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Magnetohydrodynamics (MHD) in nanofluids is crucial in boundary layer flow as it enables the manipulation of fluid motion through magnetic fields, which leads to improved stability and efficiency. This study aims to introduce a model and solutions for the boundary layer flow of a ternary hybrid nanofluid past a permeable shrinking sheet, integrating both magnetohydrodynamic and slip effects.

The model is firstly expressed as partial differential equations and subsequently converted into ordinary differential equations (ODEs) through a similarity transformation technique. A finite difference scheme with the Lobatto IIIa formula in MATLAB is applied to numerically solve the ODEs, where the respective outcomes provide insights into the skin friction coefficient, Nusselt number, velocity profiles and temperature profiles.

The results highlight the significance of enhancing magnetohydrodynamic effects and first-order velocity slip to reduce skin friction, improve heat transfer, delay boundary layer separation, increase flow velocity and lower fluid temperature. In addition, the stable numerical solution is scrutinized using response surface methodology (RSM) to validate and optimize flow control. The RSM optimization confirms that higher suction, magnetohydrodynamic effects and first-order slip levels are essential for minimizing skin friction and maximizing heat transfer simultaneously.

The presented model together with the numerical and statistical results can be used as a guidance to control the flow and heat transfer that occur within a related practical application, especially in engineering and industrial activities such as cooling technologies, energy harvesting or fluid transport in nanotechnology, where precise control of heat transfer and fluid dynamics is essential for optimizing performance and reducing energy consumption.

Enzymes play a pivotal role in orchestrating essential biochemical processes and influencing various cellular activities in tissue. This paper aims to provide the process of enzyme diffusion within the tissue matrix and enhance the nano system performance by means of the effectiveness of enzymatic functions. The diffusion phenomena are also documented, providing chemical insights into the complex processes governing enzyme movement.

A computational analysis is used to develop and simulate an optimal control model using numerical algorithms, systematically regulating enzyme concentrations within the tissue scaffold.

The accompanying videographic footages offer detailed insights into the dynamic complexity of the system, enriching the reader’s understanding. This comprehensive exploration not only contributes valuable knowledge to the field but also advances computational analysis in tissue engineering and biomimetic systems. The work is linked to biomolecular structures and dynamics, offering a detailed understanding of how these elements influence enzymatic functions, ultimately bridging the gap between theoretical insights and practical implications.

A computational predictive model for nanozyme that describes the reaction diffusion dynamics process with enzyme catalysts is yet not available in existing literature.

A vaccination strategy to cover the susceptible population is key to containing the spread of any virus during a healthcare emergency. This study quantifies the susceptibility of a region based on initial infection rates to prioritize optimal vaccine distribution strategies. The authors propose a metric, the regional vulnerability index (RVI), that identifies the degree of susceptibility/vulnerability of a region to virus infections for strategically locating hubs for vaccine storage and distribution.

A two-phase methodology is used to address this problem. Phase 1 uses a modified Susceptible-Infected-Recovered (SIR) model, ModSIR, to estimate the RVI. Phase 2 leverages this index to model a P-Center problem, prioritizing vulnerable regions through a Mixed Integer Quadratically Constrained Programming model, along with three variations that incorporate the RVI.

Results indicate a weighting scheme based on the population-to-RVI ratio fosters fair distribution and equitable coverage of vulnerable regions. Comparisons with the public distribution strategy outlined by the Government of India reveal similar zonal segregations. Additionally, the network generated by our model outperforms the actual distribution network, corroborated by network metrics such as degree centrality, weighted degree centrality and closeness centrality.

This research presents a novel approach to prioritizing vaccine distribution during pandemics by applying epidemiological predictions to an integer-programming framework, optimizing COVID-19 vaccine allocation based on historical infection data. The study highlights the importance of strategic planning in public health response to effectively manage resources in emergencies.

This study aims to investigate the flow and heat transfer characteristics of a Bingham viscoplastic fluid subjected to the combined effects of axial rotation and radial stretching of a circular disk. Building upon existing models for Bingham fluids on stationary walls, we extend the formulation to incorporate the effects of a linearly stretching disk using von Kármán similarity transformations.

The resulting system of nonlinear ordinary differential equations is solved to characterize the flow and thermal fields. Three dimensionless parameters govern the momentum layer: a swirling number capturing the balance between rotation and stretching, a Bingham number characterizing the fluid’s yield stress and a modified Reynolds number incorporating the disk stretching. The Prandtl number controls the thermal response.

For purely stretching flows, a two-dimensional flow structure emerges. However, the introduction of rotation induces three-dimensional flow behavior. Unlike previous studies suggesting that moderate Bingham numbers are sufficient for non-Newtonian effects on purely revolving disks, the findings indicate that significantly higher yield stresses are required to observe non-Newtonian characteristics under radial stretching conditions. This difference can be attributed to the enhancing influence of wall movement on the fluid dynamics. At high Bingham numbers, a two-layer flow structure develops, comprising an unyielded plug region above the disk and a yielded shear layer adjacent to the wall. The von Kármán viscous pump mechanism drives the Bingham flow within this regime.

Physical quantities such as drag force due to wall shear stress, torque resulting from tangential shear stress and Nusselt number are extracted from the quantitative data.

This study aims to explore the hydrodynamic and thermal behavior of an incompressible fluid flowing between uniformly corotating disks with finite radii. The narrow gap between the disks necessitates accounting for slip flow in the radial direction, departing from the classic no-slip model.

The author uses a perturbation approach and derives full analytical approximations to the Navier–Stokes and energy equations up to the second order. Higher-order truncations require significant numerical effort due to the complexity of the resulting expressions.

For the no-slip case, the momentum solutions perfectly match those found in the literature. The author then demonstrates the convergence of the series solutions with slip for selected specific parameter sets. Finally, the author investigates the impact of both slip and Reynolds number on the velocity field, pressure and temperature field between the inlet and outlet positions.

The key finding is that both factors lead to thinner momentum and thermal boundary layers within the corotating finite disk setup, resulting in cooler disk surfaces.

The purpose of the study is to explore the three-dimensional heat and mass transport dynamics of the magneto-hydrodynamic non-Newtonian (Casson fluid) hybrid nanofluid flow comprised of − as nanoparticles suspended in base liquid water as it passes through a flexible spinning disc. The influence of a magnetic field, rotation parameter, porosity, Darcy−Forchheimer, Arrhenius’s activation energy, chemical reaction, Schmidt number and nanoparticle shape effects are substantial physical features of the investigation. Furthermore, the influence of hybrid nanofluid on Brownian motion and thermophoresis features has been represented using the Buongiorno model. The novelty of the work is intended to contribute to a better understanding of Casson non-Newtonian fluid boundary layer flow.

The governing mathematical equations that explain the flow and heat and mass transport phenomena for fluid domains include the Navier−Stokes equation, the thermal energy equation and the solutal concentration equations. The governing equations are expressed as partial differential equations, which are then converted into a suitable set of non-linear ordinary differential equations by using the necessary similarity variables. The ordinary differential equations are computed by combining the shooting operation with the three-stage Lobatto BVP4c technique.

Graphs and tables are used in the process of analysing the characteristics of velocity distributions, temperature profiles and solutal curves at varying values of the parameters, along with friction drag, heat transfer rate and Sherwood number. It has been revealed that the radial and axial velocities decrease when the Casson parameter value increases and that the rate of heat transmission is higher in hybrid nanofluids with nanoparticles in the shape of a blade. The increase in Brownian motion and thermophoresis parameters causes a rise in the temperature profile. Also, an increase in the activation energy parameter improves the solutal curve. The use of nanoparticles was shown to improve extrusion properties, the rotary heat process and biofuel generation.

All results are presented graphically and all physical quantities are computed and tabulated. The current results are compared to previous investigations and found to agree significantly with them.

The main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treated as adiabatic. Various factors, such as the Rayleigh number (Ra), nanoparticle volume fraction, Darcy effects, Hartmann number (Ha) and effects of magnetic inclination, are analyzed for their impact on the flow behavior and temperature distribution.

The finite element method (FEM) is employed for simulating variations in flow and temperature after validating the results. Solving the non-linear partial differential equations while incorporating the modified Darcy number (10⁻³ ≤ Da ≤ 10⁻¹), Ra (10³ ≤ Ra ≤ 10⁵) and Ha (0 ≤ Ha ≤ 100) as the dimensionless operational parameters.

This study demonstrates that in enclosures with dynamically positioned bulges filled with Cu-water nanofluid, heat transfer is significantly influenced by the bulge location and nanoparticle volume fraction, which alter flow and heat patterns. The varying impact of magnetic fields on heat transfer depends on the Rayleigh and Has.

The geometry configurations employed in this research have broad applications in various engineering disciplines, including heat exchangers, energy storage, biomedical systems and food processing.

This research provides insights into how different shapes of the heated bulging area impact the hydromagnetic convection of Cu-water nanofluid flow in a dynamically bulging-shaped porous system, encompassing curved surfaces and various multi-physical conditions.

Understanding the mechanical and thermal behavior of materials is the goal of the branch of study known as fractional thermoelasticity, which blends fractional calculus with thermoelasticity. It accounts for the fact that heat transfer and deformation are non-local processes that depend on long-term memory. The sphere is free of external stresses and rotates around one of its radial axes at a constant rate. The coupled system equations are solved using the Laplace transform. The outcomes showed that the viscoelastic deformation and thermal stresses increased with the value of the fractional order coefficients.

The results obtained are considered good because they indicate that the approach or model under examination shows robust performance and produces accurate or reliable results that are consistent with the corresponding literature.

This study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.

This study introduces a proposed viscoelastic photoelastic heat transfer model based on the Moore-Gibson-Thompson framework, accompanied by the incorporation of a new fractional derivative operator. In deriving this model, the recently proposed Caputo proportional fractional derivative was considered. This work also sheds light on how thermoelastic materials transfer light energy and how plasmas interact with viscoelasticity. The derived model was used to consider the behavior of a solid semiconductor sphere immersed in a magnetic field and subjected to a sudden change in temperature.

The purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.

Governing nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.

Results show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.

Micropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

High surface area-to-volume ratios make nanoparticles ideal for cancer heat therapy and targeted medication delivery. Moreover, ternary nanofluids (TNFs) may possess superior thermophysical properties compared to mono- and hybrid nanofluids due to their synergistic effects. In light of this information, the objective of this article is to examine the blood-based TNF flow within convergent/divergent channels under velocity slip and temperature jump.

Leading partial differential equations corresponding to the problem are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The bvp4c code that uses the finite difference method is used to obtain a numerical solution.

The effect of nanoparticles may change depending on the characteristics of flow near the wall. The properties and proportions of the used nanoparticles become important to control the flow. When TNF was used, an increase in the Nusselt number between 4.75% and 6.10% was observed at low Reynolds numbers. At high Reynolds numbers, nanoparticles reduce the Nusselt number and skin friction coefficient values under some special flow conditions. Importantly, the effects of second-order slip on engineering parameters were also investigated. Furthermore, the Nusselt number increases with increasing shape factor.

Obtained results of the study can be beneficial in both nature and engineering, especially blood flow in veins.

The main innovations of this study are the usage of blood-based TNF and the examination of the effect of shape factor in convergent/divergent channels with second-order velocity slip.