Dimensionless Parameters Research Articles

How Irregular Geometry and Complex Feed Waveform Affect Pulsating Arterial Mass Transfer.

Alzheimer's disease is a progressive degenerative condition that has various levels of effect on one's memory. It is thought to be caused by a buildup of protein in small fluid-filled spaces in the brain called perivascular spaces (PVS). The PVS often takes on the form of an annular region around arteries and is used as a protein-clearing system for the brain. To analyze the modes of mass transfer in the PVS, a digitized scan of a mouse brain PVS segment was meshed and used for computational fluid dynamics (CFD) studies. Tandem analyses were then carried out and compared between the mouse PVS section and a cylinder with commensurate dimensionless parameters and hydraulic resistance. The geometry pair was used to first validate the CFD model and then assess mass transfer in various advection states: no flow, constant flow, sinusoidal flow, sinusoidal flow with zero net solvent flux, and an anatomically correct asymmetrical periodic flow. Two mass transfer situations were considered, one being a protein build-up and the other being a protein blend-down. The results showed that, for all the flows in question and both protein scenarios, there was nearly no protein clearance benefit by the anatomically correct PVS geometry. Surprisingly, solute blend-down was diffusion-dominated even for high Peclet numbers. Findings herein lead to the conclusion that minimal risk would be incurred by incorporating PVS geometry into existing reduce-order modeling arterial networks.

Non local analytical and numerical modelling of re-entrant auxetic honeycomb

Auxetic materials, characterized by their negative Poisson’s ratio, have been extensively studied for applications in energy absorption and mechanical reinforcement. Re-entrant honeycomb structures, a subtype of auxetic materials, have demonstrated superior mechanical characteristics. However, understanding the mechanical behavior of these structures at the nanoscale remained a significant challenge. To address this gap, the authors explored the influence of size on the deflection behavior of re-entrant auxetic honeycomb structures through non-local continuum mechanics. Their analytical model, incorporating the Euler-Bernoulli beam model and considering four non-dimensional geometrical parameters, was validated through numerical simulations and a comprehensive review of existing literature. The study aimed to provide valuable insights into the design and engineering of re-entrant auxetic honeycomb structures across diverse applications, contributing to the advancement of non-local elasticity theory and deepening the understanding of the mechanical behavior of auxetic structures at the nanoscale. The research laid a foundation for further exploration and optimization of re-entrant honeycomb structures, facilitating their effective utilization in fields such as MEMS/NEMS by leveraging the dimensionless parameters identified in the study.

Theoretical investigation of the convective heat transfer mechanism along a cantilever shape

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n, Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient.

Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials

Abstract The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ \mu , and a parameter η \eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.

The Blasingame method considering the effect of inter-well interference in a circular homogeneous closed reservoir

The Blasingame method is a valuable tool for analysing the diminishing production challenge in the presence of variable bottomhole pressure and diverse production conditions. It is essential to highlight that the Blasingame method views the closed reservoir as the outer boundary condition for its model. This paper introduces the concept of the equivalent well control radius and formulates the Blasingame method based on the fluid flow characteristics inherent in twin-well production, taking into account the influence of inter-well interference. This study provides an in-depth analysis of production variations in reservoirs with inter-well interference by examining Blasingame type-curve definitions of the dimensionless parameters. Additionally, it investigates key factors impacting production, including neighbouring wells’ production, distance, and opening time: variations in all three parameters lead to different levels of interference between wells, which manifests itself in the regularised production integral derivative curve with different lengths and heights of convexity. Numerical simulations employing orthogonality are conducted to validate the reliability of this method. The results of these simulations offer theoretical support for the precise evaluation of reservoirs facing similar challenges.

Hydrothermal analysis of parallel and symmetric microchannels with phase change slurry and porous fin designs

The dynamic information of microchannel systems with parallel and symmetric configurations is insufficient, which limits our ability to compare and optimize these systems in all directions. In this study, thermal and hydraulic characteristics in parallel and symmetric microchannel heat sinks (MCHSs) with porous fins cooled by phase change slurry are investigated. A 3-D steady state conjugate model is adopted to compare the effects of fin configuration, coolant type and structural parameters on hydrothermal properties of wavy MCHS. The variations of dimensionless parameters involving Nu, f, η (temperature control effectiveness) and PEF (performance evaluation factor) are considered to demonstrate the effectiveness of combined design on overall performance enhancement of wavy MCHS. Results indicate that lower temperature increment and higher pressure loss appear in wavy configuration with porous fins than in straight mode, and lowest thermal resistance arises in parallel porous fin design. At the narrow position of symmetric channel, the fluid changes from the low-speed drop-shaped micelle to high-speed bullet-shaped one with increasing A, which leads to higher Nu with larger pressure drop penalty. Due to the extended flow route and improved fluid mixing, η increases with decreasing wavelength in all cases, and η of porous microchannels with both phase change slurry and parallel fins is much larger than that of symmetric one and the one with only base fluid. Compared with wavy fin configurations with small and large ε, lower temperature and its more uniform distribution happen in the mode with medium porosity. In comparison with basic configuration, the parallel configuration with slurry as cooling medium has the maximum PEF value when the pore size is 0.14 mm, up to 1.64. Larger f increase occurs in wavy channel with increasing N, and the space shortening between adjacent channel cavities in symmetric mode makes the adjoining Dean vortices easier to contact and repel, thus making it appear larger rise of f than parallel mode. Compared with other channel parameters, it is not effective to improve the overall performance of wavy MCHS with porous fins by adjusting α. Overall, the throat effect of symmetric MCHS significantly occurs in channel configuration with larger A, bigger λ, lower ε, smaller dp, more N, and lesser α, leading to higher f rise than the parallel mode.

Standard series of transmitting equipment for hydra-jet technology based on dimensionless geometric parameters development

Introduction. The work is devoted to the calculation of series standards for the design of high-pressure transmission devices used in various hydra jet technologies, which will provide the design of these devices based on dimensionless indicators describing the relationship between their geometric and technological parameters.Materials and methods. The methodology includes the use of mathematical models and analytical approaches to assess the influence of various parameters on heat generation processes in equipment, as well as methods for statistical processing of results.Results. A histogram of temperature distribution was constructed and the data was approximated using the distribution curve of temperature values and parametric series were generated for dimensionless parameters depending on various factors such as temperature, pressure, rotational speed and linear speed. It is possible to obtain parametric series for linear dimensions from five temperature ranges and seven standard sizes depending on the pressure and rotation speed of the drill shaft.Discussion and conclusions. The results obtained provide a better definition of the relationships between rotation speed, geometric characteristics and temperature parameters through the use of dimensionless indicators and it is possible to optimize the design of such devices taking into account operating conditions and ensuring increased efficiency.

Tuning to the edge of the abyss in SU(5)

I show that if a dimensionless parameter is tuned to be close to the boundary of the positivity domain and symmetry breaking is driven by a cubic term in the Lagrangian, the scale of the physics of symmetry breaking in a quantum field theory as measured by the Higgs mass can be much greater than the dimensional scales in the classical Lagrangian. Radiative corrections produce large and physically important corrections, helping to stabilize the large VEV. The resulting picture contrasts sharply with the “modern” view of QFT as an effective field theory. I describe how this mechanism might produce the GUT scale in an SU(5) model in which the dimensional parameters in the Lagrangian are at the low scale.

Oscillatory behavior of drops in an ambient liquid under an impact

In this work, the oscillatory behavior of drops in an ambient liquid under an impact is numerically and experimentally studied using the Basilisk C and a self-designed falling drop tower facility, respectively. The numerical results of the oscillatory drops are consistent with the experimental data. A shape parameter e is proposed to describe the oscillatory behavior of the drops. Using the energy budgets of the drops, the influence of dimensionless parameters, i.e., Reynolds number Re, Ohnesorge number Oh, Bond number Bo, and viscosity ratio η on the oscillatory amplitude and period of the shape parameter e is systematically investigated. Furthermore, a scaling law between the maximum deformation of the drops during the oscillatory behavior and the dimensionless parameters is established, which can be interpreted by a mass-spring-damp model. It is found that the established model agrees well with our numerical and experimental results without any fitting parameters when the viscosity of the ambient liquid is near or smaller than that of the drop, and the maximum deformation has a clear proportionality as Oh2Re(1+Re).

The analytical solutions of squeezing flow and heat transfer in an horizontal filtering channel

Flow and heat transfer dynamics inside different industrial chambers play a vital role in understanding momentum and heat transfer during industrial operations. Analysis of such flow and heat transfer helps operators to know how the system works. To better understand the filtration process, the current study analytically investigated the internal flow and heat transfer through a porous horizontal filter channel under the influence of a uniform magnetic field while removing unwanted contaminations from the fluid inside the filter chamber. Thus, the novelty of the current study is to advance the filtration process by investigating how the top moving wall, which aims to minimise filter cake formation, affects permeates outflow (the current design). The partial differential equations (PDEs) model representing the internal flow and heat transfer during filtration is transformed into a system of ordinary differential equations (ODEs) using Lie point symmetry reduction without changing the dynamics under investigation. After that, the transformed equations are solved analytically using the perturbation approximation technique. The comparative analysis between the obtained semi-analytical and NDSolve numerical solutions was used to show the correlation of internal flow, temperature, and pressure profiles. The obtained solutions are used to find the best combination of dimensionless parameters that arise from flow and heat transfer dynamics that lead to optimum outflow. Graphical analysis of flow and heat transfer dynamics are used to indicate the combination of parameters that leads to maximum outflow based on scientific evidence. It is observed that, on average, the velocity increases significantly by 122.55% across all cases of Re ranging from 0 to 3.2 at the top permeable wall y=1. This significant increase is due to the motion of the moving wall and fluid injection happening at y=1. The results show that more chamber volume, small pores size, weak injection, weak magnetic force, and less Joule heating are crucial to increase internal temperature and permeate outflow velocity during filtration.

Coupling FELA and computation intelligent in predicting behaviour of inclination strip anchor in anisotropic and heterogeneous clays

This study introduces new numerical investigations of the uplift capacity of inclined strip anchors buried in anisotropic and heterogeneous clays. The analyses utilize Lower Bound (LB) Finite Element Limit Analysis techniques (FELA) under plane strain conditions, employing the Anisotropic Undrained Shear (AUS) failure criterion. The undrained shear strength of the clay increases proportionally with depth, and anisotropy is introduced by adjusting the ratios between the shear strengths obtained from three different tests. Four input parameters, namely, the embedment ratio (H/B), the inclination angle (α), the ratio of increasing undrained shear strength with depth (m = ρΒ/suTC0), and the factor of anisotropic parameters (re), are considered in analyzing the uplift coefficient (Fc), and a set of design charts is proposed. The effect of dimensionless parameters on the development of failure mechanisms is also investigated. Moreover, a novel method for assessing the ultimate uplift capacity of an inclined strip anchor in natural clay is given by integrating FELA with Multivariate Adaptive Regression Splines (MARS) and Extreme Gradient Boosting (XGBoost). Based on the optimal machine-learning models, this study also calculates the contribution of each input to the value of Fc via sensitivity analysis. The engineering computations for strip anchors embedded in anisotropic and non-homogenous clays can be improved with the results of these investigations and the proposed machine-learning models.

High-temperature transient-induced thermomechanical damage of fiber-reinforced ceramic-matrix composites in supersonic wind tunnel

This article is based on the supersonic directly connected wind tunnel. Through a specially designed experimental chamber, combined with infrared temperature measurement, high-speed camera, etc., in-situ monitoring of composite materials under airflow at Ma 3.0 with a total temperature of 950 ∼ 1473K was carried out. The dimensional analysis method was used to propose dimensionless parameters to characterize the thermal coupling caused by high-speed airflow thermal shock. Research has shown that the thermal coupling effect of supersonic airflow causes uneven temperature inside the material, and the thermal stress caused by temperature gradient changes (including increasing and decreasing processes) is the main reason for material damage. The damage of ceramic matrix composites under thermal shock mainly manifests as a decrease in surface roughness, surface fiber fracture and a decrease in elastic modulus. In addition, the study also found that there are damage thresholds for the thermal shock effect of airflow at different total temperatures, which helps to further understand the thermomechanical damage mechanism and degradation law of composite structure under high-temperature transient conditions.

Mathematical Solutions of Free Convection Flow of Casson Fluid in Channel with Accelerated Plate

Mathematical Solutions of Free Convection Flow of Casson Fluid in Channel with Accelerated Plate

The Influence of Soil Deformability on the Seismic Response of 3D Mixed R/C–Steel Buildings

Following effective seismic codes, common buildings are considered to be made of the same material throughout the story distribution and based on an ideal rigid soil. However, in daily construction practice, there are often cases of buildings formed by a bottom part constructed with reinforced concrete (r/c) and a higher steel part, despite this construction type not being recognized by code assumptions. In addition, soil deformability, commonly referred to as the Soil–Structure Interaction (SSI), is widely found to affect the earthquake response of typical residence structures, apart from special structures, though it is not included in the normative design procedure. This work studies the seismic response of in-height mixed 3D models, considering the effect of sustaining deformable ground compared to the common rigid soil hypothesis, which has not been clarified so far in the literature. Two types of soft soil, as well as the rigid soil assumption, acting as a reference point, are considered, while two limit interconnections between the steel part on the concrete part are included in the group analysis. The possible influence of the seismic orientation angle is explored in the analysis set. Selected numerical results of the dynamic nonlinear analyses under strong near-fault ground excitations were plotted through dimensionless parameters to facilitate an objective comparative discussion. The effect of SSI on the nonlinear performance of three-dimensional mixed models is identified, which serves as the primary contribution of this work, making it unique among the numerous research works available globally and pointing to findings that are useful for the enhancement of the seismic rules regarding the design and analysis of code-neglected mixed buildings.

Assessing nasal airway resistance and symmetry: An approach to global perspective through computational fluid dynamics.

This study aimed to explore the variability in nasal airflow patterns among different sexes and populations using computational fluid dynamics (CFD). We focused on evaluating the universality and applicability of dimensionless parameters R (bilateral nasal resistance) and ϕ (nasal flow asymmetry), initially established in a Caucasian Spanish cohort, across a broader spectrum of human populations to assess normal breathing function in healthy airways. In this retrospective study, CT scans from Cambodia (20 males, 20 females), Russia (20 males, 18 females), and Spain (19 males, 19 females) were analyzed. A standardized CFD workflow was implemented to calculate R-ϕ parameters from these scans. Statistical analyses were conducted to assess and compare these parameters across different sexes and populations, emphasizing their distribution and variances. Our results indicated no significant sex-based differences in the R parameter across the populations. However, moderate sexual dimorphism in the ϕ parameter was observed in the Cambodian group. Notably, no geographical differences were found in either R or ϕ parameters, suggesting consistent nasal airflow characteristics across the diverse human groups studied. The study also emphasized the importance of using dimensionless variables to effectively analyze the relationships between form and function in nasal airflow. The observed consistency of R-ϕ parameters across various populations highlights their potential as reliable indicators in both medical practice and further CFD research, particularly in diverse human populations. Our findings suggest the potential applicability of dimensionless CFD parameters in analyzing nasal airflow, highlighting their utility across diverse demographic and geographic contexts. This research advances our understanding of nasal airflow dynamics and underscores the need for additional studies to validate these parameters in broader population cohorts. The approach of employing dimensionless parameters paves the way for future research that eliminates confounding size effects, enabling more accurate comparisons across different populations and sexes. The implications of this study are significant for the advancement of personalized medicine and the development of diagnostic tools that accommodate individual variations in nasal airflow.

Effects by geothermal gradient on thermal response tests for boreholes

A thermal response test (TRT) on a borehole provides information needed in the design of ground heat exchangers for ground source heat pump systems. Conventional analysis of TRT data sets uses the late-time period to estimate the ground thermal conductivity and the effective borehole resistance. During this quasi-steady-state period, the transient average fluid temperature has a logarithmic linear trend, which is consistent with conventional heat transfer models that assume a uniform undisturbed ground temperature. As the depth of the borehole increases the undisturbed ground temperature increases with depth following the geothermal gradient. This paper focuses on how the geothermal gradient affects a TRT. As the geothermal gradient increases, the required time to reach the conventional logarithmic linear trend may increase beyond any practical testing duration in coaxial boreholes. Then, conventional analysis methods based on a quasi-steady-state period incorrectly estimate the ground thermal conductivity. The magnitude of this effect is controlled through a dimensionless parameter |qratio|, which includes the geothermal gradient and other test parameters. In place of conventional models, a transient model that includes the geothermal gradient and fluid thermal storage can estimate the ground thermal conductivity and local borehole resistance within the typical TRT testing duration.

Bioconvective flow of thermally radiative Casson nanofluid with aerobic microorganisms over a stretching surface

A mathematical model is proposed to analyze the flow characteristics of a thermally radiative, chemically reacting Casson nanofluid incorporating aerobic microorganisms over a stretching sheet. Nonlinear dimensionless ordinary differential equations are formulated through suitable similarity transformations. The resulting coupled system of nonlinear ordinary differential equations is numerically solved using the finite difference method with the bvp4c routine in MATLAB. The verification of the numerical solution’s accuracy is conducted by comparing it with previously established results under specific conditions pertinent to the present investigation. Skin friction coefficients, local Nusselt number, and Sherwood number are computed for various parameters and their implications for engineering applications are discussed. The investigation also explores the impact of different dimensionless parameters on velocity, temperature, mass concentration, motile microorganism density, and oxygen concentration profiles for both Casson and Newtonian nanofluids, offering a comprehensive analysis. The study highlights that suspending non-Newtonian nanofluids with fast-moving aerobic microorganisms and nanoparticles results in enhanced heat transfer rates, thus presenting potential benefits for practical applications such as the manufacturing of biofilms.

Influence of joint types on rigidity of Chebyshev elastic gridshells: A parametric analysis

Elastic gridshells (EGS) have many applications in the field of architecture. Built according to Chebyshev net geometry, the Chebyshev EGS (CGES) is a famous kind of EGS; since an arbitrary three-dimensional CEGS can be transformed into a planar state without any stretching strain. Due to its tremendous potential application in novelly deployed structures, the rigidity of CEGS is an important mechanical property to be investigated.In this study, using the analytical and finite element methods, the influence of joint types and gridshell parameters on the rigidity of CEGS subjected to point loads is studied in detail. The joint types are classified as pin joints, semi-rigidity joints, and rigid joints. A robust relation between rigidity and gridshell parameters is proposed, including Young's modulus, rod diameter, size of CEGS, joint stiffness, and rod numbers. Further, the above relation is nondimensionalized. The dimensionless rigidity is only related to the two dimensionless parameters, which are dimensionless joint stiffness and rod number. The rigidities of CEGS on four types of surfaces are calculated to verify the above relation, and satisfactory agreement is obtained. Therefore, the proposed relationship of rigidity is confirmed to be accurate and efficient for a wide range of parameters.

Experimental investigation on morphology of window-ejected flame without facade effect

As the key characteristic of window-ejected flames, flame morphology such as flame height, flame depth involves the ignition of surrounding buildings. This article experimentally investigated the flame height, the maximum flame width and the maximum flame depth ejected from a fire compartment without the facade wall effect. A small-scale compartment with a side wall opening attached to compartment top is used for simulating the situation without the facade wall. The ejected flame height, maximum flame width and maximum flame depth were recorded and measured for various opening sizes and fuel supply rates. Results show that: (1) The ejected flame height increases as the increase of fuel supply rate and decreases as the increase of opening dimension, and was obviously lower than that with the facade effect; (2) The maximum flame width increases as the increase of fuel supply rate and decreases with the increase of opening dimension, and was higher than that with the facade effect; (3) The maximum flame depth increases as the increase of fuel supply rate, and the formation of maximum flame depth was analyzed based on the ejected thermal plume momentum and the air entrainment momentum. A dimensionless parameter, which presents the complex competition mechanism between the plume momentum and the air entrainment momentum, was proposed to characterize their impacts on flame depth, by which the maximum flame depth was represented well. This work would provide theoretical support for building fire prevention and control.

Investigation on flow and heat transfer characteristics of latent functionally thermal fluid for axisymmetric flows

The utilization of heat exchangers in energy and industrial production is vital for heat exchange and transfer. The latent functionally thermal fluid (LFTF), due to its exceptional properties, can be effectively utilized in double-pipe heat exchanger as a heat transfer fluid. This study delves into the convective and heat transfer characteristics of LFTF in symmetric flow conditions. Employing the lattice Boltzmann method (LBM), various dimensionless parameters are examined, including the height-to-diameter ratio (HDR) and inner diameter size. The results show that higher Rayleigh and Stefan numbers lead to more intense reactions and heat transfer processes. Additionally, a phase change temperature of 0.7 results in a total melting time that is 1.5 times longer than at a phase change temperature of 0.1. As the inner diameter increases, the average Nusselt number decreases faster, resulting in a shorter total melting time. Specifically, when the HDR is 0.5, the total melting time is 47.61% shorter compared to an HDR of 2. This is due to the fact that the temperature collects in the upper part of the study area resulting in faster melting in the upper part and hence shorter complete melting time the smaller the HDR. In summary, understand these relationships is crucial for optimizing heat transfer processes in industrial applications.