Narrow Results

Interstitial fluid flow (IFF) and blood flow (BF) are analytically derived using the continuity and momentum equations for a cylindrical tumor. We considered a tumor as a rigid porous media with necrotic core, interstitial fluid and two capillaries. The capillaries have two pressures: arterial input and venous output. To describe BF within the capillaries and IFF inside tumor tissues, Poiseuille’s and Darcy’s laws are used. Here, we have divided the tumor into three parts. Our results show that the center of tumor has the maximum interstitial pressure. The pressure reduces toward the first capillary and between two capillaries. The reduction of pressure continues at the outside of the tumor. The effect of tilted external magnetic field is also studied. The results show that the field has a significant effect on the pressure. The magnetic field reduces the drug delivery at the center and exterior parts of the tumor. Furthermore, we have studied the effect of different parameters, such as interstitial resistance, magnetic field and necrotic core, on the interstitial pressure.

In this paper, we study the effect of the dynamical screening of the four-quark interaction on the chiral phase transition and the baryon number fluctuations at finite temperature and magnetic field in an effective model inspired by QCD in the Coulomb gauge. The screening leads to a medium-dependent coupling that generates inverse magnetic catalysis at finite magnetic field. We observe the decreasing temperature of the chiral crossover, in agreement with lattice QCD predictions, and find a critical point for large magnetic fields. We also observe a strong enhancement of the baryon number fluctuations in the vicinity of the crossover.

In this innovative study, a unique approach was engaged to simulate the flow characteristics of nanofluid inside a tank featuring a surface subjected to uniform flux. The testing fluid for this investigation was fabricated by incorporating alumina powders with varying shapes into water. The derivation of the final equations involved the application of Darcy’s law and the formulation of the stream function. The container experienced the combined efficacy of both the Lorentz force and gravity forces. The incorporation of additives resulted in a significant enhancement of the Nusselt number (Nu), demonstrating an increase of 19.8% and 40.28%, contingent on the magnitude of the Hartmann number (Ha). Moreover, an elevation in the shape factor led to a notable rise in Nu by 14%. Remarkably, as the Ha increased, there was a substantial reduction in the cooling rate by 51.33%. Furthermore, in the absence of the Ha, an escalation in the Rayleigh number (Ra) caused Nu to surge by 65.8%. This study holds paramount importance as it introduces a novel technique for simulating nanofluid flow with a sinusoidal surface, providing valuable insights into the complex interplay of forces within the container. The utilization of varying shapes of alumina powders adds a layer of sophistication to the experimentation, making this investigation a noteworthy contribution to the existing body of knowledge. The findings not only enhance our understanding of heat transfer dynamics but also offer practical implications for applications involving nanofluids in containers with nonuniform surfaces subjected to heat flux.

In this paper, we present a numerical investigation into the influence of electric and magnetic fields on the dynamics of a suspended liquid film that carries an electric current. A nonuniform magnetic field is considered utilizing a disk-shaped magnet located above the two-dimensional fluid. Electric and magnetic forces exerted on the fluid induce a new dynamical features. We perform a numerical study of the dynamics of such two-dimensional fluid system commonly named Liquid Film Motor. The presence of the nonuniform external magnetic field causes changes in the fluid’s behavior. Specifically, the previously symmetric vortex becomes asymmetric under the influence of the magnetic field. In this dynamic behavior, as the external magnetic field increases, the center of the vortex shifts in a direction perpendicular to the electric current passing through the fluid film. The unique combination of electric and magnetic field allows to manipulate the motion of the vortex without resorting to traditional mechanical methods. This finding implies that the motion of the vortex can be directed and controlled by adjusting the strength of the external magnetic field, without the need for direct contact with the fluid or mechanical tools.

Because the electron transport mechanism in graphene is heavily impacted by the strain and the ferromagnetic metal stripe as well as several other avenues, in this paper we investigate the effects of the strained barrier induced by the strain and the magnetic field generated by the ferromagnetic metal stripe on the valley polarization through numerical calculation. When the strength and the width of the strained barrier as well as the magnitude of the magnetic field are changed, the rapid variation of the valley polarization is observed. This study will be helpful for devising and manufacturing new-style valleytronic devices.

In this paper, we study the formation of Shannon information entropy in spin–orbit coupled (SOC) spin-1 antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results show that, in the absence of magnetic field and with an increase in dipole–dipole interaction (DDI), information entropy in position space $S_r$ and momentum space $S_k$ remains almost unchanged and increases, respectively. Meanwhile, the order parameter $\delta$ decreases, which implies that the system develops toward a disorder state. With the increase of SOC strength, $S_r$, $S_k$ and $\delta$ show similar dynamics behavior. Whereas, in the presence of magnetic field, $S_k$ and $\delta$ are localized in the small scope by increasing the dipole and SOC strength. In addition, the value of $S_r$ is nearly the same in this process. These results embody that the introduction of external magnetic field suppresses the role of SOC and DDI, and impedes the condensates towards disorder state. At last, the influence of geometric structure and atom number on information entropy is investigated. It is seen that a narrower trap and fewer atom number make $S_r$ decrease and $S_k$ increase.

Nowadays, therapeutics mainly depend on drug delivery and magnetic nanofragments in the human body’s circulatory system. The drug particles are infused into the bloodstream with magnetic effects during this treatment, which is normally applied and aids in releasing the medications to the proper organs under magnetic intensity. Numerous medical procedures employ this approach, such as targeted drug delivery, cancer treatments, reduction of excessive bleeding during surgery, the healing process of wounds, and magnetic attraction of blood. However, the nanoparticle’s shape factor causes faster/slower drug release before/after reaching its targeted region. This study strives to investigate the effects of nanoparticle shape on the magnetized power law fluid flow along a thin needle. Additionally, viscous dissipation, suction, and ohmic heating are also considered. The governing equations are transformed with the help of appropriate similarity transformation into a dimensionless form and solved using the Bvp4c technique. The findings reveal that the magnetic field and needle thickness reduce fluid velocity. Further, regression analysis is incorporated to provide further insight into engineering quantities. The platelet-shaped nanoparticle averagely transmits thermal energy an average of $13\%$ more than brick, $10\%$ more than the blade and $4\%$ more than cylinder-shaped nanoparticles.

Hybrid nanofluids can be designed to exhibit multiple functionalities, such as improved thermal conductivity, electrical conductivity, and magnetic properties. Magnetic hybrid nanofluids are gaining recognition in various mainstream applications, including heat transfer, solar systems, acoustic applications, and more. Further, hybrid nanofluids improve the thermal efficiency of radiators, efficiency of heating, ventilation, and air conditioning systems and drug delivery systems. Their notable advantage lies in their capacity to enhance the thermophysical properties of the constituent particles. Peristalsis of MHD hybrid nanomaterial $({\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3-{\mathrm{\text{TiO}}}_2+\mathrm{\text{water}})$ in symmetric channel is emphasized. Darcy–Forchheimer law explores nonlinear nature of porous media. Effects of Joule heating and viscous dissipation are considered. The viscosity of fluid depends on temperature. The dimensionless system after invoking lubrication approach is analyzed numerically. Characteristics of prominent variables on the quantities under interest are examined. Comparative analysis of heat transfer rate of hybrid nanofluid and nanofluid are also discussed in detail. Heat transfer rate of system increases by increasing the quantity of nanomaterial in the fluid. Therefore, the temperature of the fluid decreases and the efficiency of the system increases.

The transport phenomenon in the presence of magnetic field has diverse application in living structures, biotechnology and chemical and environmental engineering. Biomedical applications include the examples of computational biology, replacement of tissue, drug delivery, advance medical imaging, repairing of bones, complex liver and heart surgeries and kidney transplant. Motivated by the applications of magnetic in human physiology, peristaltic transport of Carreau-hybrid nanomaterial through a curved channel is studied. The hybrid nanofluid is supported with silver $(\mathrm{\text{Ag}})$ and copper oxide $(\mathrm{\text{CuO}})$ nanoparticles subject to ethylene glycol $(\mathrm{\text{EG}})$-based liquid. The complex wavy nature of physiological duct inspired to model the problem in complex wavy channel. The basic governing laws are utilized for mathematical modeling and dimensionless variables are used for the dimensionless formulation. The simplified pattern of governing problem has been revealed to the assumptions of long wavelength as well as creeping flow constricts. The computations are obtained by implanting the Newton–Dirichlet Solve (ND) algorithm. Comparative thermal observations are predicted for nanofluid $(\mathrm{\text{Ag/EG)}}$ and hybrid nanofluid (Ag–CuO/EG). The different flow and heat transfer features are plotted against the several involved parameters are presented graphically.

This paper focuses on applying the Corcione model to the microchannel. The Corcione model is highly relevant because it provides accurate empirical relationships for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. These qualities are crucial for building and improving different thermal systems. The model presents and discusses two simple empirical correlating equations for forecasting the dynamic viscosity and effective thermal conductivity of nanofluids. Hence the aim of this work is to use Corcione’s model to demonstrate the fully developed laminar flow of an electrically conducting nanoliquid through an inclined microchannel. The energy equation takes into account the physical impacts of the heat source/sink, temperature jamp, and viscous dissipation. TiO₂ nanoparticles in water are taken into consideration in this work for enhanced cooling. Using the numerical program Maple, Runge–Kutta–Fehlberg 4th–5th-order method is utilized to solve the present research. Making use of graphs, all of the flow parameters are shown, and the physical consequences on the flow and temperature profiles are thoroughly examined. It is noted that a higher inclined angle enhances the velocity profile whereas a larger temperature jump declines the temperature profile. Furthermore, Corcione’s model often has greater velocities, temperatures, and reduced surface drag forces than the Tiwari–Das model.

This research distinguishes itself by integrating machine learning algorithms to assess the impact of confined magnetic fields on vortex dynamics in hybrid nanofluid flow, through the inclusion of both vertical and horizontal magnetic field strips. Specifically, the study focuses on a vertical cavity with an aspect ratio of 1:5, where a bottom lid moves horizontally from left to right to drive the flow. We have applied a limited magnetic field consisting of vertical, and horizontal strips. The authors have developed MATLAB codes to implement an algorithm for solving the governing equations of the nanofluid flow and heat transfer. The algorithm is based on the Stream-Vorticity formulation and uses a finite difference method. The algorithm can examine how several parameters, such as magnetic field strength (0–300), nanoparticle volume fraction (0–20%), and Reynolds number (Re) (1–50), impact the characteristics of nanofluids in terms of flow and thermal properties. The results demonstrate that magnetic fields influence the stress distribution of the flow pattern and the temperature distribution. Further, the presence of a magnetic field also affects stress distribution. Moreover, it has been determined that the Nusselt number (Nu) experiences a 60% increase due to the magnetic field, while there is a remarkable rise attributed to the Re. Similarly, significant changes are observed in skin friction under both parameters. These findings carry implications for designing and operating devices.

We theoretically discuss the high-order sideband generation (HSG) in an optomechanical system affected by a magnetic field and demonstrate the magnetic field-dependent impact of HSG has certain intriguing properties. We also demonstrated that carrier-envelope phase (CEP)-dependent effect occurs in HSG when the magnetic field is certain in our paper. The magnetic field-dependent effect in an optomechanical system gives a method for controlling HSG. Our findings may have important applications in optical frequency metrology and optical communications.

The accurate synthesis of bespoke design requires complicated chemical reactions and high temperature conditions in modern nanomaterial coating techniques. These flow processes are quite complicated, involving not just viscous behavior but also mass and heat transport. Magnetic nanoparticles are utilized by nanocoatings, which are under manipulation by external magnetic fields. Mathematical models offer a low-cost window into the fundamental properties of these coating dynamics processes. This paper proposes a hybrid approach for induction effect in nanoparticle with magneto-convective nanofluid boundary layer. The hybrid technique that is being proposed involves the simultaneous application of Siberian Tiger Optimization (STO) and Multi-Fidelity Deep Neural Network (MFDNN). Hence, it is named as STO-MFDNN technique. The primary goal of this proposed method is to enhance nanoparticle solid volume fraction and minimize error during validation. The proposed technique — STO approach is utilized to optimize the process parameter and the MFDNN approach is utilized to accurately predict the nanoparticle behavior. By then, the MATLAB platform has the proposed approach implemented, and the present method is used to calculate the execution. The proposed technique displays superior outcomes in all existing systems like Wild Horse Optimizer (WHO), Fertile Field Algorithm (FFA) Seagull Optimization Algorithm (SOA). The existing technique displays the errors of 0.24%, 0.21%, 0.18% and the proposed technique displays an error of 0.15% concluding low error when compared to the existing approach.

To model several engineering and physical models, the approach of the fractional derivative is highly anticipated. As compared to the ordinary derivatives, the fractional derivatives with more flexibility can estimate the data due to the involvement of the fractional-order derivatives. Due to these advantages of the fractional approach, this study communicates with the determination of the fractional-based exact outcomes of an oscillatory rectangular duct problem of a generalized second-grade fluid. The approach of the fractional operator is involved in the relationship of the constitutive equations. For cosine oscillation of the rectangular duct, exact results of the magnetized unsteady flow problem are evaluated through the technique of Laplace transform with double finite Fourier sine transform. This study concludes that the velocity field exhibits escalating behavior relative to the improved fractional parameter. Moreover, the magnetic parameter with increasing values declines the flow field while the accelerating values of the fluid parameter enhance the velocity field.

The application of fluid flow through a rotating disk in a solar thermal power plant can help in increasing energy production, reduce costs, and improve the overall efficiency of the system. The concentrated solar power (CSP) technology can help in assisting solar energy for sustainable power generation. This work explores the heat transfer assessment of magnetized tangent hyperbolic fluid flowing over a porous rotating disk under the effects of thermal radiation, convective heating, Ohmic heating and viscous dissipation. The solution of transformed ODEs is obtained by the Legendre wavelet collocation method (LWCM). To visualize the impact of acting variables, the results are portrayed by graphs and tables. From the outcomes, it is noted that the rate of heat transfer is enhanced up to 84.79% with an increase in radiation parameter. Moreover, the radial velocity enhances as the rotation parameter is accelerated. The dual behavior in temperature outlines is obtained due to escalated values of the porosity parameter. For the validation of the present results, a tabular comparison is shown with earlier work.

The purpose of this investigation is to examine the impacts of fractional calculus on fluid dynamics and heat transfer of a nanofluid in drilling applications. More specifically, the study explores how free convection and electrical conductivity impact clay nanoparticles dispersed in engine oil—which is modeled as a Casson fluid—as they pass over a flat vertical plate. The key objectives are to: (1) determine the effects of memory effects at different timescales on temperature and momentum profiles via the Caputo–Fabrizio fractional derivative; and (2) analyze the consequences of varying different physical parameters such as magnetic field, Grashof number, nanoparticle volume fraction and Prandtl number. The objective of the investigation is to provide insight into controlling these parameters to optimize drilling processes. The Laplace method is applied to find solutions to the governing equations, and MathCad15 is utilized for illustrating the physical results. The results expose that the temperature and momentum fields are enhanced (at large times) when the fractional parameter is increased and both profiles show opposite behavior at small times. The heat transmission is enlarged with growing estimations of the volume fraction for clay nanoparticles, whereas the momentum field is declined by growing estimations of the volume fraction of nanoparticles. Further, the nanofluid motion declines by growing the magnetic field but accelerates by increasing the Grashof number. Further, this model has applications in engineering to optimize drilling operations, where performance and efficiency in refining depend upon controlling fluid flow and heat transmission. It can also be applied in fields where nanofluids are utilized to enhance heat transfer and fluid dynamics, such as petrochemicals, manufacturing and material engineering. Overall, this study establishes a vigorous foundation for further research and delivers a structure for exploring non-Newtonian NF systems from the perspective of magnetized-driven free convection flow.

This study undertakes a numerical investigation into the two-phase magnetohydrodynamic (MHD) flow of a novel Al₂O₃-Ag/ethylene glycol (30%)–water dusty Maxwell hybrid nanofluid within a porous stretched cylinder incorporates the influential factor of thermal radiation. Notably, it pioneers exploration into the flow characteristics of Maxwell nanofluids and hybrid nanofluids containing dust particles over a porous cylinder, an uncharted domain in the existing literature. By adeptly simplifying the governing partial differential equations into nonlinear ordinary differential equations (ODEs) using judiciously chosen similarity variables, our research employs MATLAB’s bvp4c scheme to obtain numerical solutions, presented both graphically and in tabular form. Our results unveil significant insights: the Maxwell fluid parameter and magnetic parameter exhibit a dual effect of enhancing heat transfer while mitigating velocity gradients. Moreover, increasing the curvature parameter exerts a favorable influence on the velocity and temperature profiles of both phases. Furthermore, the fluid-particle interaction parameter emerges as a pivotal factor shaping velocity and temperature profiles in the dust phase, while the radiation parameter notably amplifies heat transfer rates. Remarkably, our investigation reveals a notable 26% increase in total skin friction and a nearly 13.5% enhancement in heat transfer within the dusty Maxwell hybrid nanofluid configuration compared to the dusty Maxwell nanofluid arrangement. These findings hold profound practical implications for addressing real-life engineering challenges, offering invaluable insights into optimizing heat transfer and velocity profiles across diverse technical applications. They pave the way for the development of enhanced cooling mechanisms and highly efficient heat exchangers, crucial for tackling multifaceted engineering challenges.

The project focuses on simulating natural convection in a tilted quarter-elliptical chamber filled with ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–Cu/Water hybrid Nanofluid, influenced by a magnetic field (MF) at various angles. The chamber’s elliptical shape is modelled with a constant height-to-length ratio of 2. The chamber’s curved wall is cold, while one smooth wall is adiabatic, and the larger wall undergoes three types of heating. The Hartmann number (Ha), MF angle ($\lambda$), chamber wall heating type, inclination angle ($\mathrm{\Gamma })$, and Rayleigh number (Ra) are studied. Results indicate that increasing Ra leads to enhanced convection and a higher average Nusselt number. At $\mathrm{\text{Ra}}=10^4$, heat transmission is primarily through conduction, resulting in the lowest flow power. The presence of a MF slows down heat transportation, especially at $\mathrm{\text{Ra}}=10^4$. The MF’s impact is most significant when applied at a $90^{\circ }$ angle. Constant temperature chamber wall heating yields 75% and 85% higher average Nusselt values compared to sinusoidal and linear heating, respectively. The worst scenario occurs at $\mathrm{\Gamma }=-90^{\circ }$, where the computed Nusselt values and current power are lowest, highlighting the MF’s influence. According to the study, when thermal boundary circumstances and MF angles are just right, the ${\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$–Cu/water hybrid nanofluid greatly improves the transfer of natural convection heat in a tilted cavity. This suggests that thermal management in cooling structures, electronics, and energy-efficient buildings may be improved.

In this paper we introduce a class of semiclassical Fourier integral operators with global complex phases approximating the fundamental solutions (propagators) for time-dependent Schrödinger equations. Our construction is elementary, it is inspired by the joint work of the first author with Yu. Safarov and D. Vasiliev. We consider several simple but basic examples.

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic ΨDO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [24] to a more general class of magnetic fields: we consider a single particle moving in a periodic potential which is subjected to a weak and slowly-varying electromagnetic field. In addition to the semiclassical parameter ε ≪ 1 which quantifies the separation of spatial scales, we explore the influence of an additional parameter λ that allows us to selectively switch off the magnetic field.

We find that even in the case of magnetic fields with components in , e.g., for constant magnetic fields, the results of Panati, Spohn and Teufel hold, i.e to each isolated family of Bloch bands, there exists an associated almost invariant subspace of L²(ℝ^d) and an effective hamiltonian which generates the dynamics within this almost invariant subspace. In case of an isolated non-degenerate Bloch band, the full quantum dynamics can be approximated by the hamiltonian flow associated to the semiclassical equations of motion found in [24].