Simultaneous Solution Research Articles

Simultaneous solution of implicitly defined curved, linear Timoshenko beams in two‐dimensional bulk domains

AbstractA novel formulation of curved Timoshenko beams which are defined by all level sets of a scalar function in a two‐dimensional bulk domain is presented, including a corresponding finite element method for the simultaneous solution of these beams. The required geometrical setup and differential operators are introduced and the model is defined in strong form. The weak form for the simultaneous solution involves the co‐area formula. A crucial aspect is how the difference vector, describing the rotational deformation in this model, is discretized wherefore two different approaches are shown in this paper. Higher‐order convergence studies in the residual errors confirm that the proposed method is valid and achieves expected convergence rates.

Mechanistic Simulation of Salt‐Affected Soil‐Plant‐Atmosphere Continuum Dynamics in Seasonally Frozen Regions

AbstractThe salt‐affected Soil‐Plant‐Atmosphere Continuum (SPAC) is a dynamic, interactive system that is particularly complex in seasonally frozen regions where salt transport, precipitation‐dissolution, and soil freeze‐thaw processes play crucial, interrelated roles. Understanding these coupled processes and representing them with mathematical models is critical for effective management of SPAC systems. This study presents a new mechanistic approach and an improved model that integrates a chemical equilibrium module within a mechanistic‐based transport computational module (modified SHAW model). The chemical equilibrium module determines salt precipitation‐dissolution using thermodynamic theory and explains the effects of efflorescence and subflorescence on system dynamics. The model enables simultaneous solutions for heat, water, and salt transport with chemical equilibrium throughout non‐freezing and freezing seasons, as well as plant growth dynamics. Assessment of the model using laboratory experiments and field studies showed good performance, with coefficient of determination values exceeding 0.65 for simulated and measured evaporation rate, leaf area index, soil water content, salt content, and temperature. Furthermore, a comparison between simulation results considering and neglecting the impact of salt precipitation‐dissolution highlights potential inaccuracies in soil heat‐water‐salt dynamics and plant water use resulting from the omission of this process in mechanistic models.

A finite volume–based thermo-fluid-mechanical model of the LPBF process

The multi-physics coupling feature of the laser powder bed fusion (LPBF) process poses great challenges to numerical models regarding computational fidelity and efficiency. This paper proposed a finite volume–based model for predicting integrated thermo-fluid-mechanical behaviors of the LPBF process. The model directly unifies the heat transfer, fluid flow and solid mechanics simulations within a predefined mesh, enabling simultaneous solutions for the fluid domain under Eulerian description and the solid domain under Lagrangian description. Three benchmark tests accounting for individual problems were conducted to validate the model's accuracy and effectiveness. Track-scale LPBF simulations were performed to unravel the intricate interplay between thermal, fluid and mechanical behaviors. The numerical predictions of surface morphologies, molten pool dynamics and melt track dimensions aligned well with the experimental observations. The spatiotemporal evolution of transient thermal stress was accurately captured and the predicted residual stress field showed consistency with nanoindentation measurements. The proposed model was found robust in simultaneously predicting the temperature distribution, melt flow and residual stress evolutions of the LPBF process, and showed strong potential for addressing other similar multi-physics coupling problems.

Consistent solutions for simultaneous dynamic water, solute, stable isotope and radon balances to estimate average exchange fluxes between surface water bodies and groundwater

Many papers show that water, conservative solute, stable isotope and radon balances can be applied to the study of surface water – groundwater interaction. When undertaken simultaneously, such analysis provides an even more powerful method for estimating groundwater inflows and outflows, i.e. the exchange fluxes that for most people are hardest to estimate. The overarching objective of this paper is to provide practitioners with a consistent conceptual and simulation modelling framework with which to achieve a rapid initial understanding of surface water – groundwater interaction, as well as to guide the efficient and targeted acquisition of field data. This paper makes several important contributions. First, after an introduction that explains the complexities of groundwater flow patterns near surface water bodies, a set of general balance equations is developed using consistent terminology and notation. Second, after focusing on a simple conceptual model with steady groundwater inflow I, groundwater outflow O, precipitation P and ever-present evaporation E, analytical solutions are developed for transient and steady state conditions: one water balance solution is found to apply in all situations; solutions for the solute balance equation are developed for 23 different subcases; a transient balance equation for stable isotopes written in terms of 1+δ is found to apply in all situations; and a new transient solution for radon is found in terms of the upper incomplete gamma function. On the path towards developing the isotope balance equation, we present a rigorous approach, based on coupled nonlinear balance equations for abundant and rare isotope pairs (1H and 2H, then 16O and 18O), using isotope ratios and the fractions of each isotope. Third, we describe a Lake Water Balance Calculator (LWBC) written using GoldSim simulation software, a tool to help others to conduct the simultaneous analyses that we promote; we use GoldSim’s numerical methods to solve the general balance equations, we implement the analytical solutions to demonstrate that both GoldSim’s numerical methods and the analytical solutions are correct, and we also show that the 1+δ approximation is equivalent to the rigorous coupled equations, at least for heavy stable isotopes with very low abundance. Fourth, we describe field studies: we provide three examples of applications of LWBC to short-term studies of Perry Lakes East, Lake Jasper and Georgetown Billabong in Australia; we then describe WSIBal, a simulation model based on the same balance equations and describe its application to Lake Jasper over a 19-year period; finally, we describe R-WSIBal, which evolved from WSIBal, and explain its application to 2500 km of the Murray River in Australia.

Fault geometry invariance and dislocation potential in antiplane crustal deformation: physics-informed simultaneous solutions

Earthquake-induced crustal deformation provides valuable insights into the mechanisms of tectonic processes. Dislocation models offer a fundamental framework for comprehending such deformation, and two-dimensional antiplane dislocations are used to describe strike-slip faults. Previous earthquake deformation analyses observed that antiplane dislocations due to uniform fault slips are influenced predominantly by fault tips. Here, we state a general principle of fault geometry invariance in antiplane dislocations and exploit its theoretical consequence to define dislocation potentials that enable a streamlined crustal deformation analysis. To demonstrate the benefits of this theory, we present an analytical example and construct a rapid numerical solver for crustal deformation caused by variable fault slip scenarios using physics-informed neural networks, whose mesh-free property is suitable for modeling dislocation potentials. Fault geometry invariance and the dislocation potential may further the analysis of antiplane crustal deformation, particularly for uncertainty quantification and inversion analysis regarding unknown fault geometries in realistic crustal structures.

About the necessity of legal regulation of the economy of Georgia

The use of mechanisms and tools of legal regulation of inclusive economy in Georgia should significantly reduce the discord between some undesirable trends of globalisation and social justice, and support sustainable development of the Georgian economy. At the current stage of development, the Government of Georgia has to deal with two hardest challenges in economy. These are the adaptation to economic regulations of the EU and the maintenance of the country’s economic security. The simultaneous solution to the problems is possible only if the intercompatibility of social justice and inclusivity of economy is achieved. The current academic work analyses the existing socio-economic challenges in the country, based on the data generated by the National Statistics Office of Georgia. The research shows that despite a number of some positive steps taken in the direction of inclusiveness, a number of significant problems remain in the field of fair distribution of public resources as well as in the rational management of natural and human resources. Only through legal regulation of inclusive economy it is possible to improve the living environment, promote innovative entrepreneurship, enhance social security and medical services, reduce poverty, create jobs, etc. Keywords: inclusive economy, legal regulation, public good, property, employment and unemployment, social security.

Simultaneous high-throughput particle-bacteria separation and solution exchange via in-plane and out-of-plane parallelization of microfluidic centrifuges

Inertial microfluidic devices have gained attention for point-of-need (PoN) sample preparation. Yet, devices capable of simultaneous particle-bacteria solution exchange and separation are low in throughput, hindering their applicability to PoN settings. This paper introduces a microfluidic centrifuge for high-throughput solution exchange and separation of microparticles, addressing the need for processing large sample volumes at elevated flow rates. The device integrates Dean flow recirculation and inertial focusing of microparticles within 24 curved microchannels assembled in a three-layer configuration via in-plane and out-of-plane parallelization. We studied solution exchange and particle migration using singleplex and duplex samples across devices with varying curve numbers (2-curve, 8-curve, and 24-curve). Processing 5 and 10 μm microparticles at flow rates up to 16.8 ml/min achieved a solution exchange efficiency of 96.69%. In singleplex solutions, 10 and 5 μm particles selectively migrated to inner and outer outlets, demonstrating separation efficiencies of 99.7% and 90.3%, respectively. With duplex samples, sample purity was measured to be 93.4% and 98.6% for 10 and 5 μm particles collected from the inner and the outer outlets, respectively. Application of our device in biological assays was shown by performing duplex experiments where 10 μm particles were isolated from Salmonella bacterial suspension with purity of 97.8% while increasing the state-of-the-art particle solution exchange and separation throughput by 16 folds. This parallelization enabled desirable combinations of high throughput, low-cost, and scalability, without compromising efficiency and purity, paving the way for sample preparation at the PoN in the future.

OO Leo: An Active Contact Binary with Possible Solar-like Differential Rotation

With Transiting Exoplanet Survey Satellite (TESS) high-precision photometry and Large Sky Area Multi-object Fiber Spectroscopic Telescope medium-resolution spectra, we present the first light and radial velocity curve analyses for the eclipsing binary OO Leo. The simultaneous solution suggests that OO Leo is a W-subtype contact binary with a relatively low mass ratio (1/q = 0.173) and a moderate degree of contact (f = 28.1%). The asymmetry and continuous changes observed in the TESS light curve were properly modeled by one retrograde cool spot on its secondary surface. A detailed investigation of the Hα line also confirmed that the secondary star had a high level of magnetic activity. The retrograde longitudinal motion of the spot can be explained by a solar-like differential rotation in the secondary component. The orbital period investigation revealed that OO Leo is undergoing a secular decrease and a cyclic variation in its orbital period. The secular decrease may be mainly caused by mass transfer from the more massive secondary star to the less massive primary star. The cyclic period variation can be explained by the light–time effect of an invisible third body or the cyclic magnetic activity of the secondary star. The long-lived spot migration in the longitudinal direction makes OO Leo an excellent target for investigating the differential rotations of contact binaries.

Solving high-dimensional parametric engineering problems for inviscid flow around airfoils based on physics-informed neural networks

Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups, leading to high computational costs when using traditional numerical approaches to solve each setup individually. Recently developed physics-informed neural networks (PINNs) offer a novel approach to solving parametric problems, enabling the simultaneous solution of a series of similar problems. Our previous research combined PINNs with mesh transformation to learn PDE solutions in the computational space, effectively solving inviscid flow around airfoils. In this study, we expand the input dimensions of the model to include shape parameters and flow conditions, forming an input encompassing the complete state-space (i.e., all parameters determining the solution are included in the input). We spend about 18.8 h achieving the continuous solutions in a large state-space in one go, encompassing various subsonic inviscid airfoil flows encountered in engineering, thereby highlighting the model's significant advantages in addressing high-dimensional parametric problems. Once established, the model can efficiently complete airfoil flow simulation and shape inverse design tasks in about 1 s. Furthermore, we introduce a pretraining-finetuning method, enabling the fine-tuning of the model for the task of interest and quickly achieving accuracy comparable to the finite volume method.

Construction of the structure of rural electric networks taking into account the availability of renewable sources of electricity

It is noted that although the share of renewable electricity sources continues to grow and develop rapidly, the industry still faces many challenges, including how to continue to reduce electricity losses and annualized costs, improve operation and maintenance efficiency, maintain grid stability, ensure safety and reliability of the power supply system containing renewable sources of electrical energy. It is shown that an effective solution to these problems is possible only on the basis of the analysis of the prospects for the development of local electric power systems that contain renewable sources of electric energy, the development of technical and organizational support mechanisms that will contribute to the construction of modern system (schematic) solutions. It is proposed to apply the potential surface method for building the optimal structure of the rural electrical network during its design and modernization in the presence of renewable sources of electrical energy, which allows optimizing the structure of the network from the point of view of electrical energy losses and reducing annualized costs. The algorithm for forming the structure of power supply systems is described, which implements the simultaneous solution of the tasks of determining the number of load nodes, distributing electrical receivers between them, determining the design of power sources, taking into account the discreteness of the design of system elements. The results of numerical modeling based on the proposed algorithm are presented on the example of solving the problem of reconstruction of a section of the rural electricity network.

Control Co-Design Studies for a 22 MW Semisubmersible Floating Wind Turbine Platform

We present a control co-design software framework that can be used to optimize floating wind turbines and their controllers. Because this framework has many options for design variables, constraints, and merit figures, along with modeling fidelity levels, we seek to demonstrate best practices for using the tool while designing a floating platform for the new 22 MW offshore reference wind turbine developed within the International Energy Agency Wind Technology Commercialization Programme 55 on Reference Wind Turbines and Farms. During these studies, we evaluate the use of different simulation fidelity levels, the effect of using different load cases for controller tuning, and the difference between sequential and simultaneous control co-design solutions. Based on these efforts, we suggest using an algorithm that performs an initial search of the design space before optimization. We find that solving smaller optimization problems, in a sequential manner, leads to more reliable outcomes in fewer iterations than larger, simultaneous control co-design solutions. However a simultaneous CCD solution produces a platform with a 2% lower mass than the sequential CCD outcome.

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

Modeling gas flow in low-permeability formations: An efficient combination of mixed finite elements and high order time integration schemes

Numerical simulation of gas flow in low permeability formations is a challenging task due to the high nonlinearity induced by (i) the compressibility of the gas, (ii) the Klinkenberg slippage effect and (iii) the Langmuir adsorption of the gas on the pore surface. Because of these nonlinearities, modeling gas flow in low permeability formations requires a great deal of computational effort. In this work, we develop an efficient numerical model using advanced spatial and temporal discretization methods for a simultaneous solution of the coupled equations of gas flow, cubic Peng-Robinson equation of state, slippage effect and Langmuir adsorption. The spatial discretization is performed with the lumped hybrid formulation of the mixed finite element method which is well adapted for fluid flow in heterogeneous porous media. The time integration is performed with high-order methods via the method of lines (MOL) which allows large time steps and efficient solution of the nonlinear system of equations. Numerical experiments, performed for gas extraction in a heterogeneous domain, point out the high efficiency of the new model since it can be until 10 times more efficient than the classical first-order time discretization method. Results of global sensitivity analysis show that the intrinsic gas-phase permeability and the Klinkenberg factor are the most influential parameters controlling the pumping rate in the case of gas extraction in a homogeneous domain.

Enhancing thermal efficiency in MHD kerosene oil-based ternary hybrid nanofluid flow over a stretching sheet with convective boundary conditions

The increasing demand for thermal management due to the high heat density heat exchangers for different technological and industrial processes draw the attention of researchers in heat transfer analysis to investigate the simultaneous solution to this problem. Keeping this in mind, the current work addressed the utilization of ternary hybrid nanofluid, a mixture of graphene oxide with silver and copper, to examine the heat and mass transfer enhancement of MHD Maxwell fluid. In the current model, the author discussed heat and mass transfer analysis of Maxwell MHD ternary hybrid nanofluid flow across a porous medium over an extending sheet. The energy and concentration equations are expressed to include the effects of Brownian motion and thermophoretic diffusion. Additionally, the effects of thermal radiation, activation energy, chemical reactions, and convective boundary conditions are considered. The similarity transformations are used to convert the nonlinear PDEs into ODEs. The impact of embedded factors on velocity, temperature, and concentration profiles is perceived graphically and mathematically by using the HAM technique. The convergence of computed solutions is ensured by h-curves. The significant outcomes from the analysis expressed that the flow distribution increases with slip and suction/injection factors. The concentration of the ternary hybrid nanofluid increases with an increase in thermophoretic diffusion (0.1–0.5), thermal biot number, and solutal biot number (0.1–0.5), however, a declining behavior is perceived with rising quantity of Schmidt number (0.6–0.8) and Brownian motion (0.1–0.5) parameters. Nusselt number shows a dominant behaviour with a higher magnetic factor. Similarly, the skin friction increases with an increase in thermal biot number and thermophoresis factor. It is revealed that the skin friction along x− direction increases from (0.78138, 0.833702, 0.897022, and 0.972526) for ternary hybrid nanofluid. Nusselt number increases from 2 to 5% (0.208936, 0.214288, 0.219799, 0.22555) when the volume fraction varies from 0.01 to 0.04 respectively.

Metal doped TiO2 decorated carbon nanostructured materials as an emerging photocatalysts for solar fuels production

The concept of photocatalytic CO2 and H2O conversion to solar fuels and value-added products provides simultaneous solution for increased energy demands and environmental problems. However, the lack of efficient photocatalysts restrains the large-scale development of photocatalytic technology. In the present study, noble (Pt and Au) and transition metal (Ni) doped nanoflakes assembled on TiO2@carbon microrods with high surface area and rutile crystal structure is prepared via fast, versatile solvothermal method. The photocatalytic performance of the prepared nanocomposites was evaluated in two photocatalytic systems: CO2 reduction and hydrogen production via photoreforming. Pt-doped catalyst showed enhanced hydrogen production efficiency and increased CH4 selectivity, while Ni-doped catalyst exhibited remarkable CO2 reduction activity with higher selectivity towards CO. The mechanism of Pt-promoted CH4 formation and Ni- and Au-promoted CO formation was thoroughly discussed regarding kinetic and thermodynamic parameters.

Solar-Driven Multistage Device Integrating Dropwise Condensation and Guided Water Transport for Efficient Freshwater and Salt Collection.

Interfacial solar vapor generation (ISVG) is an emerging technology to alleviate the global freshwater crisis. However, high-cost, low freshwater collection rate, and salt-blockage issues significantly hinder the practical application of solar-driven desalination devices based on ISVG. Herein, with a low-cost copper plate (CP), nonwoven fabric (NWF), and insulating ethylene-vinyl acetate foam (EVA foam), a multistage device is elaborately fabricated for highly efficient simultaneous freshwater and salt collection. In the designed solar-driven device, a superhydrophobic copper plate (SH-CP) serves as the condensation layer, facilitating rapid mass and heat transfer through dropwise condensation. Moreover, the hydrophilic NWF is designed with rational hydrophobic zones and specific high-salinity solution outlets (Design-NWF) to act as the water evaporation layer and facilitate directional salt collection. As a result, the multistage evaporator with eight stages exhibits a high water collection rate of 2.25 kg m-2 h-1 under 1 sun irradiation. In addition, the desalination device based on the eight-stage evaporator obtains a water collection rate of 13.44 kg m-2 and a salt collection rate of 1.77 kg m-2 per day under natural irradiation. More importantly, it can maintain a steady production for 15 days without obvious performance decay. This bifunctional multistage device provides a feasible and efficient approach for simultaneous desalination and solute collection.

Comparative analysis of Benchmark and Aeon Blue Technologies for sustainable eFuel production: Integrating Direct Air Capture and Green Hydrogen approaches

Renewable Fuels of Non-Biological Origin (RFNBOs, a.ka. “eFuels”) are drop-in replacements for fossil fuels in the “hard-to-abate” sectors, and utilise existing distribution and storage infrastructure, but suffer from low synthetic efficiency. In particular, the low efficiency and high energy consumption of hydrogen synthesis by freshwater electrolysis remains a problem to be addressed. In the current study, we explore the potential of saltwater electrolysis (chloralkali) for the synthesis of eFuels generally, and specifically eMethanol. The study explores the use of chlorinated water in carbonate-loop pH-swing “cold capture” of carbon dioxide, and the resulting synergetic integration of the chloralkali process in eFuel syntheses. Doing so eliminates the high energy consumption of the calciner and the slaker of the benchmarked carbonate-loop thermal-swing method. It is replaced with a spontaneous chemical process in which chlorine is neutralized in the presence of carbonates. This allows the simultaneous solution of “The Chlorine Problem” of saltwater electrolysis, and a lower overall energy consumption of direct air capture when combined with green hydrogen synthesis. The only limitation on the comparison is that a large amount of carbon dioxide is over-captured when using chloralkali. That is, the ratio of hydrogen generated to carbon dioxide captured is fixed by the stoichiometry of chloralkali and not that of the eFuel. This results in an excess of carbon captured and thus a carbon-negative eFuel. We examine one configuration of secondary revenue and use it to inform the marginal cost of CO2 capture. In the system proposed by Aeon Blue Technologies (ABT), carbon dioxide is absorbed into caustic according to the standard method. Hydrogen gas is produced in a standard chloralkali electrolyzer, along with caustic for the contactor, and chlorine. Water oxidation by chlorine gives the strong acid, hydrochloric acid, and the weak acid, hypochlorous acid, which react directly with wet carbonate to release CO2. H2 and CO2 react in a methanol reactor to produce eFuel. H2 is the limiting reagent for eFuel synthesis, giving an excess of cold captured CO2. Thus, the current study underscores significant advancements in renewable fuel synthesis, particularly eMethanol, and evaluates the carbon capture and energy efficiency of a novel method. The simulation indicates that the marginal energy cost for a tonne of CO2 is ∼ 184kWh. This gives ∼ 76 % theoretical carbon capture efficiency and an overall process efficiency of 79.5 % (approximately a threefold improvement over the benchmark). The authors are unaware of a comparable method. The overall system yields a tonne of carbon-neutral e-methanol (eMeOH) while capturing an additional 3 tonnes of carbon dioxide, which means the modelled process captures over 300 % more carbon dioxide than is released upon combustion of the eFuel. In summary, this research contributes valuable insights into carbon-negative eFuel production, representing a significant scientific step in sustainable fuel production.

ОСОБЛИВОСТІ ПРОЄКТУВАННЯ МЕХАНІЗАЦІЇ КРИЛА ЛІТАКІВ ТРАНСПОРТНОЇ КАТЕГОРІЇ

The paper analyses the methods of designing wing mechanisation for transport category aircraft. The wing layout with the placement of wing mechanisation means on the leading and trailing edges of the wing is analysed. Specific requirements for wing mechanisation units are considered. The analysis takes into account the requirements of aircraft operation, which provide easy access to inspect the mechanisation units and their attachment mechanisms. The need for constant monitoring of the synchronous operation of all mechanisation sections and ensuring their smooth movement is emphasised. The design of any type of mechanisation means involves the simultaneous solution of a number of development tasks: kinematic scheme, installation and control system, support structure and the device itself. In most cases, the drive mechanisms are also developed. The design of a new aircraft is a multi-stage iterative process that includes external design, development of a technical proposal, preliminary design, detailed design, production of prototypes, ground and flight tests, which determine the actual characteristics of the aircraft and the degree of its compliance with the technical specifications. Consider the advantages created by wing mechanisation equipment. The mechanisation of the AN-140 is considered as a representative of aircraft whose wings have trailing edge mechanisation but no leading edge mechanisation. The mechanisation of the AN-74 is also considered as a representative of aircraft that use two- or three-slotted retractable flaps, winglets or nose shields of large curvature over the entire wing span. The design technologies in integrated computer information systems are characterised, which allow to build a single process of computer modelling and engineering analysis and to conduct multivariate studies to select optimal design solutions in a sufficiently short time. A block diagram of the process of detailed design of flaps is proposed.

A numerical study of MHD nonlinear mixed convection flow over a nonlinear vertical stretching sheet with the buoyancy and suction/injection effects

The current research has a primary focus on characterizing buoyancy-driven nonlinear mixed convection. This phenomenon is studied within the context of an MHD Newtonian flow over a vertically stretching sheet with nonlinear characteristics. Flow patterns resembling those studied in this context have practical applications in various industrial sectors. Such flow patterns have practical applications in several industrial sectors, including the article and pulp industry, polymer manufacturing, electronic device cooling, solar energy collection, gas turbine plants, and nuclear power generation. The governing partial differential equations (PDEs) for nonlinear mixed convection are transformed into higher-order nonlinear ordinary differential equations (ODEs) through appropriate transformations, and these transformed ODEs are subsequently solved numerically. The software MATHEMATICA is used to solve the boundary layer flow equations, employing the semi-analytical Galerkin weighted residual method (GWRM). This approach yielded simultaneous solutions for both cases suction and injection. For both the suction and injection situations, graphical results, such as velocity, concentration, and temperature profiles are included. An augmentation in the nonlinear stretching parameter results in a reduction in velocity near the surface of the sheet. Conversely, away from the sheet, velocity increases. Moreover, an increase in nonlinear stretching parameters corresponds to higher values for both temperature and concentration. An increase in the suction/injection parameter causes a decrease in the velocity, temperature, and concentration fields. In the scenario of assisting flow, an increase in the thermal buoyancy parameter leads to higher velocity but lower temperature. Conversely, in the case of opposing flow, an increase in the thermal buoyancy parameter results in higher values for both velocity and temperature. Furthermore, a numerical examination is conducted to analyze the values of skin friction, Sherwood number, and Nusselt number.

Investigating the entry of symmetric/asymmetric elastic wedge into water

Understanding the impact of fluid–structure interaction during the entry of a marine vessel into water is crucial for its design. While numerous models have been proposed to investigate the penetration of symmetric elastic wedges into water, in this study, we propose a numerical model that combines the fully nonlinear boundary element method with a mode superposition method to analyze the penetration of symmetric and asymmetric elastic wedges into water. We derive the boundary conditions of the acceleration potential within the flow field for the problem of fluid–structure interaction and use auxiliary functions to decompose the acceleration potential and extract the instantaneous added mass. Following this, the differential equations of the modes of rigid motion and elastic deformation of the body are established and solved. This approach enables the simultaneous solution of the motion and vibrations of the wedge as well as the hydrodynamic pressure. The proposed model also accounts for flow separation while the wedge is submerged, thereby prolonging the simulation. We confirmed the validity of the model through comprehensive examinations based on semi-analytical, computational, and experimental data on the problem of the entry of a symmetric body into water. We then extended our study to encompass the free-falling entry of an asymmetric elastic wedge into water. The results revealed notable discrepancies in the evolution of deformation and jet flow between the right and left boundaries during the entry of the wedge into water.