Similarity Transformation Research Articles

Numerical solutions and stability analysis of hybrid Casson nanofluid flow with MHD and heat transfer effects

AbstractThis research addresses the complex dynamics of hybrid Casson nanoliquids in flow and heat transfer applications, focusing on the interaction between fluid dynamics and thermal phenomena in the presence of magnetohydrodynamics (MHD), viscous dissipation, and Joule heating. The motivation behind this study stems from the need to enhance the efficiency of heat transfer processes in various engineering applications, such as cooling systems and electronic devices, where hybrid nanofluids can offer superior thermal performance compared to conventional fluids. The novelty of this work lies in its comprehensive numerical investigation of a hybrid Casson nanoliquid over a moving permeable surface, incorporating a detailed analysis of MHD effects, viscous dissipation, and Joule heating. Using the Tiwari and Das model to formulate the governing equations, the study employs similarity transformations to convert these equations into a system of ordinary differential equations (ODEs). MATLAB is then used to derive numerical solutions, with a stability analysis ensuring the physical dependability of these solutions. Key findings reveal that the temperature distribution of the hybrid nanoliquid shows a positive correlation with both Prandtl and Hartmann numbers. Additionally, a positive relationship between temperature and the Eckert number is observed. These insights offer valuable guidance for engineers aiming to optimize heat transfer processes using hybrid nanofluids, highlighting their potential for improved thermal management in practical applications.

Heat and mass transfer analysis in flow of Walter's B nanofluid: A numerical study of dual solutions

AbstractThis study investigates the behavior of Walter's liquid B fluid over a biaxially stretching/shrinking surface for Homann stagnation point flow, focusing on the rheological properties that are crucial for understanding physical phenomena in engineering and industrial processes. The problem is modeled using Buongiorno's model in the presence of a permeable surface subject to heat generation/absorption, Ohmic heating, and chemical reactions influenced by Arrhenius activation energy. The governing partial differential equations are solved numerically using an appropriate similarity transformation, and the results are graphically analyzed via MATLAB's bvp5c solver. The study highlights the importance of characterizing the intricate properties of viscoelastic fluids, with potential applications in biomedical engineering and materials science. The findings reveal the coexistence of two distinct flow regimes and dual solutions are obtained. It is noted that the activation energy parameter is shown to enhance mass distribution in both solutions, while chemical reactions accelerate reactant conversion but reduce mass distribution. Additionally, an increase in viscoelasticity shifts the fluid's behavior towards elasticity, creating greater resistance to shear deformation and reducing both velocity profiles.

Thermophoretic particle deposition effect on a squeezed flow of radiative Jeffrey fluid past a sensor surface with uniform heat source/sink and chemical reaction

Abstract This anticipated model investigates the time-dependent, and incompressible 2D magnetized Jeffrey liquid flowing on a sensor surface placed between two infinite parallel plates with the existence of a uniform heat source/sink. The lower plate remains fixed while the upper plate is subject to squeezing. For the heat and mass transmission processes, the consequences of radiative heat flux, chemical reaction, and thermophoretic particle deposition are applied and analyzed. The envisioned model is supported by prescribed heat and mass flux conditions. The uniqueness of the proposed model is the analysis of the unsteady squeezed flow of Jeffrey liquid over a sensor surface, accounting for radiative heat flux, thermophoretic particle deposition, and variable thermal conductivity. The model possesses applications in microfluidic sensors, biomedical devices, thermal management systems, and inkjet printing. The equations comprising the model are subject to similarity transformations. The bvp4c package is utilized to analyze the dynamic flow system. The connotation of arising parameters with the associated profiles is depicted through graphs and tables. It is examined that fluid velocity, temperature, and concentration profiles are dwindling functions of squeezed parameter. It is also witnessed that the concentration of liquid drops with an enhancement of thermophoretic and chemical reaction parameters. The validation of the truthfulness of the envisioned model is an added feature of this study.

Boundary Layer Flow of Dusty Ferrofluid: A Comparative Analysis of Stagnation Flow Influence

This research examines the characteristics of the boundary layer in the occurrence of dust particles within the ferrofluid boundary layer, aiming to understand the impact of stagnation flow or without stagnation flow in such systems. For this purpose, ferroparticles, namely magnetite (Fe3O4), are taken into consideration with kerosene and water as base fluids. The governing partial differential equations of the problem under consideration are converted into ordinary differential equations (ODEs) through the utilization of similarity transformations. Here, the equations obtained are then numerically solved utilizing MATLAB's built-in bvp4c solver. Moreover, the parameters’ effects, namely the dust particle loading, volume fraction of ferroparticles, and Eckert number to the flow with and without stagnation flow are computed and shown through tables and graphs. The findings indicate that the skin friction coefficient values for the stagnation-point flow are higher than those without stagnation-point flow. The Eckert number increases temperature profiles for both flows but more prominent in the flow without stagnation-point.

Darcy-Forchheimer magnetohydrodynamic flow of non-Newtonian Reiner-Rivlin hybrid nanofluid bounded by double-revolving disks

The applications of fluid flow and heat transfer between coaxial double-revolving disks are diverse and can be found in various engineering and scientific domains. In general, the utilization of engine oil ( EO) mixed with hybrid nanoparticles serves various purposes in engine cooling, such as maintaining viscosity-temperature properties, preventing corrosion, and achieving other cooling-related objectives. This investigation focuses on the Darcy-Forchheimer flow of a non-Newtonian Reiner-Rivlin hybrid nanofluid confined between double-revolving disks. The hybrid nanoparticles used include cadmium telluride ( CdTe) and titanium dioxide ( TiO2), combined with the base fluid engine oil. The dimensional flow equations are converted into dimensionless forms using suitable similarity transformations. Subsequently, a semi-analytical methodology known as the homotopy analysis method ( HAM) is utilized to tackle this problem. Graphs are used to determine the effects of the various flow parameters of the hybrid nanofluids on the velocities, temperature, skin friction coefficient, and the Nusselt number. After validating the findings against previous research, an attractive agreement was observed. Some major outcomes from this present problem are that axial, radial, and temperature profiles increase with the rise of the cross-viscosity parameter while the tangential velocity decreases. Radial velocity increased, and tangential velocity diminished with an enhanced magnetic field parameter. Radial velocity is increased for higher values of the dimensionless forced parameter. For higher values of the porosity parameter, the temperature profile improved. Also, the exploration of the Nusselt number and skin friction for the disks, incorporating the effects of a magnetic field and porous medium, reveals that skin friction for both disks increase with the rising Reynolds number and volume fraction of the cadmium telluride nanoparticles.

Lapscheure, etymologisch verscheurd. Een overzicht van de opvattingen, nieuwe gegevens en een voorstel tot verzoenende oplossing

The etymology of the West Flemish place name Lapscheure remains uncertain and contentious. The dispute involves both elements of the name. Gysseling (1960) interprets the second part, -scheure, as the local phonetic form of 'schuur' (barn), while Mansion (1935) and Tavernier-Vereecken (1954, 1968) suggest it means 'schoor/schor/schorre' (shore/marsh). The oldest records, such as "lappescura" (1019-30), use <u>, with later records showing <eu/ue>, indicating a Middle West Flemish pronunciation of [ø]. Tavernier-Vereecken's attempt to categorize 'schoor/schorre' within a group of ingvaeonisms (like veugel, weunen, bleuzen) lacks support in contemporary West Flemish. Conversely, unambiguous 'schuur' place names, such as the French-Flemish Ruischeure (Fr. Renescure) and Buisscheure (Fr. Buysscheure), suggest a more straightforward interpretation of 'schuur'. Mansion and Tavernier-Vereecken propose that Lapscheure derives from a personal name, such as Lappa or Lappo. Initially, Gysseling, however, considered the name could mean a repaired barn, later suggesting an Indo-European root *lap (‘bright, beautiful’), which gained little traction. The notion of a repaired barn appeared earlier in Tanghe's 1857 "Beschryving van Lapscheure". The noun lap (‘patch’) dates back to the 10th-century Old Dutch Wachtendonk Psalms and exists in all Germanic languages except Gothic. The verb lappen (‘to mend’) first appeared in 1285 (Dordrecht), possibly originating as a Northwest Germanic/Ingvaeonic term. However, naming a prominent barn this way is doubtful, whereas a personal name remains more plausible. The earliest form, with the expressive geminate -pp-, suggests Lappo as a diminutive of the frequent medieval name Landberht/Landbrecht, evolving through forms like Landbo, Lambo, Lampo, and Lampe to Lappe. This analysis aligns with similar transformations seen in medieval names, as discussed by Debrabandere (1980).

Pioneering Museum Data Transformation: Unifying Legacy Systems and Enhancing Data Integrity

In the digital era, museums confront the challenge of modernising legacy data systems to align with current standards. Part of the RECODE (Rethinking Collections Data Ecosystems) Programme (Dupont et al. 2022) examines the complex transition from disparate departmental object models to a unified system, reflecting the broader museum community's struggle with data standardisation. The case study centres on consolidating five distinct data models accumulated over two decades, each tailored to different departmental needs under various constraints. The data mapping process identifies and aligns similar fields across models, facilitating the integration of analogous data points and exposing redundancies and unique practices embedded over years. Major challenges include data complexity, diversity, and quality issues (cleaning, standardizing, and deduplicating), compounded by the massive scale of the data: currently, the Natural History Museum London (NHM) has 262,831,590 records across 8,175 fields, and a total volume of 12 TB of data, which define both the ongoing data modelling work and our future data migration. A key innovation in our process is the immediate visibility of data issues that became apparent upon migrating to Amazon Web Services (AWS). AWS serves as the staging environment for our transition to the new NHM Collections Management System (CMS) and offers an unprecedented platform for directly addressing these challenges. It enables us to query all our data—across all departments and fields—in just seconds. This capability provides a comprehensive view that was previously unattainable. The core of this presentation is sharing "lessons learned" from navigating the intricacies of an ongoing CMS transition within a museum. The endeavor to untangle and unify diverse data models is a common challenge (IEEE Big Data Governance and Metadata Management Industry Connections Activity 2020,Wu et al. 2022, Wu et al. 2021,Little et al. 2022,Woodburn et al. 2022) highlighting the importance of community engagement and knowledge exchange. Our findings underscore the necessity of cross-departmental collaboration and the benefits of a data-driven data modelling approach. By sharing our journey and the developed comprehensive object model (Collier and Woodburn 2022), we aim to contribute valuable insights to museums undergoing similar transformations. The RECODE Programme sheds light on the practical aspects of CMS modernisation through the analytics and knowledge derived from over two decades of collections data and data use.

MHD Mixed Convection Boundary Layer Casson Nanofluid Flow over an Exponential Stretching Sheet

This paper investigates the effects of radiation, internal heat source and magnetohydrodynamics (MHD) on the mixed convective boundary layer flow of a Casson nanofluid within a porous medium that is saturated and subject to an exponentially stretching sheet. The nanofluid model incorporates Brownian motion and thermophoresis, and the Darcy model is employed for the porous medium. By applying an appropriate similarity transformation, the nonlinear governing boundary layer equations are converted into a set of nonlinear coupled ordinary differential equations. These equations are then solved numerically using the Hermite wavelet method, with simulations conducted through the MATHEMATICA programming language. The analysis covers various aspects including temperature distribution, velocity, solute concentration and several engineering parameters such as skin friction coefficients, the Nusselt number (rate of heat transfer) and the Sherwood number (rate of mass transfer), all evaluated based on dimensionless physical parameters. The results indicate that elevated radiation intensifies temperatures and leads to thicker thermal boundary layers. As the Casson parameter increases, both the velocity and the momentum boundary layer become narrower. Additionally, a more pronounced chemical reaction rate reduces the thickness of the solutal boundary layer. The accuracy and reliability of the numerical Hermite wavelet method are validated through a comparative analysis with previous studies, demonstrating excellent concordance and confirming the robustness of the computational approach.

Heat and mass flux dynamics of tangent hyperbolic nanofluid flow with unsteady rotatory stretching disk over Darcy-Forchheimer porous medium

Abstract The purpose of the research is to examine a tangent hyperbolic nanofluid flowing in three dimensions (3D) axisymmetrically on an unsteady rotatory stretching disk over a Darcy-Forchheimer porous medium. First order initial value problems (IVPs) are generated from the governing partial differential equations (PDEs) through the use of similarity transformation and linearization. The Runge-Kutta sixth order (RK6) is utilized to solve the IVP system using the shooting technique and the built-in Python program ‘fsolve model10’. Articles that have already been published are used to validate the implemented approach. Graphs are used to examine how various parameters affect velocity, temperature, and concentration. Additionally, the behavior of heat, mass flux, and skin friction in response to different parameters is investigated. The study’s findings showed that as the Forchheimer number and velocity slip parameter increased, the nanofluid’s radial and tangential velocities decreased as well. As temperature and concentration slip parameters increase, correspondingly, thicker and thinner boundary layer structures are seen. The drag force in the tangential and radial direction behaves in the same manner. Both the rates of heat and mass transfers are initiated for an increase Eckert and Prandtl numbers and demotivated for power-law index number. The dissipation effect with radiation and chemical reaction plays a major role in heat and mass fluxes, respectively. The study can be used in various computer storage, coatings, lubricants, and coolants.

Optimization of nanoscale heat transport analysis of ternary hybrid nanofluid over three‐dimensional wedge geometry in magnetized environment

AbstractExponential space‐based heat source with shear‐thinning/thickening behavior offers innovative insights into the optimization of thermal transport process in complex systems, such as in the cooling of microelectronics, energy storage technologies, and biomedical devices, where accurate thermal control is critical. This study explores the investigation of an exponential space‐based heat source with effects of shear thinning/thickening behavior of a ternary infinite shear rate viscosity‐dependent Carreau water‐based nanofluid [Cu, Fe3O4, SiO2] over a three‐dimensional wedge in a magnetized environment. The interaction between heat transport and magnetic fields is explored through the behavior of the ternary nanofluid by classifying the both shear‐thinning and shear‐thickening effects. The incorporation of physical assumptions in the model gives the set of partial differential equations (PDEs) and similarity transformations are launched to convert them into ordinary differential equations (ODEs). Furthermore, bvp4c scheme is used to fetch the numerical solution. Temperature profile is increasing with exponential‐based source heat parameter due to a reduction in the rate of heat absorption by the fluid. Ternary nanofluids exhibit the highest rate of temperature increment due to the effects of multiple nanoparticles as compared to hybrid or single‐nanoparticle nanofluids. Rate of velocity decrement in ternary nanofluids compared to bi‐hybrid nanofluids and single‐particle nanofluids.

Building Engagement-Capable Environments for Health System Transformation: Development and Early Implementation of a Capability Framework for Patient, Family and Caregiver Engagement in Ontario Health Teams.

Despite widespread calls to involve patients, families and caregivers (PFCs) as partners at all levels of health system planning and design, there is unevenness in how engagement efforts are supported across these settings. The concept of 'engagement-capable environments' offers a way forward to uncover the key requirements for sustainable, high-quality engagement, but more work is needed to identify the specific competencies required to create these environments. We addressed this gap by developing a capability framework for Ontario Health Teams (OHTs), a newly established structure for planning, designing, organizing and delivering care in Ontario, Canada. The framework was co-developed by a Working Group of OHT staff and leaders, PFC partners, researchers and government personnel. Project activities occurred over four phases: (1) planning, (2) evidence review and surveying of intended users to identify key competencies, (3) framework design and (4) implementation. An evidence review identified more than 90 potential competencies for this work. These results were contextualized and expanded through a survey of OHT stakeholders to brainstorm potential competencies, supports and enablers for engagement. Surveys were completed by 69 individuals; 689 knowledge and skill competency statements, 462 attitude and behaviour competency statements and 250 supports and enablers were brainstormed. The statements were analysed and organized into initial competency categories, which were reviewed, discussed and iteratively refined by Working Group members and through broader consultations with the OHT community. The final framework includes six competency domains and four support and enabler domains, each with sub-domain elements, mapped across a three-stage maturity model. The framework has been disseminated across OHTs, and its adoption and implementation are now requirements within OHT agreements. The framework combines a strong conceptual foundation with actionable elements informed by the literature and consultations with the intended users of the framework. Although developed for OHTs, the framework should be broadly applicable to other health system organizations seeking similar health system transformation goals. Patient, family and caregiver partners were involved at all stages and in all aspects of the work. As end users of the framework, their perspectives, knowledge and opinions were critical.

Mathematical and Buongiorno nanofluid modelling to predict the thermal and solutal performance of magneto-bioconvective Casson nanofluid flowing in a rotatory disk

Abstract This study aims to improve how heat and mass move in systems that use viscoelastic nanofluids under magnetic fields. These systems are commonly used in industries like biotechnology, energy, and medical devices. The significance of this work lies in exploring the steady flow of magnetohydrodynamic (MHD) Casson nanofluids, incorporating the Buongiorno nanofluid model and swimming microorganisms. This research seeks to deepen the understanding of complex fluid behaviors by examining the effects of thermal radiation and chemical diffusion under thermal and solutal convective boundary conditions. The governing equations, which are inherently nonlinear due to the presence of multiple physical effects, are converted from two-dimensional partial differential equations (PDEs) to ordinary differential equations (ODEs) using a similarity transformation. A semi-analytical solution is derived using the collocation pseudo-spectral method within the MAPLE computational software. The study investigates how factors like Casson and magnetic parameters, Eckert number, Brownian motion, and thermophoresis affect the flow rate, temperature distribution, species concentration, and microorganism motility. These results are validated by comparing them with established benchmarks. The key findings reveal a pronounced oscillatory behavior in the temperature profile at higher Eckert number values, while increased Brownian motion and thermophoresis lead to greater nanoparticle dispersion near the disk surface. Higher Lewis and Peclet numbers lead to increased microorganism concentration, demonstrating stronger convective and advective effects. These insights are vital for optimizing drag force, thermal gradients, and mass transfer in engineering applications that involve rotating disks and magnetic fields.

Statistical analysis of bioconvective EMHD tangent hyperbolic nanofluid with thermal radiation and heat source/sink

AbstractThis study examines the influence of thermal radiation and heat source/sink of the tangent hyperbolic fluid on EMHD boundary layer flow through stretching sheets. Motile gyrotactic microorganism is considered in the fluid flow and the flow is analyzed with the impact of thermal radiation, heat source/sink, and electromagnetohydrodynamic. By utilizing the proper similarity transformations, partial differential systems are converted to ordinary differential systems. The Runge–Kutta fifth‐order method with shooting technique is used in the converted systems to solve numerically. Velocity, temperature, concentration, and microorganism density profile are discussed and represented graphically. The numerical values of drag force rate, heat transfer rate, mass transfer rate, and density of motile microorganisms are specified, compared, and results enhancement in heat transfer rate as 64.31% by radiation parameter, mass transfer rate as 97.28% by heat source/sink parameter and microorganism density rate as 28.33% by Peclet number, respectively. The buoyancy parameter diminishes the drag force by 30.39%. The multiple and quadratic regression coefficient for adjusted , multiple , residual standard error, F‐statistic, and p‐value is estimated for skin friction, Nusselt number, Sherwood number, and density of microorganism. It has significant applications which are widely used to transport biological material in bio‐microfluidics, enhance heat dissipation in high‐performance electronics, thermal management systems on spacecraft and satellites, and solar energy systems.

Computational heat transfer analysis of ternary hybrid nanofluid flow over a rotating disk using the Cattaneo-Christov model: Application of the Lobatto-III formula

This work investigated the impact of ternary nanoparticles on the flow dynamics across a revolving disk. This study examines the nanoparticles of magnesium oxide (MgO), titanium dioxide (TiO2), and CoFe2O4 that were dispersed in different liquids -water and ethylene glycol (EG). This study examines the joint impacts of a varying inclined magnetic field and CattaneoChristov heat and mass flux on the flow of two ternary nanofluids across a spinning disk. Problems of this nature predominantly arise in symmetrical phenomena through the use of similarity transformations and are relevant to engineering, physics, and applied mathematics. The phenomena were expressed as partial differential equations, which were subsequently transformed into an ordinary differential equation within the existing system. Subsequently, this work is computed with the bvp4c scheme in MATLAB. Graphical results are employed to evaluate the examination of mass and heat transfer. The velocities increase with the inclined magnetic impression for both ternary nanofluids. The temperature increases and concentration declines with the increasing volume fraction of TiO2 and CoFe2O4 for both ternary nanofluid flows. The Nusselt number declines for I-ternary nanofluid flow and increases for II-ternary nanofluid flow with the thermal and solutal relaxation parameter along with the increasing volume fraction of TiO2 and MgO. In addition, the alterations in concentration, temperature, and velocity graphs for different dimensionless parameters are briefly examined through related diagrams. The Nusselt number declines with the I-ternary group and increases with the II-ternary group for the nanoparticle MgO concentration.

Investigation of magnetite water nanofluid flow through a stretching sheet using the Hamilton and Crosser model for nanoparticle shape factor and effective thermal conductivity

The main objective of this current investigation is to study the heat and mass transfer of the convective MHD Fe3O4−H2O nanofluid through an expanding sheet in the presence of thermal radiation. The Hamilton and Crosser model describes the shape and effective thermal conductivity. The fluid flow governing PDEs has been transformed into a system of ODEs by utilizing appropriate similarity transformation. We used SQLM or Spectral Quasilinearization method to solve them numerically and draw the graphical conclusion using MATLAB software. The skin friction, the Nusselt number and the Sherwood number have been determined numerically and portrayed graphically for the pertinent parameter. It has been observed that for the increment of the volume fraction of Fe3O4 nanoparticles, the fluid velocity tends to reduce while the thermal profile is enhanced. We also observed that for the increment of the buoyancy parameter, the mass transfer is enhanced. Additionally, for the enhancement of the Schmidt number from 0.1 to 1.2, the rate of mass transfer coefficient increases very rapidly. The outcome of the current study has been compared with previously published data, and there is a satisfactory agreement.

Exploring the Thermal Behavior of Cu-water and CuO-water Power-law Nanofluids on a Rotating Circular Disc: A Computational Analysis

The current theoretical investigation focuses on the thermal behavior of a power-law nanofluid flow on a rotating circular disc. In which nanofluid is made by taking colloidal suspension of copper (Cu) and copper oxide (CuO) nanoparticles in a base fluid like water. A theoretical investigation is conducted by formulating a mathematical model of a power-law fluid (which exhibits shear thickening and thinning effects) along with the Tiwari and Das model. A similarity transformation is employed to transform the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs) and these ODEs are then numerically solved using the shooting technique. The study's findings are analyzed graphically by plotting radial, tangential, and axial velocity profiles, temperature profiles, Nusselt number, and skin friction coefficients to show how various factors affect the fluid's flow and heat transfer. It is revealed that drag force reduces in Cu-water nanofluid as compared to CuO-water nanofluid for all types of fluids (Newtonian, pseudoplastic, and dilatant fluids) and Nusselt number becomes high in Cu-water nanofluid for both Newtonian and dilatant fluids as compared to CuO-water nanofluid but in case of pseudoplastic reverse behavior is observed. Heat transfer rate in Cu-water dilatant and pseudoplastic nanofluids increases up to 20.4% and 12.5% with respect to base fluid and in CuO-water dilatant and pseudoplastic water nanofluids, it increases up to 18.6% and 15.2%.

Closing the gap between SGP4 and high-precision propagation via differentiable programming

The simplified general perturbations 4 (SGP4) orbital propagation model is one of the most widely used methods for rapidly and reliably predicting the positions and velocities of objects orbiting Earth. Over time, SGP models have undergone refinement to enhance their efficiency and accuracy. Nevertheless, they still do not match the precision offered by high-precision numerical propagators, which can predict the positions and velocities of space objects in low-Earth orbit with significantly smaller errors.In this study, we introduce a novel differentiable version of SGP4, named ∂SGP4. By porting the source code of SGP4 into a differentiable program based on PyTorch, we unlock a whole new class of techniques enabled by differentiable orbit propagation, including spacecraft orbit determination, state conversion, covariance similarity transformation, state transition matrix computation, and covariance propagation. Besides differentiability, our ∂SGP4 supports parallel propagation of a batch of two-line elements (TLEs) in a single execution and it can harness modern hardware accelerators like GPUs or XLA devices (e.g. TPUs) thanks to running on the PyTorch backend.Furthermore, the design of ∂SGP4 makes it possible to use it as a differentiable component in larger machine learning (ML) pipelines, where the propagator can be an element of a larger neural network that is trained or fine-tuned with data. Consequently, we propose a novel orbital propagation paradigm, ML-∂SGP4. In this paradigm, the orbital propagator is enhanced with neural networks attached to its input and output. Through gradient-based optimization, the parameters of this combined model can be iteratively refined to achieve precision surpassing that of SGP4. Fundamentally, the neural networks function as identity operators when the propagator adheres to its default behavior as defined by SGP4. However, owing to the differentiability ingrained within ∂SGP4, the model can be fine-tuned with ephemeris data to learn corrections to both inputs and outputs of SGP4. This augmentation enhances precision while maintaining the same computational speed of ∂SGP4 at inference time. This paradigm empowers satellite operators and researchers, equipping them with the ability to train the model using their specific ephemeris or high-precision numerical propagation data.

Artificial neural network-based computational heat transfer analysis of Carreau fluid over a rotating cone

Heat transport in a dynamically rotating cone immersed in a Carreau fluid is the subject of this investigation. The fluid is non-Newtonian, admired for its characteristics, and extensively utilized in numerous industrial domains. The study investigates the interplay between buoyancy and centrifugal forces within an analytical framework. The study employs sophisticated mathematical methods, including similarity transformations, to convert governing partial differential equations into nonlinear ordinary differential equations. These equations are then solved using the shooting method, a numerical technique that solves a boundary value problem by iteratively adjusting the initial conditions until the boundary conditions are satisfied. We employ an artificial neural network algorithm with backpropagation Levenberg–Marquardt scheme to analyze the heat transfer mechanism quantitatively. In conjunction with the shooting mechanism, we will use numerical simulation with an artificial neural network algorithm, namely the backpropagation Levenberg–Marquardt scheme. The results prove the enormous influence of centrifugation and buoyancy on complex fluid dynamics and heat exchange processes. Some critical parameters that govern the convective heat transport process are the Nusselt number, the Reynolds number, the Grashof number, and the fluid and cone rotational velocities. The research validates the requirement of considering non-Newtonian complexity and viscous dissipation when investigating heat transfer dynamics and fluid flow, facilitating more accurate expectations and improved efficiency in various industrial processes.

Intelligent Predictive Networks for Cattaneo-Christov Heat and Mass Transfer Dissipated Williamson Fluid Through Double Stratification

This study aims to develop an efficient predictive model for Cattaneo-Christov heat and mass transformation of dissipative Williamson fluid with the effects of double stratification (CCHMT-DWF-DS) using the Levenberg-Marquardt Backpropagation (LMA-BP) algorithm. The under-consideration Williamson fluid flow is magneto-hydro-dynamic, incompressible and two-dimensional through a stretching sheet. The mathematical model of nonlinear partial differential equations for physical phenomena is transformed into ordinary differential equations by means of renowned similarity transformations. The solutions of physical problem are computed by bvp4c technique through MATLAB. The LMA-BP is employed to train a backward neural network capable of accurately predicting velocity, temperature, and concentration profiles under various physical conditions such as changes in the Hartmann number , Prandtl number , Schmidt number , Williamson parameter , the relaxation time of temperature , the relaxation time of concentration , temperature stratification , and concentration stratification for generating a variety of graphical outcomes and statistics. This research is significant for its innovative use of the LMA-BP in analyzing the complex dynamics of non-Newtonian fluids specifically the Williamson fluid, alongside the Cattaneo-Christov heat and mass flux model. The obtaining graphs have been discussed in detail. The thermal and solutal relaxation factors reduce heat and mass flow while fluid motion is delayed by the time-dependent parameter and further reduced by the Hartman number. The Cattaneo-Christov heat flux model enhances simulation accuracy by integrating temporal delays in heat transfer, proving beneficial for sophisticated industrial and scientific endeavors related to non-Newtonian fluids. This analysis offers a powerful predictive tool for applications in thermal management, industrial cooling systems, and biomedical fluid dynamics, advancing machine learning in fluid mechanics.

Randomized methods for computing joint eigenvalues, with applications to multiparameter eigenvalue problems and root finding

AbstractIt is well known that a family of $${n}\times {n}$$ n × n commuting matrices can be simultaneously triangularized by a unitary similarity transformation. The diagonal entries of the triangular matrices define the n joint eigenvalues of the family. In this work, we consider the task of numerically computing approximations to such joint eigenvalues for a family of (nearly) commuting matrices. This task arises, for example, in solvers for multiparameter eigenvalue problems and systems of multivariate polynomials, which are our main motivations. We propose and analyze a simple approach that computes eigenvalues as one-sided or two-sided Rayleigh quotients from eigenvectors of a random linear combination of the matrices in the family. We provide some analysis and numerous numerical examples, showing that such randomized approaches can compute semisimple joint eigenvalues accurately and lead to improved performance of existing solvers.