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This investigation uses the Tiwari and Das nanofluid model to enhance the heat transfer rate in Sutterby nanofluid over a Riga plate. The effects of heat source/sink, viscosity dispersion, and mass flow for water-based fluids are also considered in this work. Sutterby fluid has been utilized to investigate the rheological features of nanofluids. The transverse Lorentz force produced by the Riga plate assists in the flow down the plate by producing an electromagnetic field. The main aim of this investigation is to evaluate the presence of two different types of nanoparticles in water, specifically silicon carbide (SiC) and copper (Cu). Dimensionless variables are first used to convert the mathematical model into a non-dimensional form. The similarity approach is then used to further rewrite the non-dimensional partial differential equations into a set of similarity equations. The bvp4c function in MATLAB software provides a numerical solution to these equations. The effects on temperature and velocity profiles of many physical factors, including the Reynold number, heat source/sink, and Deborah number, have been analyzed and presented. Furthermore, using tables, a detailed analysis of the skin friction coefficient and local Nusselt numbers is conducted. The results show that convective flow is suppressed when solid nanoparticles are added to the base fluid. The velocity distribution improves as Deborah and Reynold's numbers get a higher value. Also, the temperature field improves by incrementing exponential and thermal heat source/sink parameters. [ABSTRACT FROM AUTHOR]

Microorganism movement may boost the convective transfer of heat by stirring the fluid to encourage mixing. Engineers may improve heat dissipation and maintain temperatures in electrical devices, engines, and industrial machinery by varying microbe proportion and quality. This research aims to gain insight into the rheological effects of an Eyring–Powell nanofluid and the movement of gyrotactic microorganisms on the surface of the Riga plate. The propagation of linear and non‐linear mixed‐convection nanofluid through a Riga plate is also studied. The primary goal of this work is to accelerate the heat transfer rate of nanofluid. The efficiency of heat transport and the ability to postpone boundary layer separation are both influenced by the magnetohydrodynamic force produced by the Riga plate. Regulating problem is converted into dimensionless form using suitable transformations, and the resulting equations are then resolved numerically using the MATLAB program "bvp4c". The simulations are run for various variables, such as Prandtl numbers, mixed convection parameters, Hartmann numbers, Reynold numbers, Peclet numbers, and Lewis numbers. The outcomes are presented both tabularly and visually. This evaluation shows an increment in the Eyring–Powell fluid and mixed convection parameters, which causes the velocity profiles to rise. However, the reverse is true for an escalation in the magnetic parameters. In addition, the activation energy parameter increases the concentration profile. On the other hand, the Eyring–Powell fluid parameter causes the thermal field to contract. The skin friction at Nt=0.5$Nt=0.5$ is 45.13% and decreased by 24.07% when Nt=2.9$Nt=2.9$ for the linear case, while for the quadratic case, it is 43.69% at Nt=0.1$Nt=0.1$ and deceased 25.58% when Nt=2.9$Nt=2.9$. A comparison against an earlier study is also performed to determine the accuracy of the proposed model. An outstanding agreement between current findings and formerly existing solutions shows the legitimacy of the present discoveries. [ABSTRACT FROM AUTHOR]

This research venture comprehends a theoretical examination of non‐Newtonian fluid flowing peristaltic via an elliptical channel. Furthermore, the Prandtl fluid method for this elliptic duct problem is thoroughly considered. This mathematical inquiry adopts a non‐Newtonian Prandtl fluid model. A polynomial methodology is used to analyze partial differential equations that appear in nondimensional form and deliver an exact analytical solution for the temperature and velocity profile. This study is the first to utilize a novel order polynomial of degree eight having eleven constants to precisely solve the temperature equation for Prandtl fluid flow via an elliptic domain. A comprehensive graphical analysis is also provided to understand the mathematical conclusions fully. The graphs of the velocity profiles clearly show that the non‐Newtonian effects are more potent along the minor axis of the elliptical duct. The streamlined graphs accentuating the trapping phenomenon show specific closed contours close to the boundary wall of the peristaltic duct. [ABSTRACT FROM AUTHOR]

The literature showed that an empirical experiment creates another part of exploration that has been made in the field of thermal science, such that today, modern researchers are more directed to utilize hybrid types of nanoparticles due to their efficient thermal conductivity compared to single nanoparticles. The study of the hybrid flow of nanofluid is essential in many scientific and industrial arguments, such as power generation, medical equipment, oil refineries, and so forth. Furthermore, it has distinctive features to advance the expertise of their energy sources and cooling methodologies. Incentives by this research postulation: The significant objective of this investigation is to design a mathematical model of Prandtl hybrid nano liquid flow over a Riga plate when nanoparticles of aluminum alloys (AA7072 and AA7075) are suspended in engine oil. Mixed convection, activation energy, and heat radiation are also considered. The nanomaterial is modeled using a modified Buongiorno model that considers the functional qualities of hybrid nanofluids. The simulated PDEs are converted into a collection of nonlinear ODEs with appropriate and relevant similarity transformations, which are numerically addressed using finite‐difference‐oriented bvp4c procedure in MATLAB. Graphs and tables are used to evaluate and show the impacts of different factors on velocity, temperature, concentration fields, skin friction number, and Nusselt number. The velocity profile develops with the enhancement of Prandtl fluid parameters. With the increment in the magnetic parameter, both temperature and concentration profiles improve, but in the case of the Brownian motion parameter, the concentration profile declines. In terms of heat transfer, hybrid nanofluids outperform ordinary nanofluids. The current results provide an equitable contrast against the results that already exist. [ABSTRACT FROM AUTHOR]

This analysis aimed to explore the blood-based non-Newtonian hybrid nanofluid flow in elliptical stenosed artery with single- and multi-walled carbon nanotubes as nanoparticles. The Carreau fluid model is incorporated to assess the non-Newtonian rheology of blood-based nanofluid for mild stenosis. In particular, the carotid artery is responsible for delivering blood to the brain. If normal blood circulation is disrupted or in the case of severe stenosis, blockage of the carotid artery can lead to the development of brain disability or stroke, which in turn can lead to death. The idealized mathematical equation is transformed into a nondimensional form and solved analytically via the perturbation method through a novel polynomial technique. These analytical solutions are explored and explained graphically. The system’s disorder and variability are assessed by completing an entropy production analysis. The disruption in blood flow due to the presence of nanoparticles causes uncertainty in the flow nature. This uncertainty is dealt with by fuzzy analysis of temperature distribution by accounting for the nanoparticle volume fractions as triangular fuzzy numbers. It is noticed that stenosis shapes and height greatly impact the flow characteristics. The nanoparticles’ percentage in fluid affected the temperature profile. The non-Newtonian characteristics of blood are found to be more dominant along the minor axis, and an effectively higher disorder is produced in this direction. It is observed that the temperature of nanofluid emerged as a triangular fuzzy number of symmetric shape. [ABSTRACT FROM AUTHOR]

This analysis considers the magnetized third-grade fluid stream and microorganisms over a non-linear stretchy cylinder. The radiation impacts are taken into consideration. The effects of the governing flow at the cylinder are represented in the form of PDEs employing boundary layer approximations. The system of the PDEs is further reduced in dimensionless form after applying the similarity transformations. The dimensionless system of non-linear ODEs is solved through the numerical technique bvp4c. The effects of radiation and magnetism on the third-grade liquid over a non-linear extending cylinder are highlighted in graphs and numerically in tabular form. The influence of fluid variables on the velocity curve, such as third-grade parameters, second-grade coefficients, and Reynolds number, is illustrated and explored. Suitable ranges for the parameters |$({1 \le \eta \le 10,\ 0.2 \le {{\alpha }_1} \le 0.5,\ 0 \le {{\alpha }_1} \le 1.5,\ 0.1 \le \beta \le 0.3,\ 0.1 \le \gamma \le 1.6,\ 0.05 \le M \le 0.15,\ 0.5 \le \delta \le 2.0,\ 0.7 \le Pr \le 1.3,\ 0.1 \le Rd \le 0.4,0.1 \le}$|   |${e \le 0.4})$| are chosen depending upon the convergence of the numerical method. The widths of the velocity and momentum boundary layers are revealed to be increasing functions of the curvature parameter. The temperature curve declines when boosting third-grade parameters, thermal stratification, and Hartmann number while boosting up for curvature and radiation parameters. [ABSTRACT FROM AUTHOR]

This research focuses on exploring the significance of chemical reactions and thermal radiation on the magnetohydrodynamic (MHD) flow of a Casson–Williamson nanofluid (CWNF) over a stretching sheet. The objective is to comprehend how these factors influence the flow and heat transfer. A mathematical model, comprising partial differential equations adjusted into ordinary differential equations (ODEs) via utilizing some transformation. These ODEs are then tackled by MATLAB's BVP4C method, which is part of the finite difference technique. Results are verified by comparison with existing literature and are depicted visually and in tabular format. Additionally, the study explores the effects of external factors such as magnetic fields and the Lewis number on parameters like Nusselt number, friction factor, and Sherwood number. Furthermore, heat generation in MHD CWNF is analyzed, along with a thorough evaluation of heat transfer near a stretching sheet with a permeable layer. The findings suggest that growing Brownian motion factor (N b) and thermophoresis coefficient (N t) enhance the rate of heat transfer, signifying improved heat transfer rates. Similarly, higher N t values are associated with enhanced Sherwood numbers, indicating better mass transfer. Conversely, higher N b values lead in lower local Sherwood numbers. Physically, an increase in Brownian motion causes significant displacement of nanofluid particles, boosting their kinetic energy and thereby enhancing heat generation within the boundary layer. It is noted that the Eckert number (Ec) reflects the impact of different Ec values on temperature distribution. As Ec increases, there is a proportional increase in fluid temperature due to frictional heating, which stores heat energy within the fluid. This effect becomes more pronounced for non-linear stretching surfaces, demonstrating the response of the thermal region to viscous dissipation. Viscous dissipation has the potential to enhance convective heat transfer, leading to amplified temperature distribution and thickening of the thermal layer. [ABSTRACT FROM AUTHOR]

BACKGROUND: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters. OBJECTIVE: To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform. METHODS: The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP. RESULTS: Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis. CONCLUSION: Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids have emerged as a promising field of research in recent years, finding applications in various industries and sectors. The entropy generation and impact of an inclined magnetic field on a water-Ethylene Glycol (50:50) mixture-based nanofluid over a poignant thin needle has been investigated under slip conditions. The flow is swotted using thermal and velocity slip boundary conditions. The numerical effects of an inclined magnetic field on the flow of ferrous and aluminum oxide nanoparticles in a hybrid nanoliquid with as base fluids have been examined. The non-dimensional ODEs along with boundary conditions are solved by numerical technique based on the Runge–Kutta fourth-order method. Velocity profile has been analyzed for the magnetic parameter, inclined angle and volume fractions. The Bejan number provides insights into the balance between heat transfer and entropy generation in a system. From the numerical values of skin friction coefficient and Nusselt number, it is analyzed that Al 2 O3 possesses 1.01% and 1.06% of high heat transfer rate and high surface drag force than Fe 3 O4. Heat transfer profile has been analyzed for entropy generation and the Bejan number. The applications of hybrid nanofluids are vast, and one specific area where they can be utilized is in horizontal needle systems. [ABSTRACT FROM AUTHOR]