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Nanofluidics have better thermal properties than regular fluids, which makes them useful for heat transfer applications. This research investigated the complex dynamics of confined magnetic forces that influence the rotation of nanostructures and vortex formation in a tri-hybrid nanofluid (Ag, Al2O3, TiO2) flow regime. The study shows that the magnetic field can change the flow and heat transfer of nanofluidic, depending on its direction and strength. The study also provides insights into the complex physics of nanofluid flow and heat transfer, which can help design devices that use nanofluids more efficiently for cooling electronics, harvesting solar energy, and generating power from fuel cells. We used a single-phase model to model the nanofluids while the governing partial differential equations were solved numerically. An alternating-direction implicit approach has been employed to analyze the impact of confined magnetic fields on the nanofluid flow and thermal properties. Unlike previous studies that assumed uniform magnetic fields, we introduced multiple confined magnetic fields in the form of horizontal and vertical strips. Using our custom MATLAB codes, we systematically examined various parameters, including the magnetic field strength, number of strips and their position, and nanoparticle volume fraction, to assess their effects on nanofluid flow and thermal characteristics. Our findings revealed that the confined Lorentz force induced the spinning of tri-hybrid nanoparticles, resulting in a complicated vortex structure within the flow regime. In the absence of a magnetic field, a single symmetric vortex can be seen in the flow field. However, the introduction of magnetic sources stretches this vortex until it splits into two smaller, weaker vortices in the lower cavity, rotating clockwise or counterclockwise. Furthermore, the magnetic field strength significantly reduces both skin friction and the Nusselt number, while Reynolds numbers mainly affect the Nusselt number.

The study of fluid dynamics in the context of flow across a rotating disk is highly important since it has extensive applications in multiple industries, as well as in engineering and scientific fields. The objective of our current research is to investigate the heat transfer in the vicinity of a Stagnation Point of a Maxwell nanofluid flow passing over a porous rotating disk. A rotating disc is a phenomenon where a circular arc is formed at every point on the disc as it rotates uniformly around an axis. The shear stress at the interface between the disc and the spinning fluid provides information about the amount of power required to overcome friction and move the disc and the heat transfer is influenced by the alterations in the flow field inside the region. The heat and mass movement are studied in the context of a chemical process. Firstly, convert the PDEs into ODEs, suitable self-similarity transformation is used. After applying transformations, for graphical purpose we have used the Bvp4c technique. A variety of graphs (2D, Contour, vector plots, and Stream lines) and tables depict the impact of active parameters on the fluid's capacity to transfer significance. Velocity outline decreases for the greater values of the Deborah number values. The temperature profile improved with an improvement in the Nb parameter, while the opposite trend we noticed on ϕ (ζ). The findings of this study will have advantages in various fields, including transportation operations, architectural design systems, increased oil recovery systems, and medicinal applications that utilize nanofluids. [ABSTRACT FROM AUTHOR]

The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes. [ABSTRACT FROM AUTHOR]