Central composite design to optimize the heat transfer rate in unsteady Boger hybrid nanofluid flow over a permeable slow rotating disk

• Magnetic and magnetocaloric properties of Fe doped La–A–Ca manganite were studied. • A one-dimensional AMR model was developed and validated using Gd as reference. • Key operating parameters controlling AMR performance were identified and analyzed. Active magnetic regeneration is a key enabling technology for extending the operating temperature span of magnetic refrigeration systems across a wide temperature range. In this work, the thermodynamic performance of an active magnetic regenerator (AMR) based on L a 0.65 A 0.25 C a 0.1 M n 0.99 F e 0.01 O 3 manganite oxides is investigated using a one-dimensional numerical model. The model incorporates experimentally determined magnetocaloric properties derived from isothermal magnetization and heat capacity measurements, allowing a system-level assessment of the cooling performance. Gadolinium is used as a reference material to validate the numerical approach, with its magnetocaloric properties obtained from a mean-field theory description. The results indicate that, due to their moderate magnetocaloric response, the studied manganite oxides require relatively high magnetic fields ( 7 T) to reach cooling performances comparable to those achieved by gadolinium under permanent-magnet fields. Nevertheless, owing to their broad operating temperature range, these materials are capable of generating an AMR temperature span of approximately 30 - 40 K under a magnetic field of 2 T. These results highlight the thermodynamic trade-offs between magnetic field strength, temperature span, and material properties that govern AMR operation, and provide insight into the realistic potential and limitations of manganite-based materials for regenerative magnetic refrigeration systems.

Machine learning-augmented finite element modeling for transient hemodynamics in human arteries.

Innovation in magnetic resonance imaging (MRI) is often focused on achieving higher magnetic field strengths, allowing for increased sensitivity and image resolution. Although many clinical settings have access to 1.5 T or 3.0 T MRI systems, 7.0 T systems are becoming more common and human research magnets as high as 11.7 T are in use (Boulant et al. Nature Methods, 2024, 21, 2013–2016). However, higher field is not always better. For example, higher magnetic fields experience more significant variations (B0 and B1 field inhomogeneities) that can introduce image artefacts. High magnetic fields also come at a high price, with the rule of thumb that the price scales directly with the field strength. To increase accessibility and have a broader health impact, the use of low-field MRI systems is being investigated in clinical populations ranging from stroke (Bhat et al. Journal of Magnetic Resonance Imaging, 2021, 54, 372–390) to pregnancy (Aviles Verdera et al. Radiology, 2023, 309, e223050). In this issue of BJOG, Bansal et al. used a 0.55 T MRI to image the cervix in late gestation in 97 low-risk pregnancies as part of the MiBirth study. This prospective cohort study, run by a multidisciplinary team and a Patient and Public Involvement group, aimed to use a combination of imaging modalities (ultrasound, MRI) and relevant anatomy (uterus, cervix, pelvis, placenta and foetus) to predict the mode of birth. In this work, the authors assessed the feasibility of using low-field MRI to provide measurements of cervical remodelling. They found their image reconstruction and automated segmentation protocols were of good quality, with high inter-rater reliability for cervical length, volume, and internal and external os diameters. A larger cervical stroma volume during late gestation, suggesting failure to remodel, was associated with an increased risk of caesarean section. Although knowledge about the possible mode of delivery is important in preparation for the birth experience, there is still much work to be done to accurately predict adverse birth outcomes (e.g., preterm birth) using MRI. The potential benefits of this study are twofold. First, compared with ultrasound, MRI may be able to detect more subtle changes in cervical morphology and provide details of cervical microstructure and hydration (Oláh, BJOG, 1994, 101, 255–257). Second, low-field MRI has several advantages including reduced image artefacts, the potential for a larger bore size to accommodate pregnant individuals and a lower cost. With the rising price and uncertainty of cryogen availability (liquid nitrogen and liquid helium), another advantage of low-field MRI systems is that they do not require superconducting magnets and therefore can be cryogen-free. They may also be designed to be portable, allowing the system to be brought to the bedside and increasing accessibility to this advanced medical imaging modality. Future areas of research should include a longitudinal study design in a cohort at high risk for preterm birth. Almost 70% of the participants were White and imaged at one hospital. Future studies should focus on using low-field MRI in more diverse populations and settings. In tandem with clinical studies using low-field MRI systems, biomedical engineers and imaging physicists must continue to develop software and hardware solutions (e.g., denoising methods and low-noise electronics) to improve the image quality at low fields. This may usher in a new and exciting era of initial screening and monitoring during pregnancy using low-field MRI. The author takes full responsibility for this article. The author has nothing to report. The author declares no conflicts of interest. The author has nothing to report.

Dual Reciprocity Boundary Element Method analysis of MHD Brinkman–Rivlin–Ericksen viscoelastic flow past cylindrical obstacles in porous microchannel

Magnetic field-enhanced interfacial photo-thermal evaporation within the liquid organic hydrogen carrier

A detailed overview of the ultimate magnet design developed within Work Package 8 of the collaborative European project HITRIplus is presented. Focused on the development of superconducting magnets for ion therapy synchrotron and gantry systems, the study introduces an innovative approach utilizing a curved Canted Cosine Theta layout magnet based on Nb Ti superconductor. The design targets a central magnetic field strength of 4 T, an 80 mm aperture, and a maximum ramp rate of 0.4 T/s, while addressing the challenge of a tight 1.65 m bending radius. This paper highlights the latest advancements in magnetic and mechanical designs, as well as the construction and assembly procedures for the curved former. The rope cable conductor utilizes a 2×7 layout, optimizing current density distribution with a 1.5 kA current per rope. Key advancements include magnetic and mechanical design improvements, construction readiness, and a detailed comparison of assembly procedures with and without an iron yoke. The vertically split iron yoke design manages thermal contraction through innovative approaches, including tapered iron laminations and aluminium clamps. Alu minium bronze is selected for the curved former, with machining and validation tests highlighting its suitability. Additionally, the paper explores field quality analysis before and after magnet energization, addressing geometric yoke optimization to enhance field uniformity. Progress in conductor development, winding, and wax impregnation tests, and assembly trials are presented, with a focus on ensuring robustness and field accuracy in both yoke-inclusive and yoke-free configurations.

Predicting the relative roles of gravitational collapse and stellar feedback in star formation within extreme, low-density environments—such as the tidal tails produced by galaxy mergers—remains a fundamental challenge. These environments provide unique natural laboratories for testing star formation theories under conditions analogous to the early universe. However, existing models often fail to reconcile large-scale gravitational dynamics with localized feedback processes in such diffuse media. To bridge this gap, a reproducible, open-sciencebased theoretical framework is presented that integrates public, multi-wavelength observational datasets with high-resolution resistive magnetohydrodynamic (MHD) simulations. Our methodology is built on archival data from three flagship observatories: the James Webb Space Telescope (JWST), which is used to study young stellar populations and newly formed clusters. This telescope provides high-resolution infrared imaging and spectroscopy, enabling precise measurements of stellar ages, masses, and dust extinction. Atacama Large Millimetre/submillimetre Array (ALMA): used to trace cold molecular gas and analyze kinematic structures. These public datasets are used as quantitative constraints in resistive magnetohydrodynamic (MHD) simulations that incorporate magnetic fields, radiative cooling, sub-grid star formation, and stellar feedback, ensuring that the simulation results remain consistent with observational reality. Using the open-source code PLUTO, we model the formation of tidal structures while resolving key plasma physics, including localized resistivity to capture magnetic reconnection effects. Synthetic observations are directly generated from simulation outputs using radiative transfer post-processing, enabling point-by-point comparison with real data. To rigorously quantify agreement between model and observation, we implement a Bayesian inference framework that propagates observational uncertainties and yields posterior constraints on key parameters (e.g., magnetic field strength, feedback coupling efficiency). Through this integrated pipeline, the aim is to determine whether star formation efficiency in lowdensity tails is regulated by gravitational confinement from tidal compression or by localized feedback. Expected outcomes include quantitative estimates of virial stability parameters for observed gas complexes, spatial correlation analyses to gauge feedback coupling efficiency, and statistically robust constraints on uncertain model parameters. This framework is fully reproducible: all data are public, simulation codes are opensource, and analysis scripts will be archived with a DOI upon acceptance. By transparently linking theory and observation, this approach provides a methodological blueprint for studying star formation in interacting systems, with direct implications for galaxy evolution models and future observational strategies.

Low-field MRI (B0 ≤ 0.2 T) is emerging as a technology with the potential to revolutionize clinical diagnostics and patient monitoring. The reduction in magnetic field strength comes along with a decrease in the cost of the scanners and the infrastructure required for their operation. This, in turn, enables the development of compact, portable systems that extend imaging capabilities to locations and scenarios that were previously inaccessible. This democratization has empowered research groups worldwide to design and build their own scanners, resulting in a surge of new devices. However, the majority of low-field scanners are optimized for human studies, which limits their application in preclinical research and constrains the testing and development of contrast agents tailored for low-field regimes. In particular, hyperpolarized agents hold considerable promise for low-field MRI due to their capacity to enhance signal and provide metabolic imaging of living systems. This signal enhancement counteracts the inherently low signal-to-noise ratio of thermally polarized studies, which is the main limitation of low-field MRI. To exploit this potential, hyperpolarization studies frequently require the detection of X-nuclei, such as 13C and 15N, thereby emphasizing the need for versatile, multinuclear preclinical scanners. In this study, we present an open-source multinuclear low-field MRI scanner that has been specifically designed for hyperpolarized preclinical research. The device operates at 66 mT and allows the detection of 1H, 23Na, 13C, and 15N nuclei. Comprehensive documentation and complete CAD designs are provided to facilitate replication and adaptation by the research community. To illustrate the performance of the system, the results of the acquisition of NMR spectra from each nucleus are presented, as well as the first images obtained with the scanner. This platform aims to bridge the gap in preclinical low-field MRI, enabling rigorous invivo testing of novel contrast agents and supporting broader innovation in the field.

The interaction between the solar wind and the atmosphere of Venus leads to the formation of an induced magnetosphere, within which pronounced dawn–dusk asymmetries are observed in magnetic field pileup and ion transport. These asymmetries are known to depend on the orientation of the interplanetary magnetic field (IMF), but the underlying physical mechanisms governing this dependence remain incompletely understood. The aim of this study was to investigate how different IMF orientations influence magnetic field pileup, mathrm O ^+ ion distribution, and horizontal plasma transport in the induced magnetosphere of Venus, and to identify the dominant electromagnetic forces responsible for the resulting dawn–dusk asymmetries. We employed a multi-fluid magnetohydrodynamic (MHD) model to simulate the solar wind–Venus interaction under different IMF orientations. The model was used to analyze the spatial distribution of magnetic field strength, mathrm O ^+ ion number density, horizontal velocity, and ion flux. In addition, individual electromagnetic force components, including the motional electric field, the ambipolar electric field force, and the boldsymbol J B force, were quantitatively examined. The simulations show that when the IMF is not perpendicular to the solar wind flow, the dawnside, corresponding to the hemisphere toward which the IMF points in the simulation setup, exhibits stronger magnetic field pileup and enhanced horizontal plasma transport than the duskside. This dawn–dusk asymmetry weakens when the IMF orientation approaches perpendicularity to the solar wind. Force analysis reveals that the boldsymbol J B force is the primary driver of the asymmetric plasma transport. The magnetic field component normal to the planetary surface displays opposite signs on the dawn and dusksides, generating horizontal magnetic gradients and oppositely directed current density systems, which in turn produce asymmetric boldsymbol J B forces. These results demonstrate that the radial magnetic field structure and the resulting boldsymbol J B force play a critical role in controlling dawn–dusk asymmetries in plasma transport within Venus’ induced magnetosphere. The findings highlight the importance of electromagnetic forces, particularly the boldsymbol J B force, in shaping the structure and dynamics of the solar wind–Venus interaction under varying IMF orientations.

The Schrödinger equation is solved analytically for a particle subject to an enhanced Pöschl-Teller (EPT) potential in the presence of an external magnetic field and an Aharonov-Bohm flux field that induces topological phase effects. The bound state ro-vibrational energy equations are obtained using the generalized fractional Nikiforov-Uvarov method in conjunction with the Pekeris approximation scheme. The fractional order is introduced as an effective parameter that accounts for nonlocal and anharmonic ro-vibrational interactions that are not fully represented within the standard integer order framework. Based on these energy expressions, the mean thermal magnetization is derived within the partition function formalism. Numerical applications to diatomic molecules such as CO (X 1Σ+), Cs2 (3 3Σg+), ICl (X 1Σg+), 7Li2 (1 3Δg), Na2 (C(2) 1Πu), and NaK (c 3Σ+) show that the mean percentage absolute deviation values decrease from 0.0990%, 0.1407%, 1.0027%, 1.9504%, 0.1234%, and 0.9811% to 0.0905%, 0.1020%, 0.5501%, 1.1756%, 0.0474%, and 0.4840% when fractional parameters are incorporated, indicating improved agreement with experimental data and enhanced flexibility of the ro-vibrational energy model. The analysis further shows that, at fixed temperatures, the mean thermal magnetization of the Na2 (C(2) 1Πu) dimer increases with increasing magnetic field strength, highlighting the sensitivity of the system to external field variations. These results establish the EPT potential combined with a fractional order formulation as a reliable and adaptable analytical framework for describing the quantum and thermomagnetic behavior of diatomic molecules influenced by magnetic and topological quantum fields.

Abstract Unveiling the launching and driving mechanisms of powerful jets in active galactic nuclei is crucial for understanding the coevolution of supermassive black holes and their host galaxies. 1156+295 is a blazar at a redshift of z = 0.729 and exhibits significant variability in long-term radio monitoring. Using multifrequency Effelsberg single-dish flux density data from 2007 to 2012, we performed synchrotron self-absorption (SSA) spectral modeling and extracted the turnover frequency and turnover flux density. By combining SSA spectral modeling with the core size and brightness temperature from quasi-simultaneous very long baseline interferometry images, we estimated the jet magnetic field strength and magnetic flux and investigated their temporal evolution in 1156+295. The evolution of radio flux density, spectral shape, and jet structure is consistent with the shock-in-jet framework. The inferred magnetic flux reaching or exceeding the magnetically arrested disk threshold, together with evidence that magnetic energy release precedes the radio flares, supports a magnetically driven jet scenario. Overall, our results place magnetic field measurements, spectral evolution, and inner-jet structural changes on a common timeline, providing observational constraints on their coupled evolution during flares.

Triaxial induction logging is particularly outstanding in identifying reservoir parameters including anisotropic strata, inclined boreholes and horizontal wells. However, the coplanar systems follow the traditional induction method of using a shielding coil to offset the direct coupling. This method results in severe horns in the coplanar coil response, which makes it more difficult to evaluate the water (oil) saturation of the reservoir. In this study, we used an analytic method to derive the magnetic field in a finite-thickness anisotropic medium by applying tangential continuity of the electric and magnetic field strengths, introducing the magnetic vector potential and Bessel functions. The response model influenced by different parameters was established. Under the same environmental parameters, the measurement range of the vertical and horizontal conductivities was larger than that of the traditional coplanar system. The apparent conductivity of the target layer was closer to the true value of the vertical conductivity in the layered strata, with an accuracy improvement of 78.9%. Furthermore, the improved coplanar system mechanism was revealed by analyzing the spatial distributions of eddy currents and the magnitudes of the magnetic fields generated. Finally, we designed an experimental device for a coplanar sensing system. Under the same parameters, the received signals of the improved coplanar system were greater than those of the traditional coplanar system in the air, which laid a foundation for the quantitative evaluation of stratigraphic anisotropy response characterization and inversion.

Abstract The Voyager spacecraft (V1 and V2) provide unique in situ measurements of perturbations propagating beyond the heliopause through the very local interstellar medium (VLISM), including the shocks and pressure fronts whose origin is debated. In particular, a jump in magnetic-field strength, observed by V1 in 2020.4 at 149.3 au from the Sun, was followed by a distinct “hump” and persistently strong magnetic field, both requiring theoretical explanation. This paper offers an interpretation of those observations using a self-consistent, MHD model of the solar wind–local interstellar medium interaction driven by the OMNI and Interplanetary Scintillation data combined with a turbulence analysis of Voyager data. Our simulations convincingly demonstrate that global, solar-cycle-driven compressions, on hitting the heliopause, can reproduce those puzzling V1 observations. They appear to be associated with solar cycle 24, whereas similar interstellar magnetic-field structures can occur once per cycle. The turbulence analysis reveals time-dependent magnetic compressibility that persists up to 165 au at scales below 10 days. Turbulence intermittency at scales below 1 hr is mostly confined to specific intervals, possibly associated with a broad foreshock region. The apparent disappearance of intermittency since 2022 reflects the turbulence weakening rather than a fundamental change in VLISM properties. We predict that V1 will record relatively strong magnetic-field strengths until ∼2030, followed by weaker, infrequent perturbations. At V2, we expect multiple solar-driven compressions before 2026, followed by a major event induced by solar cycle 25 around 2030. New Horizons is expected to cross the termination shock at 80 ± 2 au in 2031.

Compact steep spectrum (CSS) sources generally show weak Doppler boosting, yet some exceptions show multi-year-scale radio flux variability and high-energy activity. Since 2022, the CSS quasar 3C 138 has been in a radio high state accompanied by multiple gamma-ray outbursts, offering unique opportunities to study changes in jet physical conditions. We estimated the synchrotron self-absorption (SSA) magnetic field (B_ SSA) in the SSA core of 3C 138 during its high state and compared it with the equipartition magnetic field (B_ eq) to assess the core field environment. Using extended Korean Very long-baseline interferometry Network (KVN) data at 22, 43, 86, and 129 GHz (2024–2025), we calibrated the visibilities and modeled resolved components with circular Gaussians. A single-zone SSA model fitted to the core spectrum provided the turnover frequency and peak flux density, from which we estimated the B_ SSA and B_ eq. We used Very Large Array and Atacama Large Millimeter/submillimeter Array data to constrain the broadband spectra with the same model. The KVN SSA core shows a turnover at about 33 GHz and a peak flux of about 1.45 Jy. The inferred B_̊m SSA is far below equipartition, with B_ ̊m SSA /B_ ̊m eq The flux variability of 3C 138 is driven by a compact, particle-dominated core. Shock-driven particle injection in the inner jet could account for the core brightening and the production of X-ray/gamma-ray emissions through an inverse-Compton process without requiring extreme relativistic beaming effects.

This investigation examines the momentum, thermal, and species transport characteristics of an ethylene glycol-based copper nanofluid over a rotating disk configuration, incorporating the combined influences of an aligned magnetic field and Arrhenius activation energy. The mathematical model, comprising nonlinear partial differential equations for momentum conservation, energy balance, and concentration distribution, is reduced to a system of ordinary differential equations through appropriate similarity transformations. Numerical solutions are obtained using the BVP5C algorithm, yielding detailed velocity, temperature, and concentration profiles across the boundary layer. The principal novelty of this work lies in the simultaneous consideration of activation energy effects and aligned magnetic field orientation on nanofluid behavior in rotating disk geometry, a combination not previously addressed in the literature. A systematic parametric study examines how key physical quantities like magnetic field intensity, nanoparticle volumetric concentration, activation energy parameter, and Schmidt number—influence the heat and mass transfer characteristics of the system. The results demonstrate that increasing magnetic field strength produces a retarding effect on fluid motion, with both radial and tangential velocity components diminishing as the Lorentz force intensifies. Furthermore, the activation energy parameter exhibits a pronounced influence on species transport, significantly modifying concentration distributions and mass transfer rates at the disk surface. These findings contribute to the fundamental understanding of nanofluid behavior under coupled magnetic and chemical reaction effects, with potential implications for thermal management systems and biomedical applications

This paper investigates relativistic magneto-fluid spacetimes admitting generalized almost Schouten solitons and their gradient analogs within the framework of the Einstein field equations. By coupling the soliton structure with the magneto-fluid energy–momentum tensor, explicit relations are obtained between geometric invariants of spacetime and physical quantities such as fluid density, pressure, magnetic field strength, and magnetic permeability. Under quasi-conformal, [Formula: see text]-flat, and [Formula: see text]-flat curvature conditions, strong rigidity results are derived, showing that the spacetime reduces to an Einstein or constant-curvature model under natural algebraic assumptions. The influence of soliton parameters on the expanding, steady, and shrinking behavior of the spacetime is characterized explicitly. Energy conditions associated with generalized almost Schouten solitons are analyzed, and it is shown that the timelike convergence condition implies both the strong and null convergence conditions, allowing the application of Penrose-type singularity theorems and guaranteeing the existence of trapped surfaces and black hole regions. The harmonic and Schrödinger–Ricci harmonic properties of the soliton-induced [Formula: see text]-form are completely characterized, while in the gradient case the soliton potential satisfies a Poisson-type equation governing its qualitative behavior. Several physically relevant regimes, including dust, dark matter, radiation, and vanishing magnetic permeability, are examined, and an explicit four-dimensional Lorentzian example is constructed to confirm the existence of nontrivial generalized almost Schouten solitons.

Abstract We investigate the linear onset of convection in a rotating plane layer permeated by a uniform horizontal magnetic field perpendicular to the rotation axis, a configuration relevant to dynamics within Earth’s tangent cylinder and complementing recent investigations [Barman and Sahoo 2025. Phys. Scr. 100 125018]. The primary objective is to examine how partial thermal stratification modifies convective initiation across three thermal states—fully unstable, weakly stable, and strongly stable—over rotation rates corresponding to Ekman numbers E = 10 −3 , 10 −4 , 10 −5 , thermal-to-magnetic diffusivity contrasts characterized by Roberts numbers q = 0.01, 1, 10, and magnetic field strengths spanning Elsasser numbers 0 ≤ Λ ≤ 10. Analysis of convective onset, supported by locally derived scaling relations, shows that introducing a stable segment raises the critical threshold for convection and promotes smaller-scale structures, particularly under rapid rotation. When magnetic forcing is weak, rotational effects dominate, strengthening the vertical alignment of convective motions and enhancing the stabilizing influence of stratification, thereby delaying convective onset. In contrast, strong magnetic forcing maintains broader convective rolls even at rapid rotation, although penetration into the stable layer remains limited. Magnetic damping is most pronounced at low to moderate diffusivity contrasts and weakens when magnetic diffusion becomes dominant, while the penetration depth decreases with increasing rotation and magnetic intensity in strongly stratified regimes. This study shows that partial stable stratification significantly modifies the onset of rotating magnetoconvection under a horizontal magnetic field by increasing the instability threshold, favoring smaller-scale structures, and limiting convective penetration into the stable layer, with the combined effects of buoyancy, rotation, and magnetic forces shaping the flow morphology. These results extend classical plane-layer magnetoconvection models and provide insight into planetary core dynamics—such as within Earth’s tangent cylinder—where stable stratification and magnetic feedback coexist, while also highlighting contrasts between weak-field planetary interiors and strong-field stellar environments.

Recent research has indicated the existence of slow diffusion phenomena in pulsar wind nebulae (PWNe), where the diffusion coefficient of particles is significantly smaller than the value considered to be the average in the Galaxy. We aim to explore the particle slow diffusion mechanism in the frame of a time-dependent model with particle advection and diffusion. Based on the turbulence theories, the gyroresonant interactions between the particles and turbulent waves are considered, which enables us to determine the diffusion coefficients of particles within nebulae via the turbulence injection scale and magnetic field components (ordered magnetic field and turbulent magnetic field). Meanwhile, by considering injection, advection, adiabatic loss and radiative loss of particles, the multiband nonthermal emission from a PWN is produced by the relativistic leptons through synchrotron radiation and inverse Compton process. The diffusion coefficient increases with injection scale, whereas it decreases with the turbulent-to-ordered magnetic field strength ratio. Meanwhile, effects of turbulent injection scale and magnetic field components on spectral energy distributions (SEDs) are analyzed. This model is applied to HESS J1420-607, and the observed spectral energy distribution of photon emission is reproduced well. The results suggest that (1) the particle cooling processes are dominated by adiabatic loss in lower-energy bands and IC scattering losses dominate for the higher-energy particles; (2) the advection is the most prominent process to particle transport within this nebula, and the diffusion only plays a role in the high-energy band. More importantly, our model estimates the current diffusion coefficient at an electron energy of 1 TeV 2.6 times 10^ cm^2s^-1, and the slow diffusion mechanism may be caused by the small-scale turbulent injection and relatively ordered magnetic field distribution within HESS J1420-607.

Vacuum arc remelting (VAR) is essential for producing premium titanium alloys, where an externally applied alternating magnetic field enables circumferential stirring to control ingot homogeneity. However, current magnetic field parameter design relies on empirical trial-and-error approaches, lacking systematic theoretical guidance. To address this issue, this study establishes a comprehensive multi-physics framework through a two-dimensional axisymmetric swirl model integrating electromagnetic, fluid dynamics, thermal, and solute transport phenomena. Our findings demonstrate that both the magnetic field strength and period exhibit optimal operating ranges, which directly influence ingot homogeneity. As magnetic field strength increases progressively, ingot uniformity shows a distinctive non-monotonic response—initially improving before subsequently deteriorating. Correspondingly, with increasing stirring period, macrosegregation undergoes a distinct three-stage evolution: initial mitigation, subsequent aggravation, and final alleviation. These phenomena originate from the small-scale circulatory flow generated by the external magnetic field on the surface of the VAR molten pool. The interactions among the flow, the solute diffusion layer, and the mushy zone collectively alter elemental diffusion behavior, ultimately determining the homogeneity of the ingot. This study provides a theoretical foundation for precise control of ingot homogeneity in titanium alloy VAR processes and demonstrates significant potential for engineering applications.