Velocity Equation Research Articles

Foreshock Ion Motion Across Discontinuities: Formation of Foreshock Transients

AbstractIn the ion foreshock, hot flow anomalies (HFAs) and foreshock bubbles (FBs) are two types of foreshock transients that have the strongest fluctuations, which can disturb the magnetosphere‐ionosphere system and increase shock acceleration efficiency. They form due to interaction between the foreshock ions and solar wind discontinuities: the direction of the foreshock ion‐driven current and whether it decreases or increases the magnetic field strength behind the discontinuity determine whether the transient's formation can be promoted or suppressed. Thus, to predict the HFA and FB formation and forecast their space weather effects, it is necessary to predict the foreshock ion‐driven current direction. In this study, we derive analytical equations of foreshock ion velocities within discontinuities to estimate foreshock ion‐driven current direction, which provides a quantitative criterion of HFA and FB formation. To validate the criterion, we use Acceleration Reconnection Turbulence & Electrodynamics of Moon's Interaction with the Sun to observe pristine solar wind discontinuities and calculate discontinuity parameters. We use Magnetospheric Multiscale to observe the foreshock ion motion around the discontinuities and show that the data support our model. This study is another step toward a predictive model of HFA and FB formation so that we can forecast their space weather effects at Earth using solar wind observations at lunar orbit or L1.

Power Efficient Design a Compliant Robotic Leg Based on Klann's Linkage

This article presents the analysis and optimization of a compliant robotic leg based on Klann's linkage. This leg is specifically designed to efficiently distribute its power requirement over its complete motion cycle, avoiding large peaks in the energy drawn from the battery. The structural compliance of the leg will be shown to be able to both provide a satisfactory walking motion and a timely energy boost to help with the gait. Klann's linkage is selected here as the basic kinematic structure of the leg to demonstrate the proposed methodology, namely to combine in a single structure both a complex trajectory generation and energy storage/release. This work is first aiming at proposing a thorough kinematic analysis of that mechanism using planar screw theory. The latter will be shown to be able to efficiently provide the velocity equations of the linkage as well as its force input–output relationship and singularity conditions. In a second part of this article, the previous kinetostatic model will be used to design and optimize a compliant version of the leg optimizing the power required for the robot to move. Finally, experiments will be shown to support the proposed approach.

A mathematical study on thermal performance of aluminum and titanium alloys based hybrid nanofluid using a multiparametric fractional operator

The principal aim of this article is to establish a new fractional model for an all-inclusive analysis of heat transfer and flow dynamics of hybrid nanofluids. For the case study, a hybrid nanofluid composed of kerosene oil and aluminum and titanium alloy nanoparticles is investigated. This work also examines the role of shape factors for blade, lamina, hexahedron, cylinder, and column-like shapes, in addition to evaluating the synergistic properties of preceding particles. Natural convection, generalized thermal slip condition, and ramped velocity function are fundamental factors behind flow instigation. Initially, the mathematical relation for the thermal flux is generalized for the development of a fractional model, and to serve this purpose, Fourier law is exposed to the Prabhakar operator. The partial coupling of heat and velocity equations further leads to the incorporation of generalized thermal flux into the flow equation, which transforms the classical governing system into a fractional one. The acquirement of exact solutions for the formulated fractional system involves two major steps: the inclusion of adequate dimensionless parameters, followed by the application of the Laplace transform. Various graphical illustrations are supplied using these solutions to interpret variations occurring in thermal and flow behaviors of the under-investigation hybrid nanofluid due to several associated parameters. Moreover, the influences of relevant contributing factors such as volume concentration, fractional parameters, and shape constants on shear stress and thermal efficacy are elucidated by tabulating the numerical outcomes. The results indicate that the thermal efficiency of kerosene oil can be enhanced up to 26.5% by hybridizing it with uniform fractions of aluminum and titanium alloys. The velocity of flow reduces as the collective volume concentration of considered alloys increases. It is observed that lamina-shaped nanoparticles are the most significant in terms of improving thermal characteristics. The temperature function is attenuated as a result of positive alterations to fractional parameters. Furthermore, the increase in buoyancy force strength causes the flow to accelerate significantly.

Heat transfer analysis of fractional model of couple stress Casson tri-hybrid nanofluid using dissimilar shape nanoparticles in blood with biomedical applications

During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called “ternary hybrid nanofluid”. In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide text{Fe}_{3} text{O}_{4}, platelet shaped zinc left( text{Zn} right), and cylindrical shaped gold left( text{Au} right), which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction phi_{hnf} of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction phi_{hnf} of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped text{Fe}_{3} text{O}_{4} enhances up-to 4.63%, platelet shaped left( text{Zn} right) nanoparticles enhances up-to 8.984% and cylindrical shaped gold left( text{Au} right) nanoparticles enhances up-to 10.407%.

Analytical modeling of vertical distribution of streamwise velocity in open channels using fractional entropy

Following the work of Chiu based on classical Shannon entropy, several kinds of generalized entropies have been explored in literature for studying open-channel flow. In this work, we explore a new kind of entropy, namely fractional entropy, which is based on the popular fractional calculus, to derive the vertical distribution of streamwise velocity in open channels. The velocity profile is derived analytically using the series approximation for the Lambert function. Also, the entropy index (i.e., the order of the fractional derivative) is considered a varying parameter and is computed along with the Lagrange multipliers by solving a nonlinear system using the second-order moment constraint, i.e., the momentum balance equation. The derived velocity equation is validated with selected laboratory and field data and compared with the Shannon, Tsallis, and Renyi entropy-based velocity profiles. It is observed that the proposed model can predict the measured values well for all the cases and the model corresponding to the entropy-based momentum coefficient formula is superior to all the abovementioned models. Further, the effects of Lagrange multipliers and the entropy index on the velocity profile are discussed. Also, the entropy index values for all the data are not close to zero, which specializes the entropy into the classical Shannon entropy, and hence, the approach justifies the applicability of the fractional entropy over the Shannon entropy in the context of open-channel flow velocity. Moreover, the methodology is developed based on an approximation of the series, which is based on a convergence criterion. This criterion needs to be verified against each of the data sets and, therefore, may become a difficult task for handling large data sets. To address this issue, this study provides a possible way of reformulating the mathematical model in terms of a nonlinear system with inequality constraint as a scope for future research. Finally, it is expected that the study can be further extended to study other kinds of important hydraulic variables such as sediment concentration, shear stress, etc.

Should We Use the Men Load–Velocity Profile for Women in Deadlift and Hip Thrust?

Injuries are common in team sports and can impact both team and individual performance. In particular, hamstring strain injuries are some of the most common injuries. Furthermore, hamstring injury ratios, in number of injuries and total absence days, have doubled in the last 21 seasons in professional soccer. Weakness in hip extensor strength has been identified as a risk factor in elite-level sprinters. In addition, strength imbalances of the hamstring muscle group seem to be a common cause of hamstring strain injuries. In this regard, velocity-based training has been proposed to analyze deficits in the force-velocity profile. Previous studies have shown differences between men and women, since there are biomechanical and neuromuscular differences in the lower limbs between sexes. Therefore, the aim of this study was to compare the load-velocity profile between males and females during two of the most important hip extension exercises: the hip thrust and the deadlift. Sixteen men and sixteen women were measured in an incremental loading test following standard procedures for the hip thrust and deadlift exercises. Pearson's correlation (r) was used to measure the strength of the correlation between movement velocity and load (%1RM). The differences in the load-velocity relationship between the men and the women were assessed using a 2 (sex) × 15 (load) repeated-measures ANOVA. The main findings revealed that: (I) the load-velocity relationship was always strong and linear in both exercises (R2 range: 0.88-0.94), (II) men showed higher velocities for light loads (30-50%1RM; effect size: 0.9-0.96) than women for the deadlift, but no significant differences were found for the hip thrust. Based on the results of this study, the load-velocity equations seem to be sex-specific. Therefore, we suggest that using sex-specific equations to analyze deficits in the force-velocity profile would be more effective to control intensity in the deadlift exercise.

A Simple Line-Element Model for Three-Dimensional Analysis of Steady Free Surface Flow through Porous Media

Considering the fact that only pores can transport water, pores in the homogeneous control volume are conceptualized as a three-dimensional orthogonal network of line elements, which is in contrast to the continuum hypothesis in traditional numerical approaches. The related flow velocity, hydraulic conductivity and continuity equation equivalent to the continuum model are formulated based on the principle of flow balance. Subsequently, the unified form for flow velocity and continuity equation is established based on the local coordinate system, and a finite line-element method is developed, in which three-dimensional steady free surface flow is reduced to one-dimensional form, and the numerical difficulty is greatly decreased. The proposed line-element model is validated by the good agreements of free surface locations with other methods through steady flow in a rectangular dam and a right trapezoidal dam, respectively. It is found that the proposed line-element model is not heavily dependent on the mesh size and penalty parameter. Steady free surface flow on the left bank abutment slope of the Kajiwa Dam in Southwestern China is further evaluated, and a parabolic variational inequality algorithm based on the continuum model is also employed for comparison. The consistent results indicate that the proposed line-element model can capture the steady free surface flow behavior as well as the continuum-based method. Moreover, the proposed line-element model can rapidly achieve accurate solutions whether for simple examples or for complicated engineering applications.

The effect of collisions on the rayleigh-taylor instability in magnetized quantum plasma

Rayleigh-Taylor instability occurs at the interface between light and heavy fluids whenever the heavier fluid is accelerated by the light one. An important issue is the stability conditions of these systems. Various parameters such as density difference between two fluids, density inhomogeneity length, magnetic field, viscosity, collision can affect the stabilization or destabilization of the system. So far, some of these factors have been investigated in the fields of classical and quantum physics. This process has also been studied in both linear and nonlinear states. Here we consider a collisional magnetic inhomogeneous quantum plasma. For the inhomogeneity profile of density as an exponential function, we calculated the second ordinary equation for the disturbed velocity. Since the differential equation does not have an analytical solution, we have calculated the growth rate curve using numerical methods and obtained the disturbed velocity profile in the discontinuity. Then the effects of different parameters such as collision, magnetic field, quantum effects, and density difference of two fluids on the system stabilization are studied. The various branches of the instability growth rate curve and its relationship with the turbulent velocity profile in discontinuity are also discussed.

Nematic Liquid Crystal Flow with Partially Free Boundary

We study a simplified Ericksen-Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier-Stokes equation for the fluid velocity with a transported heat flow of harmonic maps, and both of these parabolic equations are critical for analysis in two dimensions. The boundary conditions are physically natural and they correspond to the Navier slip boundary condition with zero friction for the velocity field and a Plateau-Neumann type boundary condition for the map. In this paper we construct smooth solutions of this coupled system that blow up in finite time at any finitely many given points on the boundary or in the interior of the domain.

Spatiotemporal distributions of air-sea CO2 flux modulated by windseas in the Southern Indian Ocean

The Southern Indian Ocean is a major reservoir for rapid carbon exchange with the atmosphere, plays a key role in the world’s carbon cycle. To understand the importance of anthropogenic CO2 uptake in the Southern Indian Ocean, a variety of methods have been used to quantify the magnitude of the CO2 flux between air and sea. The basic approach is based on the bulk formula—the air-sea CO2 flux is commonly calculated by the difference in the CO2 partial pressure between the ocean and the atmosphere, the gas transfer velocity, the surface wind speed, and the CO2 solubility in seawater. However, relying solely on wind speed to measure the gas transfer velocity at the sea surface increases the uncertainty of CO2 flux estimation. Recent studies have shown that the generation and breaking of ocean waves also significantly affect the gas transfer process at the air-sea interface. In this study, we highlight the impact of windseas on the process of air-sea CO2 exchange and address its important role in CO2 uptake in the Southern Indian Ocean. We run the WAVEWATCH III model to simulate surface waves in this region over the period from January 1st 2002 to December 31st 2021. Then, we use the spectral partitioning method to isolate windseas and swells from total wave fields. Finally, we calculate the CO2 flux based on the new semiempirical equation for gas transfer velocity considering only windseas. We found that after considering windseas’ impact, the seasonal mean zonal flux (mmol/m2·d) increased approximately 10%-20% compared with that calculated solely on wind speed in all seasons. Evolution of air-sea net carbon flux (PgC) increased around 5.87%-32.12% in the latest 5 years with the most significant seasonal improvement appeared in summer. Long-term trend analysis also indicated that the CO2 absorption capacity of the whole Southern Indian Ocean gradually increased during the past 20 years. These findings extend the understanding of the roles of the Southern Indian Ocean in the global carbon cycle and are useful for making management policies associated with marine environmental protection and global climatic change mitigation.

Induced Navier’s Slip with CNTS on a Stretching/Shrinking Sheet under the Combined Effect of Inclined MHD and Radiation

The present article investigates viscous fluid flow’s heat and mass transfers over a stretching/shrinking sheet using the single and multi-wall carbon nanotube models. The analysis considers the effects of thermal radiation, induced slip, mass transpiration, and inclined magnetic force. The effect of the carbon nanotube model on fluid flow has not been considered in previous studies. By exploiting the similarity variable, the governing nonlinear partial differential equations are converted into nonlinear ordinary differential equation. The derived equations are solved analytically, and we obtained an exact solution for the velocity and energy conservation equation. The physical parameters of interest such as induced slip parameter, suction/injection, magnetic field, thermal radiation, and shear stress are analyzed and presented graphically. In particular, we show that the fluid flow in a single wall carbon nanotube transfers more energy than the multivalued nanotubes.

Automatic diagnostic system for segmentation of 3D/2D brain MRI images based on a hardware architecture

Magnetic resonance imaging is among the advanced diagnostic testing tools for brain health issues. This method captures a series of detailed head images. These images are then printed and diagnosed by a specialist doctor to demonstrate differences in the brain tissue. Accordingly, additional diagnostic information can be given to determine the extent of the damage and the appropriate treatment methods. In this paper, and in order to facilitate the work of the specialist doctor and help him, we propose an automated hardware architecture for 3D/2D segmentation on MRI images to diagnose differences in brain tissue. For this, we used the metaheuristic technique based on Particle Swarm Optimization (PSO); for which we proposed improvements both for the velocity and position equations and for the fitness function. The goal of the work is to develop a real time automatic system for MRI images segmentation with improved metrics such as accuracy, sensitivity, specificity, dice metrics, execution time and resources utilization. The proposed hardware architecture was synthetized and then co-simulated using Matlab-Vivado System (VSM) for Field Programmable Gate Array (FPGA). Results show that our 3D segmentation method benefited from 2D segmentation with 95.39% accuracy rate and 87.97% DSC similarity (for 5-level segmentation) with 4.57 ms execution time for the case of BraTS 2013 dataset of brain MRI Images.

A THEORETICAL APPROXIMATION FOR LAMINAR FLOW BETWEEN ECCENTRIC CYLINDERS

Taylor-Couette flow between two concentric cylinders has received much attention due to its use in various applications, including biomedical devices, micro electro-mechanical systems, polymer pumping and electric motor cooling. Due to the complex interaction of the viscosity and the involved geometry within the confined space, different flow regimes are dominant under different conditions, affecting the fluid dynamics and heat transfer. In analyzing the mentioned flow, besides the experimental and computational studies, analytical models have been developed with varying levels of complication. In the present study, using the homotopy of both the flow and the domain geometry between the concentric and eccentric cylinders, a practical formula for flow between eccentric cylinders is developed. In doing so, an appropriate transformation function for the geometry is developed and embedded into the velocity equation for the concentric cylinders. The resultant equation is tested against flow simulation results. A validity margin analysis is performed based on the variation of the mass flow rate between the cylinders. It is seen that the proposed model for eccentric cylinders is applicable for all gap distances, unlike the previous models that are restricted to narrow gaps. Finally, a separate formula to quantify the error in the estimates of the present method is also derived, which involves the ratio of the cylinders and the eccentricity.

Threshold of motion of coral reef sediment under currents in flume experiments

AbstractThis study experimentally documented the thresholds of critical motion for tropical shallow marine carbonate sediments by conducting a total of 225 laboratory experiments that included the analysis of nine median sediment diameters and five water depths. A shape factor, Sf, which quantifies the shape of a single particle, was evaluated during the investigation. Both the critical Shields parameter and the incipient mean velocity were used to represent the critical thresholds of motion. The thresholds of motion for coral reef sediment were then compared with the results from quartz sand. The experimental results show that the critical threshold of motion is smaller for coral reef sediment than for quartz sand of the same median sieve diameter due to differences in particle shape in spite of the coral reef sediment being of higher density. For diameters higher than 1.425 mm, the critical Shields parameters and incipient mean velocities tend to have similar values to quartz sand. The differences between the two increased significantly for median sieve diameters <1.075 mm. Based on the experimental data, Shields curve bands and equations for the incipient mean velocity for sediments of differing shape factors were obtained for tropical shallow marine carbonate sediments as well as marine carbonate grains.

Non-equilibrium effect modeling and particle velocity estimation for particulate flow in porous media

The complex dynamics of fluid and particles flowing through pore space demands some relaxation time for particles to catch up with fluid velocity, which manifest themselves as non-equilibrium (NE) effects. Previous studies have shown that NE effects in particle transport can have significant consequences when relaxation time is comparable to the characteristic time associated with the fluid flow field. However, the existing models are lacking to account for this complicated relation between particles and fluid. In this paper, we adapt the general form of the harmonic oscillation equation to describe NE effects in the particulate flow system. The NE effect is evaluated by solving coupled mass balance equations with computational fluid dynamic (CFD) techniques using COMSOL Multiphysics®. A simplified straight-tube model, periodic converging–diverging tube model, and SEM image of a real pore network are applied in NE analyses. The results indicate that the time variation of the NE effect complies with the theory of stability. Two key parameters of the oscillator equation are amplitude (A) and damping ratio (ζ), where the former represents the magnitude of NE and the latter is an indication of flow path geometry. The velocity equations for particle transport in different flow path geometries are derived from the proposed NE equation, offering a quick estimation of particle velocity in the particulate flow. By conducting simulation on the SEM image of a real pore structure, the equivalent radii of the pores where particles move through were obtained. The outcome of this work can shed light on explaining the complex NE effects in porous media. The generalized equation to model NE can help temporarily decouple particle transport equations from fluid equations, facilitating much advanced particulate flow modeling problems in the large-scale problems.

Thermal investigation into the Oldroyd-B hybrid nanofluid with the slip and Newtonian heating effect: Atangana–Baleanu fractional simulation

The significance of thermal conductivity, convection, and heat transportation of hybrid nanofluids (HNFs) based on different nanoparticles has enhanced an integral part in numerous industrial and natural processes. In this article, a fractionalized Oldroyd-B HNF along with other significant effects, such as Newtonian heating, constant concentration, and the wall slip condition on temperature close to an infinitely vertical flat plate, is examined. Aluminum oxide (Al2O3) and ferro-ferric oxide (Fe3O4) are the supposed nanoparticles, and water (H2O) and sodium alginate (C6H9NaO7) serve as the base fluids. For generalized memory effects, an innovative fractional model is developed based on the recently proposed Atangana–Baleanu time-fractional (AB) derivative through generalized Fourier and Fick’s law. This Laplace transform technique is used to solve the fractional governing equations of dimensionless temperature, velocity, and concentration profiles. The physical effects of diverse flow parameters are discussed and exhibited graphically by Mathcad software. We have considered 0.15≤α≤0.85,2≤Pr⁡≤9,5≤Gr≤20,0.2≤ϕ1,ϕ2≤0.8,3.5≤Gm≤8, 0.1≤ Sc ≤0.8, and 0.3≤λ1,λ2≤1.7. Moreover, for validation of our present results, some limiting models, such as classical Maxwell and Newtonian fluid models, are recovered from the fractional Oldroyd-B fluid model. Furthermore, comparing the results between Oldroyd-B, Maxwell, and viscous fluid models for both classical and fractional cases, Stehfest and Tzou numerical methods are also employed to secure the validity of our solutions. Moreover, it is visualized that for a short time, temperature and momentum profiles are decayed for larger values of α, and this effect is reversed for a long time. Furthermore, the energy and velocity profiles are higher for water-based HNFs than those for the sodium alginate-based HNF.

Design of an Integrated Controller for a Sweeping Mechanism of a Low-Dust Almond Pickup Machine.

California is the world's biggest producer and exporter of almonds. Currently, the sweeping of almonds during the harvest creates a significant amount of dust, causing air pollution in the neighboring urban areas. A low-dust sweeping system was designed to reduce the dust during the sweeping of almonds in the orchard. The system includes a feedback control system to control the sweeper brushes' height and their angular velocity by adjusting the forward velocity of the harvester and the brushes' rotational speeds to avoid any extra overlapping sweeping, which increases dust generation. The governing kinematic equations for sweepers' angular velocity and vehicle forward speed were derived. The feedback controllers for synchronizing these speeds were designed to optimize brush/dust contact to minimize dust generation. The sweepers' height controller was also designed to stabilize the gap between the brushes and the orchard floor and track the road trajectory. Controllers were simulated and tuned for a fast response for agricultural applications with less than a second response delay. Results showed that the designed system has acceptable performance and generates low amounts of dust within the acceptable range of California ambient air quality standards.

Calculation Model of Bottom Hole Flowing Pressure of Double-Layer Combined Production in Coalbed Methane Wells

Bottom hole flowing pressure (BHFP) is the key factor to determine a reasonable working system and achieve long-term stable production of coalbed methane (CBM) wells. However, there is no special BHFP model for double-layer combined production (DLCP). Generally, the constant mass model (CMM) for single-layer production is applied to treat the double reservoirs as a whole, ignoring the changes of fluid mass in each section and the acceleration pressure drop in the reservoir section. The calculation results have great errors, and the BHFP of the lower reservoir is used to adjust the production system of the two reservoirs, which does not meet the requirements of the upper reservoir. In this paper, the expression of acceleration pressure drop assumed to be zero in CMM is decomposed and derived, the relationship between acceleration pressure drop and unit length radial flow is established, and then the pressure drop formula of reservoir section with radial inflow is obtained. The reservoir is divided into several sublayers, and the pressure drop equation for each sublayer is established. According to the water flow and gas flow in the reservoir and nonreservoir sections, the corresponding velocity equations of water phase and gas phase are derived. The above equations are combined to establish the variable mass model (VMM) for DLCP with three stages. The field data are substituted into the VMM and the CMM, and the accuracy of the new model is verified. The results show that in the stages of double-layer water production and double-layer gas production, the errors of the two models are less than 5%, while in the stage of gas-water coproduction, the error of the VMM is 2.75%-6.58%, and the error of the CMM is 7.15%-15.18%. The VMM is more accurate. In addition, in the stages of water production and gas-water coproduction during DLCP, the BHFP of the two reservoirs differs greatly, with a maximum difference of 49.1%. Therefore, the two reservoirs need to adjust the production rule according to their respective BHFP. To sum up, the VMM can accurately give the BHFP of each reservoir, which is more realistic. It also solves the problem that one BHFP cannot accurately adjust the production rule of the two reservoirs, so as to provide technical support for the formulation of optimal production rule and the realization of high production.

Induced by heat source on unsteady MHD free convective flow of Casson fluid past a vertically oscillating plate through porous medium utilizing finite difference method

In this research, the unsteady MHD flow of a Casson fluid past a vertical plate that oscillates while maintaining a constant wall temperature and the heat source is the subject of this article. The fluid is electrically conductive and moves through a porous media. Partial differential equations with initial and boundary conditions are used to model this phenomenon. There are a few appropriate non-dimensional variables introduced. Using the finite difference method(FDM), the consistent dimensionless equations with circumstances are resolved. The energy and velocity equations are solved precisely. Expressions for Nusselt number and skin friction are also assessed. The outcomes of computations are analyzed for newly developing flow parameters. Additionally, skin friction and the Nusselt number effects are explained using table values. Furthermore, increasing the heat source parameter causes a rise in temperature and velocity.

Threshold velocity for the collisional growth of porous dust aggregates consisting of cohesive frictionless spheres

Understanding the collisional outcomes of dust aggregates and their dependence on the material properties of the constituting particles is of great importance for understanding planet formation. Recent numerical simulations have revealed that interparticle tangential friction plays a crucial role in energy dissipation during collisions between porous dust aggregates, but the importance of friction for the collisional growth of dust aggregates remains poorly understood. Here we demonstrate the effects of interparticle tangential friction on the collisional growth of dust aggregates. We performed numerical simulations of collisions between equal-mass porous dust aggregates consisting of cohesive and frictionless spheres. We changed the collision velocity and impact angle systematically and calculated the collisional growth efficiency as a function of the collision velocity. We found that the threshold velocity for collisional growth decreases when dust aggregates are made of frictionless spheres compared to frictional spheres. Our results highlight the importance of tangential interactions for the collisional behavior of dust aggregates and indicate that the predictive equation for the threshold velocity should be reconstructed.