Nondimensionalization Technique Research Articles

Exploring the Dynamic Behavior of a Tapered Stenosed Artery: An Investigation into Its Unsteady Model

In this communication, blood flow is considered in a two-phase model of the tapered stenosed artery. Non-Newtonian and Newtonian models are considered in inner and outer regions, respectively. The transverse magnetic field is applied externally on the presumed pulsatile flow of blood to examine the nature of blood flow. It is anticipated that, in the inner region, blood follows the Jeffrey fluid model, and in the outer region, it follows the Bingham Plastic fluid model. The mathematical model of this system is formulated, a non-dimensionalization technique is used, and a numerical solution is obtained using the Finite difference method, one of the most suitable numerical methods for the formulated problem. The expressions for the primary/fundamental characteristics in determining the effect of blood flow are developed to explore the consequence of hematocrit, time component, tapering angle, and magnetic field. Scilab software is employed for mathematical simulations, revealing that flow characteristics within a stenosed artery undergo significant alterations, while the presence of a magnetic field aids in partially regulating the flow characteristics.

Further insights into steady three-dimensional MHD Sakiadis flows of radiating-reacting viscoelastic nanofluids via Wakif’s-Buongiorno and Maxwell’s models

AbstractKeeping in mind the stress relaxation tendency of many viscoelastic multi-phase flows (e.g., polymer solution flows and transport phenomena of red cell suspensions within blood media), the present research investigation intends principally to develop a realistic model for revealing properly the aspects of reacting-radiating Maxwell nanofluids during their laminar boundary layer flows in the steady regime over a horizontal impermeable surface under a transversal magnetic influence. For this purpose, the principal leading differential formulation is derived theoretically by linking Wakif’s-Buongiorno approach with Maxwell’s model. By invoking fundamentally the general boundary layer assumptions and the passive control strategy for the nanoparticles, the governing PDEs’ formulation is simplified accordingly and then stated properly for the case of the convective heating condition at the impermeable bi-stretching surface. By executing a feasible non-dimensionalization technique, the monitoring ODEs’ system is achieved successfully, whose solutions are presented precisely in different illustrative scenarios using Richardson’s extrapolation method. After carrying out successfully several validating tests, it is demonstrated that the weakly viscoelastic feature has generally a slight delaying effect on the nanofluid motion. This dynamical weakening can be reinforced more with the generation of thermal energy by intensifying the external magnetic field source. Additionally, these physical factors show an intensifying influence on the surface drag forces. However, a dropping impression is seen for the local heat transfer at the contact surface. Contrary to the broadening impact of the radiative heat transfer as well as the convective heating and thermophoresis mechanisms on the thermal and mass boundary layer regions, it is witnessed that the first-order chemical reaction mechanism and Brownian’s motion exhibit a shrinking impact on the mass boundary layer region.

A Universal Graphical Solution to Calculating Seepage in Excavation of Anisotropic Soils and Non-Limited Scenarios

The interaction between groundwater and civil engineering works is a key aspect in geotechnical design. In the case of excavations confined in sheet pile walls, steel sheeting, diaphragm walls, cut-off walls, or cofferdams, this design requires the estimation, among other soil mechanics properties, of the groundwater flowing into the excavation (seepage) caused by piezometry depletion. Numerical methods, graphical solutions, and analytical procedures are the methodologies traditionally used to solve this issue, solutions of which require an understanding of basic soil mechanical properties, hydraulic conditions and structure geometry. In this work, the discriminated non-dimensionalization technique is applied to obtain, for the first time, the dimensionless groups that govern the seepage, in anisotropic conditions, in large-scale scenarios where groundwater flow is not conditioned by impervious bedrock or the length of the back of the wall: π1=ab,π2=kxb2kyc2 and, π3=T/b. Numerical simulations are carried out to check the validity of dimensionless groups and to develop three sets of type curves that relate to these groups. Once the physical and geometrical data are known, the seepage (Q), the characteristic depth (T*) and the characteristic horizontal extension (L*) can be directly and easily calculated from these abacuses. The influence of anisotropy on the characteristic lengths is also addressed.

Mathematical Modeling and Analysis Using Nondimensionalization Technique of the Solidification of a Splat of Variable Section

In this work, the solidification and cooling process of an irregularly shaped splat is modeled using the network simulation method. The procedure for its implementation, which uses the finite difference method and optimized circuit analysis algorithms, allows the precise incorporation and assessment of the effect of certain conditions in the thermal process, offering its specificity and high performance in numerical simulation. It should be noted, on the one hand, that the geometry used for the simulation has been obtained from experimental splat data visualized using an electron microscope and, on the other hand, that the model implements both the phase change phenomenon and the variability of the material properties with temperature. Finally, the study of the physical behavior of the problem is carried out using the mathematical technique of nondimensionalization, allowing the interpretation of the results obtained by simulation, where the formation of horizontal bars and columns that maintain the structure of the splat while the solidification process is taking place stands out. It is worth highlighting the obtaining, among others, of two monomials. The first relates the phenomenon of radiation to conduction and is equivalent to the Nusselt number with convection, and the second relates the solidification time with the Stefan number.

An Application of Inverse Problem and Universal Solutions for Pumping Wells in Unconfined Aquifers

As far as we know, universal solutions (or type-curves) for scenarios of flow through anisotropic unconfined aquifers due to pumping wells cannot be found in the literature. On the contrary, those theoretical solutions in hydrogeological manuals are commonly based on Dupuit solutions for isotropic soils or simplifying other characteristics of the chosen medium. In this study, the application of the discriminated nondimensionalization technique allowed for the inclusion of vertical and radial hydraulic conductivities in the data set, with which the monomials ruling unknown variables of the problem, pumping flow and seepage surface in their dimensionless form are obtained. One of the main findings of this research is depicting these relationships as type-curves from a large number of precise numerical simulations based on the Network Simulation Method. The other main finding is an easy-to-apply methodology to estimate vertical and radial hydraulic conductivities employing these type-curves. This methodology can be considered as an inverse problem. In addition, an example of the problem is presented, in which the influence that measure deviations may have on the estimated values of the hydraulic conductivities in anisotropic soils is also studied and discussed.

Mathematical Model to Calculate Heat Transfer in Cylindrical Vessels with Temperature-Dependent Materials

In this article, a mathematical model capable of simulating the heat transfer of cylindrical vessels whose properties are dependent on temperature is proposed. As a case study, it compares, from an approach of their heat transfer and chemical migration characteristics as a function of the temperature reached, different materials commonly used for the manufacture of water bottles. More specifically, the materials studied were aluminium, polyethylene terephthalate, and polypropylene. The validation of the model consists of an experiment carried out in the laboratory with three water bottles of each of the materials under study, as well as simulations using the Network Simulation Method to recreate the heat transfer that occurs through the walls of the bottles. On the other hand, the nondimensionalization technique is also applied, which allows us to obtain the weight of each of the variables on the problem, as well as the existing relationship between them. Finally, an outside temperature of 30 °C to 50 °C is simulated, which is a common temperature range in southern Europe during the summer season, and an initial temperature of 20 °C for the water contained in the bottle to know the behaviour of the materials and what the final temperature of the water would be after one hour.

Characterization of Flow under Impervious Dams: Dimensionless Groups and Universal Solutions

As far as we know, no dimensionless solutions for infiltrated flow under dams in anisotropic media exist since those that can be found in manuals refer to isotropic soils. The novelty of this work is the presentation of universal solutions in the form of abaci for water flow, average exit gradient, uplift force, and its application point for this type of soil. These solutions are obtained by the application of the discriminated nondimensionalization technique to the governing equations in order to find accurate dimensionless groups that control the results of the problem. In particular, the ratio of permeabilities corrected by a geometrical aspect relationship appears as a governing group, so anisotropy can be considered as input information. In this way, the sought solutions are a function of the emerging groups. Numerical solutions are used to successfully verify the results obtained, which in turn are compared to those of other authors for isotropic scenarios.

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

This study attempts to provide an approach to studying the nonlinear stability of a vertical cylindrical interface between two Oldroyd-B prototypes. An unchanged axial electric field influences the system, and porous medium, and the effects of heat and mass transfer (MHT) are considered. Hsieh's modulation and the viscous potential flow (VPT) are used to abbreviate the mathematical analysis. The viscoelastic Oldroyd-B model significant role in geothermal, engineering and industrial enhancement motivated us to carry out this in-depth investigation. The methodology of the nonlinear technique depends mainly on solving the linear equations of motion and applying the appropriate nonlinear boundary conditions. Numerous non-dimensional physical numbers are exposed using a non-dimensional technique. The stability conditions are theoretically achieved and numerically verified. As a limiting case, the linear dispersion equation is accomplished, and a set of stability diagrams is reachable. Together with the nonlinear stability method, a Ginzburg–Landau equation is derived. Subsequently, both theoretical and numerical methods are used to achieve the nonlinear stability criteria. Furthermore, a precise perturbed approach for surface deflection is achieved theoretically and numerically using the Homotopy perturbation method and the extended frequency conception. Along with the linear approach, it is found that the structure becomes unstable by the Laplace, Reynolds, Weber, and elasticity quantities as well as the linear MHT parameter. Furthermore, the stability zones are enhanced in the nonlinear instability approach.

Modification and Its Application of Identification Inputs for Hydraulic Arms

This paper discusses an identification input for nominal hydraulic arms. First, we focus on an input-output nonlinearity which exists even in the absence of nonlinear friction and prevents us from observing and measuring the input-output behaviors. Second, we propose a new identification input based on the physical parameters of hydraulic arms via the special nondimensionalization technique. Third, we show the effectiveness of the new identification input experimentally. Finally, we show an application of the proposed new identification input to observe and measure the input-output behaviors. Especially, in the frequency domain, we identify the uncertainty that was impossible for the conventional identification input.

Scrutinization of entropy on MHD Eyring–Powell C71500–Ti6Al4V nanoparticles suspended in a C2H6O2−H2O hybrid base fluid with heat generation

AbstractMicroporous channels are extensively elaborated technologies in a variety of engineering, and scientific applications, for example, microelectromechanical systems that are useful in developing the heat exchangers in miniaturized products such as heat sinks of the microchannel, micromixtures, and fuel cells of miniaturized products. Hybrid nanofluids have a better thermal performance as compared to the nanofluid. Based on this, the present study aims to concentrate on the magnetohydrodynamics Powell–Eyring hybrid nanofluid flow in a vertical porous channel with the aspects of porous medium, magnetism, convective condition, dissipation energy, heat generation, and radiation. A nondimensional technique is applied to alter the governing equations into a nonlinear system of ordinary differential ones that contain the convective boundary condition. The RKF 4–5th order method coupled with the shooting method has been utilized to find the numerical solution. From the perspective of numerical results, it is clear that the entropy generation boosts up for Grashof number, Biot number, and radiation parameter and it is the minimum for magnetism, Darcy number, and Eyring–Powell parameters. The comparison of results has been performed and it provides an excellent agreement.

Performance evaluation of venturi aeration system

The venturi aeration is an effective practice to increase the dissolved oxygen accessibility in the water bodies. This study aims to optimize the various geometrical parameters of the venturi aeration system. A non-dimensional technique was applied to find the optimum performance of various geometric parameters i.e. throat lengths (tl), number of air holes (N), and converging and diverging angles (α and β). These experiments have been carried out using 1124 L capacity of tank having dimensions of 105 cm long, 105 cm wide and 102 cm deep. The experiments were conducted at a constant flow velocity of water (1.096 m/s) with varying throat length (tl = 20–100 mm keeping 20 mm as interval between two consecutive length), number of air holes (N = 1–17 at an equal hole to hole distance of 5 mm between them), and converging and diverging angles (α and β = 10°, 15°, 20° and 25°). Multiple non-linear regression equations were also developed from the linear relation with the dependent variable (Non-dimensional form of standard aeration efficiency, NDSAE) and independent variables (tl and N). With the geometrically optimized venturi aerator the optimum performance was found for tl =100 mm, N = 17, and α and β = 15°. The maximum value of standard oxygen transfer rate (SOTR) and standard aeration efficiency (SAE) obtained was 0.0216 kgO2/h and 0.611 kgO2/kWh respectively. From the non-dimensional study, it was found that the NDSAE is the function Reynolds number (Re) and Froude number (Fr). The simulation equations were developed on the basis of Re and Fr for NDSAE, and subjected to 7.378 × 10−6 <Re < 3.689 × 10-5 and 0.163 <Fr < 0.817, respectively.

Numerical simulation of a prostate tumor growth model by the RBF-FD scheme and a semi-implicit time discretization

The aim of this work consists of finding a suitable numerical method for the solution of the mathematical model describing the prostate tumor growth, formulated as a system of time-dependent partial differential equations (PDEs), which plays a key role in the field of mathematical oncology. In the literature on the subject, there are a few numerical methods for solving the proposed mathematical model. Localized prostate cancer growth is known as a moving interface problem, which must be solved in a suitable stable way. The mathematical model considered in this paper is a system of time-dependent nonlinear PDEs that describes the interaction between cancer cells, nutrients, and prostate-specific antigen (PSA). Here, we first derive a non-dimensional form of the studied mathematical model using the well-known non-dimensionalization technique, which makes it easier to implement different numerical techniques. Afterward, the analysis of the numerical method describing the two-dimensional prostate tumor growth problem, based on radial basis function-generated finite difference (RBF-FD) scheme, in combination with a first-order time discretization has been done. The numerical technique we use, does not need the use of any adaptivity techniques to capture the features in the interface. The discretization leads to solving a linear system of algebraic equations solved via the biconjugate gradient stabilized (BiCGSTAB) algorithm with zero-fill incomplete lower–upper (ILU) preconditioner. Comparing the results obtained in this investigation with those reported in the recent literature, the proposed approach confirms the ability of the developed numerical scheme. Besides, the effect of choosing constant parameters in the mathematical model is verified by many simulations on rectangular and circular domains.

Dimensionless characterization of the non-linear soil consolidation problem of Davis and Raymond. Extended models and universal curves

Abstract The dimensionless groups that govern the Davis and Raymond non-linear consolidation model, and its extended versions resulting from eliminating several restrictive hypotheses, were deduced. By means of the governing equations nondimensionalization technique and introducing the characteristic time concept, both in terms of settlement and pressures, was obtained (for the most general model) that the average degree of settlement only depends on the dimensionless time while the average degree of pressure dissipation does it, additionally, on the loading ratio. These results allowed the construction of universal curves expressing the solutions of the unknowns of interest in a direct and simple way.

Flow Field Characterization and Visualization of Grid Fin Subsonic Flow

Grid fins are unconventional control surfaces consisting of an outer frame supporting an inner grid of intersecting planar surfaces. Although afflicted with higher drag, these have been credited for their enhanced lifting characteristics at high angles of attack and high Mach numbers, alongside reduced hinge moments accounting for the recent upsurge in their usage on numerous aerospace applications. Present investigations carry out elaborate flow field visualization and characterization underlining the rudimentary physics through a sequence of subsonic numerical simulations performed at different angles of attack and different gap (between the members) to chord ratios on a simplified grid fin variant called cascade fin. The study makes use of a new nondimensionalization technique called cumulative nondimensionalization to decipher the effect of cascading on individual members of the fin. Hence, after a comprehensive examination of the aerodynamic coefficients, pressure coefficient distribution, pressure gradient, velocity gradient, boundary layer velocity profile, and flow field visualization, the study elucidates physics associated with hastened stall angle, augmented lift-drag, and bounded efficiency accretion for gap increment.

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Static analysis of functionally graded thin rectangular plates with various boundary supports

Present study deals with static analysis of functionally graded (FG) rectangular plates subjected to various possible boundary conditions within the framework of classical plate theory. Material properties of the FG plate are assumed to vary continuously in the thickness direction according to power-law form. The trial functions denoting the transverse deflection of the plate are expressed as simple algebraic polynomials. Uniformly distributed load (UDL) and hydrostatic pressure are considered to be the external mechanical loads. Rayleigh–Ritz method along with mechanical kinematic relations and non-dimensionalization technique are employed in the numerical modeling to obtain the system of linear equations for the pure bending. Here the main objective is to study the effect of aspect ratio and volume fraction of the constituents on numerical factors associated with centroidal deflection, bending moments and normal stresses. New results for these factors are presented after checking the convergence pattern and validation has been done with the available results in special cases.

Soft material adhesion characterization for in vivo locomotion of robotic capsule endoscopes: Experimental and modeling results

The objective of this work is to validate an experimental method and nondimensional model for characterizing the normal adhesive response between a polyvinyl chloride based synthetic biological tissue substrate and a flat, cylindrical probe with a smooth polydimethylsiloxane (PDMS) surface. The adhesion response is a critical mobility design parameter of a Robotic Capsule Endoscope (RCE) using PDMS treads to provide mobility to travel through the gastrointestinal tract for diagnostic purposes. Three RCE design characteristics were chosen as input parameters for the normal adhesion testing: pre-load, dwell time and separation rate. These parameters relate to the RCE׳s cross sectional dimension, tread length, and tread speed, respectively. An inscribed central composite design (CCD) prescribed 34 different parameter configurations to be tested. The experimental adhesion response curves were nondimensionalized by the maximum stress and total displacement values for each test configuration and a mean nondimensional curve was defined with a maximum relative error of 5.6%. A mathematical model describing the adhesion behavior as a function of the maximum stress and total displacement was developed and verified. A nonlinear regression analysis was done on the maximum stress and total displacement parameters and equations were defined as a function of the RCE design parameters. The nondimensional adhesion model is able to predict the adhesion curve response of any test configuration with a mean R2 value of 0.995. Eight additional CCD studies were performed to obtain a qualitative understanding of the impact of tread contact area and synthetic material substrate stiffness on the adhesion response. These results suggest that the nondimensionalization technique for analyzing the adhesion data is sufficient for all values of probe radius and substrate stiffness within the bounds tested. This method can now be used for RCE tread design optimization given a set of environmental conditions for device operation.

Non-dimensional system for analysis equilibrium point mathematical model of tumor growth

In this paper we presented analysis equilibrium point of mathematical model tumor growth use non-dimensional technique. This technique is useful to simply equation that complicated as a mathematical model that present in this paper. This mathematical model describes the effect of tumor infiltrating lymphocytes (TIL) and interleukin-2 (IL-2) on the dynamics of tumor cells. The steps of this technique are presented. With this technique we can be to determine more accurately the equilibria of our system which form nonlinear dynamics of system ordinary differential equation that coupled.

Generation of Series of High Frequency DNI Years Consistent with Annual and Monthly Long-term Averages using Measured DNI Data

In recent years, many researchers are suggesting that statistical approaches are needed to achieve sound estimates of the economic feasibility of commercial Concentrating Solar Thermal Power (CSTP) plants. A key element of such statistical approaches is the capacity of generating large series of high-frequency years which are consistent with the estimated variability of the monthly and annual values of the relevant meteorological variables.This paper presents a method of using high-frequency solar Direct Normal Irradiance (DNI) measurements to generate high frequency DNI series consistent with the variability and distribution of natural series, and also matching monthly and annual long term averages. The method takes advantage of a novel technique for the nondimensionalization of measured high-frequency daily DNI curves. This nondimensionalization technique makes it possible to consistently use measured solar DNI data to generate new daily curves of high-frequency DNI data and the subsequent long series of high-frequency DNI years. The novel technique for the nondimensionalization of measured high-frequency daily DNI curves is based on the nondimensionalization of the temporal scale by dividing the elapsed Universal Time (UT) since sunrise by the total elapsed UT from sunrise to sunset and on the nondimensionalization of the solar DNI scale by dividing each actual solar DNI value by the corresponding DNI value of the clear-day solar DNI envelope curve.

Modeling of Parasitic Fringing Capacitance in Multifin Trigate FinFETs

In this brief, we analyze the effects of geometrical parameters on the parasitic fringing capacitance of sub 22-nm multifin FinFETs. An analytical model is proposed to compute the fringing capacitance using a conformal mapping technique. To minimize the number of model fitting parameters, nondimensionalization technique is used. The proposed model for gate to source/drain fringing capacitance considers the fin number, whether the fin location is at the edge of the gate, and the source/drain pad that connects the fins. The accuracy of this model is verified with a 2- and 3-D field solver, Raphael.