Fluid Flow Research Articles

Double‐sided queues and their applications to vaccine inventory management

AbstractWe consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.

Effect of oscillation parameters on weld surface morphology during laser beam oscillation welding of stainless steel

During laser beam oscillation welding (LBOW), the weld surface morphology is important because it influences the appearance of the workpiece and reflects the welding quality, and the oscillation parameters have an important effect on the weld surface morphology. Therefore, a combination of experimental research and numerical simulation is conducted to investigate the influence of oscillation parameters, including oscillation mode, oscillation frequency, and oscillation amplitude, on the weld surface morphology during LBOW. The calculation encompasses the oscillation trajectory, combined velocity, and energy distribution on the weld surface, varying with different oscillation parameters. A three-dimensional heat transfer and fluid flow model with the oscillation heat source is established to simulate the temperature and fluid flow behavior inside the weld pool. When the heat input is constant, an increase in oscillation frequency results in a decrease in weld width and a smoother surface. As the oscillation frequency increases, the weld width decreases, the surface becomes smooth, and the energy distribution on the weld surface becomes more uniform. The fact that the period of the surface pattern is almost equal to the oscillation period indicates a direct correlation between the formation of weld surface pattern and the oscillation trajectory in LBOW. Among all the oscillation modes, the minimum combined velocity which is equal to the welding velocity occurs at the inflection point in the linear oscillation mode, and the variation in combined velocity of the laser beam is the smallest for circular oscillation mode. The surface pattern is primarily influenced by the oscillation trajectory and fluid flow within the weld pool. Under conditions of lower oscillation frequencies or larger oscillation amplitudes, the fluid flow is weaker, and the surface pattern is primarily influenced by the oscillation trajectory. Conversely, when the fluid flow is stronger, the surface pattern is mainly determined by the fluid flow within the weld pool under conditions of higher oscillation frequencies or smaller oscillation amplitudes. This study explains the formation mechanisms of weld surface patterns and provides insights and guidance for selecting optimal oscillation parameters in LBOW.

Machine learning in viscoelastic fluids via energy-based kernel embedding

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce energy-compatible families of kernel functions corresponding to a given viscoelastic stress model. Each kernel implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) in which distances and angles are computed and whose squared norm equals the total mechanical energy. Additionally, we present a solution to the preimage problem for these kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of energy-compatible kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using energy-compatible kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.

Investigation of Third-Grade fluid flow in an inclined Microchannel: Utilizing the Hermite wavelet technique for second law analysis

Microfluidics serves as an interdisciplinary bridge between thermal and engineering fields, offering flexible solutions for addressing heat transport obstacles across diverse sectors. This study explores entropy production in the flow of a third-grade fluid through an inclined microchannel, considering radiation and convective heating effects. The analysis includes various factors such as viscous dissipation, natural convection, Joule heating, magnetic fields, and a uniform heat source/sink. The aim is to assess the energy efficiency of the system by minimizing entropy generation. To achieve this, governing equations are transformed into dimensionless forms using non-dimensional parameters. These equations are then solved using the Hermite wavelet method, a novel approach in this field. The impact of the Biot number on temperature exhibits a dual nature: temperature increases towards the upper plate of the channel while decreasing towards the lower plate. Similarly, entropy generation displays a dual behavior for higher values of Qt and Re, decreasing at the lower plate and increasing at the upper plate. This research offers valuable insights for optimizing energy efficiency in various applications, including pumps, heat exchangers, and energy systems, with potential applications in electronics cooling and renewable energy collection.

Novel hybrid BTMS by considering safety and driving cycle under extreme fast charge/discharge rates

A battery thermal management system integrating phase change material and mini-channels, with a focus on safety and economic considerations, is proposed to enhance thermal performance across various working conditions, safety scenarios, and realistic driving cycles while minimizing energy consumption. A battery thermal model and PCM simulation model were developed and validated using experimental data. Numerical analyses were conducted to compare the combination of PCM and liquid cooling (hybrid cooling) with fully liquid cooling under different charge/discharge rates and realistic driving cycles, evaluating their safety characteristics, power consumption, and thermal efficiency. The results demonstrated that the hybrid cooling approach can effectively maintain both the maximum temperature and the temperature difference within a desirable range, even when the inlet velocity is reduced from 0.12 to 0.05 m/s compared to liquid cooling. Additionally, the hybrid BTMS provides better working conditions for the battery pack, requiring only 4 × 10−5 W of pumping power compared to 16 × 10−5 W in the liquid cooling system. This underscores the capability of the designed BTMS to cool high-capacity battery packs with significantly lower fluid flow rates. Furthermore, the performance of the proposed cooling system was examined in the event of liquid channel failure, with results showing that the hybrid BTMS can successfully maintain the battery's maximum temperature within an allowable range during fast charge/discharge processes. Lastly, evaluations under realistic driving conditions revealed the superiority of hybrid cooling in reducing peak temperatures and minimizing battery temperature variation.

Investigation on the oblique water entry of the flared cavity

An experimental study of the oblique water entry of a flared cavity is reported in this paper. A numerical model is established that takes gas compressibility into account. This model effectively captures the additional flow phenomena that occur due to gas expansion and contraction within the cavity. There is a significant fluctuation phenomenon during the oblique water entry of the flared cavity, which is reflected not only in the movement of the water entry bubble but also in the slamming pressure. This fluctuation phenomenon is caused by the bottom cavity of the flared cavity, which adds the additional processes of external fluid inflow and internal fluid outflow compared with the closed-bottom structure, leading to additional flow due to conventional flow separation. When the external liquid flows into the cavity, the additional flow reduces the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to contract. At the same time, the external liquid inflow causes the gas in the cavity to compress and the slamming pressure to increase. When the liquid flows out of the cavity, the additional flow increases the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to expand. Meanwhile, the internal fluid outflow causes the gas in the cavity to expand and the slamming pressure to decrease.

A computational investigation for heat and fluid transport with electro-osmosis phenomenon in a scraped surface heat exchanger

Scraped surface heat exchangers (SSHEs) have prominently shown their eminence in various food, chemical and in pharmaceutical industries when the regular processing of fluids and pertinent materials is encountered. The heat transfer analysis of Williamson fluid flow with electro osmotic effects in a narrow-gap SSHE is designed by implementing constant temperature difference between the gaps of the rotor and the stator. A fluid model is established by using lubrication approximation theory and Debye-Huckel simplifications. The computational solution is elaborated by implementing renowned BVP4C technique in MATLAB. Exact solution of Poisson-Boltzmann equation for different scenarios of SSHE is gathered, whereas solution for velocity, stream functions and temperature in various parts of SSHE are explored computationally. Impact of various crucial physical flow parameters like, Weissenberg number, mobility of the medium number, electro osmotic parameter on the velocity profile, stream function, temperature profile, and pressure gradient has been explored graphically. The numerical solution is compared with artificial neural network (ANN) and an absolute alignment of BVP4C solution is observed with ANN solution. It is reported that fluid flow is lifted with enhancing the viscoelastic behavior and exhibits dual behavior for electroosmosis phenomenon and mobility of medium parameter. Also, it is seen that temperature of the fluid is significantly declines with Weissenberg number and is surges with enhancing mobility of medium and Brinkman number. By increasing the Brinkman number conduction phenomenon is slow down and heat produced due to viscous dissipation, raises the temperature of the fluid. The viscoelastic effect could be of enormous significance in applications, like Polymer processing in certain heat exchangers, and in mixing and blending foodstuffs etc.

Physical field of dual-frequency ultrasonic vibration and its effect on solidification behavior of MgZnY alloy

A three-dimensional model was established for coupled simulation of the physical field in a liquid subjected to dual-frequency ultrasonic vibration. The effect of sonotrode position, tip shape, and vessel on the distributions of acoustic pressure and acoustic streaming were clarified. The influence of physical fields on the solidification behavior of Mg alloy was investigated. The simulation results show that the interaction between the two ultrasounds was weakened as the sonotrode spacing increased, and the radiating angle had little effect on the acoustic pressure distribution. The volume mean pressure in the liquid radiated by the plane tip was the smallest, but with the greatest acoustic streaming intensity. In contrast, the spherical tip radiated the highest volume mean pressure in the liquid medium, but the acoustic streaming was severely suppressed. Attributed to the smooth spherical surface that facilitated fluid flow, high flow velocity could be achieved using a round-bottomed crucible without severe acoustic pressure attenuation. The experimental results show that cavitation and acoustic flow caused the coarse dendrites to turn into fine isometric crystals. The acoustic flow accelerated the melt flow and alleviated the segregation and precipitation of Zn elements, leading to a decrease in the content and size of the second phase in the billet.

Investigation on corrosion behavior of the atmospheric pressure air cooler tubes caused by multiphase flow

Air coolers are important heat exchangers and widely used in the petroleum and petrochemical industries. The leakage of air cooler tubes due to corrosion frequently happened and seriously affected normal production process leading to unplanned shutdowns, so the corrosion behavior of the air cooler tubes needed to be clarified urgently. In this work, the corrosion behavior of the atmospheric pressure air cooler tubes was investigated by computational fluid dynamics (CFD) simulation and experimental study. It was depicted that the gas–liquid erosion corrosion was the main reason for the leakage of air cooler tubes and the collision angle between the fluid flow and the wall at the inlet of the tubes was the key factor that affects the corrosion behavior of the multiphase flow inside the air cooler tubes. The corrosion was most severe when the collision angle is 30 degree. With the purpose to migrate corrosion, the improvement measure was proposed from the perspective of collision angle elimination. The porous plates were installed and the lifetime of the air cooler tubes was extended to 4 times that of the original conditions, which indicated the installation of porous plates is an effective measure to reduce corrosion.

The effect of well temperature on the microstructure and the mechanical performance of bismuth-based plugs in well plugging and abandonment operations

Bismuth-tin (BiSn) alloys are considered promising candidates as potential alternatives to cement for well plugging and abandonment (P&A) applications to prevent any uncontrolled flow of deep reservoir fluids to the surface. As the temperature in the well varies with depth, the final microstructure of the BiSn alloy after its solidification might be influenced, and consequently the mechanical performance of the alloy will also be affected. The aim of this study is to evaluate the microstructural evolution of the BiSn alloy after solidification, at temperatures between 20 °C and 90 °C, to reflect in situ conditions from approximately 800m to 3 km depth. Microstructural characterization was carried out by using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The microstructural analysis revealed that the plug subjected to the lower temperature resulted in finer microstructure, whereas the grain size of the material was increased at higher temperatures. Additionally, the theoretical lever rule was employed to validate the microstructural findings. The observed microstructures were also correlated with tensile tests, which showed that the plug at 20 oC had a yield strength of 67,25 MPa, whereas the yield strength of the plug at 90 oC was only 41,64 MPa. In addition, hydraulic push-out tests further confirmed that lower testing temperatures correlate with higher pressure tolerance of the plug. The plug at 20 oC could withstand 113,5 bar, compared to the plugs at 60 oC and 90 oC which could withstand 90,4 and 50,9 bar, respectively. From all the experimental tests conducted, the outcome was that the lower temperature of 20 oC resulted in a material with a finer microstructure, which plays an important role in enhancing the mechanical properties of the bismuth-based plug. This study aims to advance the understanding of BiSn alloy performance in plug and abandonment (P&A) operations, thereby supporting the industry's efforts to qualify BiSn alloys as effective well-barrier materials.

Effects of different momentum ratios and Reynolds number in a T-junction with an upstream elbow

This study focuses on analysing thermal mixing in T-junctions with varying momentum and Reynolds number ratios, utilizing computational fluid dynamics (CFD) simulations. The T-junction is a critical component of the primary nuclear thermal–hydraulic circuit within a pressurized water-cooled reactor (PWR). The T-junction connects the pressurizer (PRZ) with the steam generator (SG) and the reactor pressure vessel (RPV). Water from the PRZ and the SG are at different temperatures and incomplete thermal mixing occurs when these two fluid streams meet at the T-junction. This incomplete thermal mixing can induce thermal stratification of the water within the T-junction as well as thermal striping phenomena. Thermal striping phenomena can lead to fluctuations of the temperature at the inner pipe wall of the T-junction. Thermal stratification and thermal striping phenomena can induce thermo-mechanical fatigue and eventual pipe failure which can affect the safety of the reactor. Therefore, a high-fidelity, mechanistic understanding of the turbulent thermo-fluid mixing within T-junctions of PWRs might lead to improvements in component reliability and safety within nuclear power plants (NPPs).The primary aim of the research, presented in this paper, is to understand and quantify the effect of variations in the momentum ratio on the turbulent fluid flow within T-junctions. This is achieved by either varying the branch pipe diameter while keeping the inlet velocity constant (part one) or by adjusting the branch pipe inlet velocity while maintaining a constant diameter (part two). Despite the different variations in momentum ratios, the specific momentum ratios under consideration in both parts of the study remain consistent (namely 98 and 66.4). It is also noteworthy that the momentum ratios considered in the paper can be classified as wall-jet and impinging-jet, according to the definition in (Hosseini, Yuki, & Hashizume, 2008). It should be noted that the momentum ratio is manipulated by adjusting the flow parameters, leading to variations in the Reynolds number ratio between the main pipe inlet and the upstream branch pipe at the T-junction. The turbulent flows in the cases that are considered are simulated using the Improved delayed detached eddy simulation (IDDES-SST) model. The numerical results from these simulations indicate, for the considered momentum ratios, that maintaining the same momentum ratio does not produce similar mean flow behaviour and turbulent quantities of interest (QoI). For instance, the size of the flow recirculation zone is more likely linked to the diameter of the branch pipe. Moreover, the turbulent QoI and temperature fluctuations at the determined locations are likely affected by the changed flow recirculation zone as well as the Reynolds number of the branch pipe flow.

Effects of baffles and springs in shell and multi-tube heat exchangers: Comparative approach

Shell and multi-tube heat exchangers (SMTHX) are widely used in various industries such as power generation, chemical processing, and refrigeration due to their high efficiency and flexibility. Improving heat transfer within an SMTHX is critical for enhancing overall performance and efficiency. This study investigates the comparative effectiveness of using baffles versus spring wires to enhance heat transfer in SMTHXs. Both experimental and numerical analyses were conducted over a Reynolds number range of 8500–12500, focusing on key parameters such as the Nusselt number, pressure drop, and exergy efficiency. The experiments were performed with a variable cold water flow rate on the shell side and a constant flow rate on the tube side. The numerical model was validated against experimental results. The findings reveal that the Nusselt number increases to 62 with baffles and to 65.5 with spring inserts, representing improvements of 1.54 and 1.61 times, respectively, compared to a plain tube under identical conditions. While the pressure drop for baffles is significantly higher than for spring inserts, the springs show a pressure drop that is 87 % of that observed with baffles. Additionally, exergy efficiency is superior with spring inserts. These results demonstrate that spring inserts are more effective than segmental baffles in enhancing heat transfer in SMTHXs. The study provides valuable insights into the mechanisms of heat and fluid flow, supported by visualizations of velocity, temperature, and pressure contours and streamlines.

Entropy generation in newtonian vs non-newtonian nanofluid flow under vibration

Numerical investigation into the effects of vibration on heat transfer and entropy generation in Newtonian and Non-Newtonian nanofluid flows through pipes reveals enhanced heat transfer via intensified fluid agitation and improved particle dispersion. Thermal entropy generation analysis shows reduced irreversibility in vibrated flow, indicating improved flow mixing. Vibration enhances heat transfer by intensifying fluid agitation and promoting particle dispersion near the wall, resulting in a significantly more uniform temperature distribution along the pipe, approximately 100 times more than steady-state flow. This study underscores vibration’s potential to optimize heat transfer and reduce entropy generation in nanofluid systems, emphasizing velocity and rheological impacts. Comparison of vibrated flow to steady-state flow for Newtonian and non-Newtonian fluids reveals significant improvements under vibration, particularly at lower Reynolds numbers where non-Newtonian fluids exhibit pronounced effects. Future research directions include exploring thermal radiation’s impact on entropy generation, analyzing different nanofluid compositions, and investigating varied boundary conditions and geometries to advance understanding in this field. This study provides valuable insights into the complex interplay among vibration, fluid dynamics, and heat transfer in nanofluid flows. Its findings have practical implications for optimizing thermal management systems in diverse engineering applications.

Implementing microfluidic flow device model in utilizing dural substitutes as pulp capping materials for vital pulp therapy

Vital pulp therapy (VPT) has gained prominence with the increasing trends towards conservative dental treatment with specific indications for preserving tooth vitality by selectively removing the inflamed tissue instead of the entire dental pulp. Although VPT has shown high success rates in long-term follow-up, adverse effects have been reported due to the calcification of tooth canals by mineral trioxide aggregates, which are commonly used in VPT. Canal calcification poses challenges for accessing instruments during retreatment procedures. To address this issue, this study evaluated the mechanical properties of dural substitute intended to alleviate intra-pulp pressure caused by inflammation, along with assessing the biological responses of human dental pulp stem cells (hDPSC) and human umbilical vein endothelial cells (HUVEC), both of which play crucial roles in dental pulp. The study examined the application of dural substitutes as pulp capping materials, replacing mineral trioxide aggregate (MTA). This assessment was conducted using a microfluidic flow device model that replicated the blood flow environment within the dental pulp. Computational fluid dynamics simulations were employed to ensure that the fluid flow velocity within the microfluidic flow device matched the actual blood flow velocity within the dental pulp. Furthermore, the dural substitutes (Biodesign; BD and Neuro-Patch; NP) exhibited resistance to penetration by 2-hydroxypropyl methacrylate (HEMA) released from the upper restorative materials and bonding agents. Finally, while MTA increased the expression of angiogenesis-related and hard tissue-related genes in HUVEC and hDPSCS, respectively, BD and NP did not alter gene expression and preserved the original characteristics of both cell types. Hence, dural substitutes have emerged as promising alternatives for VPT owing to their resistance to HEMA penetration and the maintenance of stemness. Moreover, the microfluidic flow device model closely replicated the cellular responses observed in live pulp chambers, thereby indicating its potential use as an in vivo testing platform.

Techno-economic analysis and optimization of a binary geothermal combined district heat and power plant for Puga Valley, India

This article investigates the energy, exergy, and economic performance of a Puga Valley-specific binary geothermal combined district heat and power plant, taking into account geotechnical data and related cost functions. The power plant uses an organic Rankine cycle (ORC) with R123 as the working fluid, utilizing waste heat for district heating to enhance efficiency. Variations in operating and design parameters such as geothermal fluid flow rate, temperature, and ORC temperature of the evaporator and condenser are found to have significant effects on the overall performance of the system and cost rate. A multi-objective grey wolf optimization technique based on artificial neural networks has been used to determine the ideal values of the above-mentioned parameters. The optimization study revealed a Pareto optimal curve with overall exergy efficiency and total cost rate as objective functions from which the optimal point was identified using the technique for order preference by similarity to the ideal solution (TOPSIS) method. While operating the proposed CHP plant at TOPSIS optimal point, the plant delivers a net electrical output of 1.08 MW alongside 4.19 MW of thermal energy, resulting in a total cost rate of 33.84 USD/h, with energy and exergy efficiencies peaking at 32.26 % and 36.8 %, respectively. The exergy analysis at the optimal point also revealed a notable reduction of 550 kW in the total exergy destruction rate compared with the base-case scenario. Furthermore, the design requirements of a 5 MW net power output CHP plant for effective recovery of the Puga Valley geothermal resource are discussed.

Controlling convective heat transfer of shear thinning fluid in a triangular enclosure with different obstacle positions

The free convection of a non-Newtonian fluid in an equilateral triangular cavity containing a triangle obstruction in various positions is investigated numerically in this paper. The research is carried out using the finite element method. The sloped side walls are adiabatic, while the bottom is kept heated. At the obstacle, three positions are examined. The effects of different power law indexes on free convection have been investigated. The temperature field, fluid flow, and heat transfer are all highly influenced by the obstacle's location, Rayleigh number, and power law index. The resulting outcomes are confirmed using existing results in the literature and verified using a grid sensitivity analysis. A comparison of the current results to those found in the literature demonstrates the study's dependability and trustworthiness.

Designing turbulence with entangled vortices

Matter entanglement is a common chaotic structure found in both quantum and classical systems. For classical turbulence, viscous vortices are like sinews in fluid flows, storing and dissipating energy and accommodating strain and stress throughout a complex vortex network. However, to explain how the statistical properties of turbulence arise from elemental vortical structures remains challenging. Here, we use the quantum vortex tangle as a skeleton to generate an instantaneous classical turbulent field with intertwined vortex tubes. Combining the quantum skeleton and tunable vortex thickness makes the synthetic turbulence satisfy key statistical laws, offering valuable insights for elucidating energy cascade and extreme events. By manipulating the elemental structures, we customize turbulence with desired statistical features. This bottom-up approach of designing turbulence provides a testbed for analyzing and modeling turbulence.

The influence of temperature-dependent variable viscosity and suction on a natural convective heat transfer in magneto generated plume

The study provides novel and valuable insights into the behavior of fluid flow and heat transfer in a generated plume under the influence of an aligned magnetic field, which is a complex and less-explored area in fluid dynamics. Incorporating variable viscosity and suction effects adds to the realism and applicability of the model, as it accounts for more realistic conditions where fluid properties change with temperature and external forces influence the flow. A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow dynamics. Subsequently, a numerical solution is derived with stream function formulation for the system of coupled partial differential equations, which transmuted it into ordinary differential equations. To achieve this, the numerical properties of the problem are established through the utilization of a Shooting method in tandem with the MATLAB tool bvp4c. The graphical representations of both missing and specified boundary conditions, analyzes the influences of the viscosity parameter ε, suction parameter ξ, magnetic force parameter S, Prandtl number Pr and magnetic Prandtl number γ. The impact of these parameters on the heat transfer and fluid flow is given in detail. Inclusion of suction velocity counteracted the effects of temperature-dependent viscosity. The velocity f′, current density ϕ″, temperature θ, skin friction f″ and magnetic flux ϕ′ depicted an enhanced behavior while heat transfer rate θ′ dropped with an increment in viscosity parameter ε. However, for an increasing suction parameter ξ, the reverse trend of these properties is observed as compared to the viscosity parameter ε. The inclusion of suction counteracted to the effects of variable viscosity. Understanding how heat plumes behave under magnetic fields the study aims to provide insights that can be applied to real-world scenarios, such as improving cooling systems in industrial applications, enhancing environmental safety measures, and optimizing biomedical engineering processes.

Energy-stable auxiliary variable viscosity splitting (AVVS) method for the incompressible Navier–Stokes equations and turbidity current system

In this work, we develop a novel energy-stable linear approach, which we name as auxiliary variable viscosity splitting (AVVS) method, to efficiently solve the incompressible fluid flows. Different from the projection-type methods with pressure correction, the AVVS method adopts the viscosity splitting strategy to split the original momentum equation into an intermediate momentum equation without divergence-free constraint and an advection-free momentum equation. A time-dependent auxiliary variable which has exact value 1 is introduced to construct a supplementary equation. The new model not only inherits the same dynamics of original incompressible Navier–Stokes equations, but also facilitates us to design linearly decoupled and energy-stable time-marching scheme. Comparing with the conventional projection-type schemes, the present method leads to an energy dissipation law with respect to kinetic energy instead of a modified energy including velocity and pressure gradient. In each time step, only two parabolic equations with constant coefficients and one Poisson equation need to be solved. Therefore, the numerical implementation is highly efficient. Moreover, the proposed AVVS method can be directly extended to construct linear, decoupled, and energy-stable scheme for the turbidity current system with slight modifications on the right-hand side of supplementary equation. Extensive numerical experiments are implemented to validate the accuracy, energy stability, and capability in complex fluid simulations.

Analysis of Entropy Generation via Non-Similar Numerical Approach for Magnetohydrodynamics Casson Fluid Flow with Joule Heating.

This analysis emphasizes the significance of radiation and chemical reaction effects on the boundary layer flow (BLF) of Casson liquid over a linearly elongating surface, as well as the properties of momentum, entropy production, species, and thermal dispersion. The mass diffusion coefficient and temperature-dependent models of thermal conductivity and species are used to provide thermal transportation. Nonlinear partial differential equations (NPDEs) that go against the conservation laws of mass, momentum, heat, and species transportation are the form arising problems take on. A set of coupled dimensionless partial differential equations (PDEs) are obtained from a set of convective differential equations by applying the proper non-similar transformations. Local non-similarity approaches provide an analytical approximation of the dimensionless non-similar system up to two degrees of truncations. The built-in Matlab (Version: 7.10.0.499 (R2010a)) solver bvp4c is used to perform numerical simulations of the local non-similar (LNS) truncations.