The present research was developed to find out the effect of heated cylinder configurations in accordance with the magnetic field on the natural convective flow within a square cavity. In the cavity, four types of configurations—left bottom heated cylinder (LBC), right bottom heated cylinder (RBC), left top heated cylinder (LTC) and right top heated cylinder (RTC)—were considered in the investigation. The current mathematical problem was formulated using the non-linear governing equations and then solved by engaging the process of Galerkin weighted residuals based on the finite element scheme (FES). The investigation of the present problem was conducted using numerous parameters: the Rayleigh number (Ra = 10³–10⁵), the Hartmann number (Ha = 0–200) at Pr = 0.71 on the flow field, thermal pattern and the variation of heat inside the enclosure. The clarifications of the numerical result were exhibited in the form of streamlines, isotherms, velocity profiles and temperature profiles, local and mean Nusselt number, along with heated cylinder configurations. From the obtained outcomes, it was observed that the rate of heat transport, as well as the local Nusselt number, decreased for the LBC and LTC configurations, but increased for the RBC and RTC configurations with the increase of the Hartmann number within the square cavity. In addition, the mean Nusselt number for the LBC, RBC, LTC and RTC configurations increased when the Hartmann number was absent, but decreased when the Hartmann number increased in the cavity. The computational results were verified in relation to a published work and were found to be in good agreement.

The numerical simulation of free convection flow within a square-shaped enclosure for various orientations of elliptic blockage (EB) is performed in the present study. The bottom wall of the cavity remains uniformly heated, where the left and right (side) walls as well as the boundary wall of the elliptic blockage are insulated and the top wall remains at a cool temperature. As $Pr$ remains constant, the effects of different values of $Ra$ have a great influence on overall fluid flow and temperature gradient for three different locations: bottom elliptic blockage (BEB), center elliptic blockage (CEB) and top elliptic blockage (TEB), as a mass flow circulation has been identified, and a state of equilibrium has been established within the fluid flow simulations along with the isotherm contours. The outcomes of the numerical analysis are presented with the streamlines, isotherms, and variations of the average Nusselt number.

This study presents Reinforcement Operator Learning (ROL)—a hybrid control paradigm that marries Deep Operator Networks (DeepONet) for offline acquisition of a generalized control law with a Twin-Delayed Deep Deterministic Policy Gradient (TD3) residual for online adaptation. The framework is assessed on the one-dimensional Kuramoto–Sivashinsky equation, a benchmark for spatio-temporal chaos. Starting from an uncontrolled energy of 42.8, ROL drives the system to a steady-state energy of 0.40 ± 0.14, achieving a 99.1% reduction relative to a linear–quadratic regulator (LQR) and a 64.3% reduction compared with a pure TD3 agent. DeepONet attains a training loss of 7.8 × 10 ⁻⁶ after only 200 epochs, enabling the RL phase to reach its reward plateau 2.5 × sooner and with 65% lower variance than the baseline. Spatio-temporal analysis confirms that ROL restricts state amplitudes to ± 1.8 —three-fold tighter than pure TD3 and an order of magnitude below LQR—while halving the energy in 0.19 simulation units (33% faster than pure TD3). These results demonstrate that combining operator learning with residual policy optimisation delivers state-of-the-art, sample-efficient stabilisation of chaotic partial differential equations and offers a scalable template for turbulence suppression, combustion control, and other high-dimensional nonlinear systems.

To characterize tuberculosis transmission and assess the impact of important interventions, a data-driven SEITR TB model is created. The potential for disease persistence has been calculated using the basic reproduction number. To determine the factors most significantly affecting the spread of tuberculosis, stability and sensitivity analyses are conducted. Strengthened treatment measures and optimized distancing significantly lower infection levels, according to numerical simulations. The Least Squares Fitting technique is used to validate real epidemiological data with a model solution. And the results emphasize that the best combinations of social distancing and treatment not only reduce the number of infections but also provide a cost-effective strategy for public health planning. Additionally, two numerical techniques, namely Pearson correlation and Partial Rank Correlation Coefficients (PRCC), are utilized to assess the sensitivity of model parameters. It is noted that the outcomes of these two methods are in agreeable comparison with one another regarding sensitivity analysis.

This study is aimed at examining the computational modeling of the blood flow of a trihybrid nanofluid with nanoparticles such as Ag, Au, and Cu to simulate the hemodynamics parameters and heat transfer within a constricted channel geometry that directly parallels the flow conditions in a stenosed artery. The flow is defined as an unsteady, incompressible, laminar Newtonian fluid, with blood exhibiting Newtonian properties at elevated shear rates. An algorithm for mass, velocity, and energy, as well as a fine element‐sized mesh, was developed using the computational fluid dynamics (CFD) technique based on the finite element method. Here, systematic observation of the effect of varying nanoparticle volume fractions ( ϕ = 3 % , 9 % , 15 % ) and Reynolds numbers (Re) on the resulting flow velocity profiles. Although maximal velocity is geometrically concentrated at the stenosis throat, the critical determining factor of patient danger is the concentration‐dependent change in fluid viscosity. Increasing ϕ raises effective viscosity (Brinkman model), progressively flattening the velocity profile into a blunt, plug‐like regime; paradoxically, this near‐uniform plug, lacking the gradual wall‐to‐core velocity gradient of a parabolic profile, is unable to resist the adverse pressure gradient at the abrupt poststenotic expansion, causing simultaneous cross‐sectional deceleration and abrupt flow separation that sustains larger, more energetic recirculation zones than those observed at lower ϕ . This disturbed distal flow that generates large and persistent recirculation zones downstream of the stenosis, which are associated with increased thrombotic risk due to disturbed flow patterns. Conversely, the increase in ϕ drastically increases thermal conductivity, making the heat transfer process nearly independent of flow speed, that a key insight for forthcoming contained thermal therapies. Eventually, this research delivers a mechanistic link between fluid rheology, flow instability, and thrombotic risk, signifying that therapeutic strategies need to prioritize the management of fluid viscosity to stabilize poststenotic flow fields and mitigate associated cardiovascular complications. This work is the first effort to evaluate the impact of trihybrid nanofluid rheology on the exacerbation of poststenotic flow instability at clinically relevant Re. This reveals that a critical higher nanoparticle loading ( ϕ ) improves thermal conductivity. The present findings have direct significance for biomedical applications like targeted photothermal therapy (PTT), antimicrobial vascular intervention, and nanoparticle‐mediated drug delivery in cardiovascular disease management. The computed 18% enhancement in conductive heat flux at ϕ _T = 15 % further establishes a quantitative performance baseline for the design of nanofluid‐based thermal management systems in biomedical microdevices.