain the microorganisms to ensure the thermal stability. The problem is modeled in nonlinear partial differential system which is further communicated via HAM. The convergent analysis is ensured and later on physical illustrations to problem in view of parameters are discussed. It is observed that thermal phenomenon controls due to mixed convection parameter while increasing impact for Williamson fluid parameter is observed. The magnitude of oscillation of Nusselt number due to Prandtl number is enhanced without any phase difference. The obtained results may convey different engineering applications like extrusion systems, chemical processes, thermal management systems, heating and cooling application, plasma, manufacturing processes.

This paper describes the bioconvection phenomenon and its significant influence on the thermal features of the flow of bi-viscous Bingham (BVB) nanofluid past a vertically stretching flat surface. The analysis of the impact of convection parameters is considered along with various other forces. Meanwhile, the flow of BVB nanofluid is put through the slip conditions defined by Thompson and Troian for the velocity at the boundary. The flow of BVB nanofluid is modeled using the partial differential equations (PDEs) under the assumptions of thermophoresis and Brownian motion which occur due to the movement of nanoparticles. Along with these forces, the radiation is also considered so that the obtained results are close to the practical scenarios. Thus, using the proper Lie group similarity transformations, the intended mathematical model is converted into ordinary differential equations (ODEs). The resulting equation system is encoded using the RKF-45 technique, and the outcomes are explained using graphs and tables. The solutions found for the model showed that, for higher ranges of the non-Newtonian fluid parameter, the velocity decreases while the heat transferred by the nanofluid increases. The availability of motile density at the surface grows as the Péclet number rises, whereas the Schmidt numbers decline in their respective profiles.

The main goal of our research is to find the connection between micro particles and microorganisms motion in the Nature, considered as Brownian’s Motion within the fractal’s nature. For ceramics and generally material science it is important to clarify the particles motion and other phenomena, especially for grains and pores. Our idea is to establish control over the relation order–disorder on particle motion and their collision effects by Brownian motion phenomena in the frame of fractal nature matter. We performed some experiments and got interesting results based on microorganism motion initiated by different outer energetic impulses. This is practically the idea of biomimetic correlation between particles and microorganisms Worlds, what is very original and leads towards biunivocal different phenomena’s understanding. Another idea is to establish some controlling effects for electro ceramic particle motion in chemical-materials sciences consolidation by some phenomena in the nature. These important research directions open new frontiers with very specific reflections for future of microelectronics materials.

Nanofluids, due to their complex behavior and enhanced thermal properties, are utilized across chemical, biotechnology and thermal engineering disciplines. They are particularly integral to heat transfer processes in heavy machinery and vehicles. This study introduces a novel method for analyzing heat transfer within a tetra nanofluid system through a hybrid analytical and numerical approach. Our research primarily examines the dynamics of a magneto Williamson hybrid tetra nanofluid embedded with motile gyrotactic microorganisms. The study is designed around two scenarios: one investigates the behavior of an Al₂O₃–Cu–CuO–Cobalt/Engine oil nanofluid under suction conditions, and the other under injection conditions. By employing similarity variables, we transform the original fluid flow equations into nonlinear differential equations to further explore the influence of various physical parameters on the fluid’s flow. Such parameters include the nanofluid temperature and velocity as well as the concentration of nanoparticles, and the volume fraction of motile gyrotactic microorganisms. The optimization of the numerical results for skin friction, Nusselt number, Sherwood number and microorganisms concentration is validated through response surface optimization techniques. Additionally, the study utilizes Matlab‘s bvp4c function to examine the thermal efficiency and characteristics of fluid flow across a spectrum of parameter values.

The main aim of the present work is the content analysis of the Portuguese National Curriculum and the Primary School textbooks where microorganisms are concerned. The content analysis through categories created a priori were used as methodology. In all analysed documents the topic microorganisms did not emerge in a clear way. However, several indirect themes related to microorganisms were found in the National Curriculum and textbooks of the Environment Study issue. These themes can be explored with pupils through experimental activities. The Science Education in primary schools can be introduced with proposals of activities involving microorganisms and contributing to a better understanding of the children's world.

This theoretical thermal continuation deals with the radiative flow of Williamson nanofluid subject to the inclusion of microorganisms. The further modification in the bio-convective model is done by incorporating the heat source/sink and activation energy phenomenon. The motivation for the choice of Williamson nanofluid is referred to multidisciplinary rheological impact which may enhance the heating phenomenon upon inclusion of nanoparticles. A bidirectional moving surface is the source of inducing flow patterns. The governing expressions which result via thermal model are numerically simulated with a shooting scheme. The impact of flow parameters is identified for velocity change, heat transfer rate, concentration, and microorganism profile. Moreover, the numerical results in terms of different tables are framed out for observing the fluctuated pattern of heat transfer, concentration impact, and microorganism change. The outcomes simulated from the model reflect that a lower velocity rate is results for the velocity ratio parameter. The external heat source attributed the enhancement of heat transfer. Moreover, the concentration profile improves with activation energy and convection constant.

This study describes the Casson (a non-Newtonian fluid) nanofluid bioconvection flow across a spinning disc in the presence of gyrotactic microorganisms, many slips and thermal radiation. Also, the flow is considered as a reversible flow. The esterification process is taken into account. Using the proper variables, a system of extremely nonlinear PDEs is converted into a system of ODEs. To arrive to the solution of such equations, a numerical approach is used. Using the bvp4c approach, nonlinear flow equations can be numerically solved. Investigated are the effects of different numbers on the thermal field, volumetric concentration of nanoparticles and microbiological field. The key characteristics of the parameters in relation to the profiles of the velocity, temperature, concentration and microorganisms are graphically assessed with appropriate physical effects. A graphical explanation is provided for the wall shear stress, local Nusselt number, local Sherwood number and local motile density number. Rate of motile density number shows a prominent difference between reversible and irreversible flows for Brownian motion and Peclet number. The results of the theoretical simulations have dynamic applications in the fields of biotechnology and thermal engineering.

The antimicrobial activity of new meso-tetrakis(N-methyl-6-quinolinyl)-substituted porphyrins and meso-tetrakis(N-methyl-6-quinolinyl)-substituted chlorins is described. The dark toxicity and photosensitising potentials of free-base (TQP and TQC) and its Sn(IV)-complexes [(TQP)Sn(IV) and (TQC)Sn(IV)] were tested on Gram-positive (Staphylococus aureus), Gram-negative (Escherichia coli and Pseudomonas aeruginosa) bacteria and two species of yeasts (Candida albicans and Rhodotorula bogoriensis). The results described in this paper show that TQP and (TQP)Sn(IV) did not inhibit the growth of S. aureus in the dark, but efficiently photosensitize the inactivation of this Gram-positive bacteria. These porphyrins have no appreciable photosensitizing activity towards Gram-negative bacteria. However, (TQP)Sn(IV) shows high dark toxicity against E. coli and P. aeruginosa. The free-base derivatives demonstrated dark activity only in the case of P. aeruginosa. We suppose that these meso-tetrakis(N-methyl-6-quinolinyl)-substituted porphyrins can bind to the Gram-negative bacteria outer membrane receptors that transported vitamin B₁₂. The meso-substituted chlorins TQC and (TQC)Sn(IV) have shown similar efficiency in the dark- and photoinactivation of S. aureus. They revealed a middle level of dark toxicity towards Gram-negative bacteria. The Sn(IV)-complex of chlorin in comparison with free base and metalloporphyrins are more effective in photoinactivation of Gram-negative bacteria. Yeasts, such as Candida albicans and Rhodotorula bogoriensis are more sensitive to photodynamic inactivation as bacterial cells. The effects of (TQP)Sn(IV) and (TQC)Sn(IV) are more expressed than effects of free bases.