Non-dimensional Representation Research Articles

A dimensionless heat transfer coefficient for free convection that is more appropriate than Nusselt number

Heat transfer in flows created by buoyancy, or natural convection, is a widely studied topic across various disciplines spanning natural flows as well as those with engineering applications. The convective heat transfer rate on a surface is commonly represented by the Nusselt number (Nu), a ratio of convective to diffusive transport, expressed often as RanPrm, where Ra is the Rayleigh number, the buoyancy forcing parameter, and Pr the Prandtl number. Motivated by the observation that n∼1/3 for turbulent convection, which implies the heat flux is independent of the length scale (L, characteristic length related to the geometry), we propose an alternate and physically more meaningful non-dimensional heat transfer parameter, denoted by Cq. Cq is derived using only the near wall variables and does not contain L. For n=1/3, Cq is constant. Even for laminar convection, where n∼1/4, Cq∼Ra−1/12, a weak function of Ra. We show that for natural convection over several geometries and a wide range of Ra, the Cq values within a narrow range while the corresponding Nu values span several orders of magnitude. We also show that Cq is akin to the non-dimensional representation of wall shear stress, skin friction coefficient Cf. We believe that just like Cf, Cq will be an equally useful non-dimensional measure of heat transfer in natural convection flows.

Oscillatory and transient role of heat transfer and magnetic flux around magnetic-driven stretching cylinder under convective boundary conditions

The magnetic outcomes are frequently implemented for assessing fluid specifications around stretching magnetized surfaces and energy producing technology of thermodynamics. Magnetohydrodynamic reactors and magneto-hydrodynamic generators are two primary methods for producing magnetic flux through ionized fluids along a warmed and magnetized stretched surface. The desired outcomes of the current work are to investigate magnetic flux and heat transmission in the presence of convective boundary conditions using an electrically-conducting fluid over a stretchable cylinder. Most of the parameters are considered in the discussion with intensity and variance due to time dependent methodology. The suggested fluctuating dynamic computational framework is formulated for associated forms of coupled model under boundary variables. The appropriate non-dimensional variables are used to transform the complicated mathematical expression into a non-dimensional representation. To make the non-dimensional representation easier to work for efficient statistical calculations, it is reduced further. Later, for a variety of variables, significant computations are performed via the implicit finite difference methodology. The main finding of current communication is to explore the prominent slip effect in temperatures for every Biot number around all positions. From a physical standpoint, the phenomenon was predictable since surface heat flux is employed as sporting source to increase heat transmission in electric-conducting fluids. For every possible angle, the field of magnetism increases with minimal intensity of surface heat flux. Since, magnetizing functions referred to as an insulating layer that diminishes high temperatures across surfaces and fluids.

Oscillatory and Periodical Behavior of Heat Transfer and Magnetic Flux along Magnetic-Driven Cylinder with Viscous Dissipation and Joule Heating Effects

Several primary mechanisms are less utilized in engineering and recent technologies due to unsustainable heating. The impact of viscous dissipation and Joule heating is very important to examine current density and heat rate across a magnetized cylinder. The key objective of this examination was to insulate excessive heat around the cylinder. The present effort investigated the impact of viscous dissipations, Joule heating, and magnetohydrodynamics (MHD) on the transitory motion of convective-heat transport and magnetic flux features of dissipative flows throughout a magnetized and warmed cylinder at suitable places. The suggested turbulent dynamical structure of mathematics is offered for an associated method of partial differentiation equations impacted by boundary values. The complex equations are translated via non-dimensional shapes by using relevant non-dimensional numbers. The non-dimensional representation has been improved to make it easier to conduct uniform computational calculations. The computational answers for these linked dimensionalized formulations have been achieved using the Prandtl coefficient Pr, Joule heating parameter ζ, Eckert number Ec, the magneto-force number ξ, the buoyancy parameter λ, and multiple additional predefined factors. The important contribution of this work is based on non-fluctuating solutions that are utilized to examine the oscillating behavior of shearing stress, rate of fluctuating heat transport, and rate of fluctuating magnetic flux in the presence of viscous dissipation and Joule heating at prominent angles. It is shown that the velocity of a fluid increases as the buoyancy parameter increases. The maximum frequency of heat transmission is illustrated for each Eckert variable.

Effectiveness of Stefan blowing on MHD slip flow of Prandtl–Eyring nanofluid over an elongating sheet with activation energy and viscous-Ohmic dissipation

This work examines the Stefan blowing effect on the magnetized stagnation point flow of Prandtl–Eyring nanoliquid along a nonlinear elongating surface under the influence of numerous slips. In this study, the impressions of internal heat sources, nonlinearly varying radiation, activation energy with binary chemical reactions, viscous dissipation, and Joule dissipation are taken into account. The thermal flux associated with thermal radiation is computed using Rosseland’s approximation for an optically thick environment. The controlling dimensional mathematical equations are transformed into nondimensional representations using appropriate similarity transmissions. Numerical temperature, velocity, and concentration solutions are obtained using a shooting method based on secant iteration and the Runge–Kutta–Fehlberg method. Using tabular and graphical displays of numerical data, the physical effects of a number of relevant parameters on the nanoliquid temperature, velocity, and concentration are examined. By contrasting the current results with information that has already been published for a few limiting circumstances, the validity of the acquired results is demonstrated. The effects of physical features on the local surface drag coefficient, rates of mass and heat transfer are demonstrated using numerical data shown in tabular form. For increasing values of the Stefan blowing parameter, fluid velocity decreased. The fluid temperature tends to rise as a result of thermal radiation.

Second law analysis on Ree-Eyring nanoliquid and Darcy Forchheimer flow through a significant stratification in the gyrotactic microorganism

PurposeThe modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.Design/methodology/approachIncorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.FindingsThe authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.Originality/valueAccording to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

Time‐dependent mixed convection of Prandtl–Eyring hybrid nanofluid flow over a vertical cone: Entropy analysis

AbstractThe current work is motivated by the rising applications of non‐Newtonian hybrid nanofluids and entropy optimization in large‐scale industries. The Prandtl–Eyring nanofluid model, one of the numerous non‐Newtonian fluid models, is developed using molecular theory rather than empirical formulas. This study investigates the mixed convection flow of Prandtl–Eyring nanofluids from a vertical conical surface. This problem's governing equations are highly nonlinear and linked. Mangler's nonsimilar transformations were used to obtain a nondimensional representation of the governing equations. The obtained equations were linearized and discretized using Quasilinearization and the implicit finite difference method. This study concludes that, compared to Newtonian fluids, Prandtl–Eyring fluids have reduced surface friction and fluid velocity. When comparing the Prandtl–Eyring hybrid nanofluid to the Newtonian hybrid nanofluid, we find that the latter improves energy transmission by about 11%. With the Prandtl–Eyring hybrid nanofluid model instead of the standard Newtonian model, entropy generation (EG) can be reduced. Energy transport efficiency is improved by changing the nanoparticles shape from spherical to lamina. Concisely at , the and boosted approximately by 29% and 17%, respectively, when shapes of the nanoparticles are changed from spherical to the lamina. The findings of heat transfer strength and surface friction coefficient are in excellent agreement with previously reported data.

Propagation characteristics of an elastic bar coupled with a discrete snap-through element

Wave propagation characteristics of an elastic bar coupled at one end with a single degree of freedom, bi-stable, essentially nonlinear snap-through element are considered. The free end of the bar is subjected to sinusoidal excitations. A novel approach based on multiple time scales and harmonic balance method has been proposed to analytically investigate the reflected wave from the nonlinear interface and the dynamic response of the snap-through element. A unified approach to the non-dimensional representation of the governing equations of motion, boundary conditions and system parameters, which is consistent across all the externally applied excitation frequencies and excitation amplitudes, has been developed. Through Taylor series expansion of the non-autonomous forcing functions arising in the governing differential equations and natural boundary condition about an initial stable configuration of the system and the proposed asymptotic method, approximate closed-form analytical solutions have been derived for sufficiently small amplitudes of the excitation pulse. Numerical results obtained through a finite difference algorithm validate the asymptotic model for the same small amplitudes of the excitation pulse. A stability analysis has been subsequently performed for the discrete snap-through element by using the extended Floquet theory for sufficiently large amplitudes of the excitation pulse by approximating the displacement at the nonlinear interface as a sinusoidal function of time, and the Mathieu plot of the excitation frequency vs the excitation amplitude showing the stable and unstable regions for the motion of the snap-through element has been generated. The expressions derived here give the most comprehensive and consistent description of the wave propagation characteristics and the motion of the snap-through element, which can be directly used in finite difference analysis over a wide range of parameter values of the excitation pulse.

Numerical solution of Rosseland’s radiative and magnetic field effects for Cu-Kerosene and Cu-water nanofluids of Darcy-Forchheimer flow through squeezing motion

ObjectiveThe goal of this research is to examine the effects of a squeezing motion of magnetohydrodynamic (MHD), Darcy–Forchheimer nanofluids that comprises Copper nanoparticles suspended in kerosene fluid and Copper nanoparticles in host fluid water flow. Rosseland’s radiative flux and viscous dissipation are taken into account. The Rosseland approximation's thermal radiation is a factor in the energy equation. Squeeze test are usually use to determine the rheological properties of highly viscous nanofluid. Squeezing motion of Cu/water and Cu/Kerosene investigates the viscosity of nanofluids which is essential for the determining the thermo-fluidic behavior of heat transfer fluids. MethodologyThe governing mathematical model is simplified via the boundary layer assumptions and then translated into non-dimensional representations by suitable transformations. A numerical approach named bvp4c is used to get the solutions of the governing ODEs with given values of physical parameters. Bvp4c is finite difference code implementing in Lobatto IIIa techniques. A collected polynomial through Lobbato IIIa solver yields a C1-continous results which is convergent in the integration interval up to fourth order accuracy. The flow and energy characteristics through relevant parameters have been analyzed in graphical and tabulation representation. Different characteristics, such as skin friction and the Nusselt number, are taken into account while calculating velocity and temperature profiles. ResultsThe outcomes indicate that squeezing parameter slow down the flow field in the case of sheets are far away from each other, when both sheets come closer, velocity rise for the squeezing quantity. In the presence of squeezing motion of plates, the temperature rises significantly when volume fractions range is high. Local Nusselt values are much higher for Cu-Kerosene as compared to Cu-water while taking volume fraction with other physical parameters.

Influence of the DCB/Wedge beam kinematics on the identification of the cohesive parameters of interfaces

DCB and Wedge tests are widely used in experimental fracture mechanics in order to identify fracture properties of materials or assembled parts, like toughness. In order to extract data from those experiments, it is very common to model the sample as two adhesive beams with a crack growing in between as an external loading is applied. This study is devoted to investigating the influence of two types of beam kinematics on the identification of the cohesive zone parameters of interfaces. A critical comparison between beam models based on an Euler–Bernoulli or a Timoshenko beam kinematics is carried out in the case of the DCB and Wedge loaded DCB tests. The size of the process zone extent is used as a parameter to evaluate the difference between the two models predictions. Euler–Bernoulli kinematics neglects the effect of shear stress on the beam’s deflection whereas Timoshenko kinematics accounts for it. The aim of the present work is to evaluate the validity of each kinematics, both used in the literature, especially when the process zone length becomes comparable to the specimen’s height. In both frameworks, an analytical prediction is presented and compared over a wide range of cohesive zone parameters and beam geometries, using a non-dimensional representation. Our results show that when we compare both kinematics in term of the fracture process zone, the relative error varies from a few percent to more than 1000%, depending on the specimen’s geometry, properties and the loading conditions. In addition, for many cases, no Euler–Bernoulli kinematics can fit the Timoshenko kinematics, especially around the fracture process zone. The cases for which Timoshenko and Euler–Bernoulli kinematics yield similar results are highlighted. The model and the results of the study can be used as a guideline for users in order to determine which model is required in order to get an accurate determination of the cohesive parameters in their particular system of interest.

Numerical study of the combustion regimes in naturally-vented compartment fires

Numerical simulations are performed to investigate the classical compartment fire problem involving a single door opening. Three different configurations were considered, namely a full-scale (ISO 9705), an intermediate and a small-scale enclosure with various opening heights and widths. A large number of numerical simulations was carried out using the CFD code Fire Dynamics Simulator (FDS)(version 6.7.0). Based on the variation of the average temperature inside the compartment, three combustion regimes were identified namely well-ventilated, transitional and under-ventilated regime. This variation also allowed us to identify the boundaries between regimes. Furthermore, by adopting a non-dimensional representation of the fire heat release rate inside the compartment as a function of the Global Equivalence Ratio (GER), a clear demarcation between these combustion regimes was obtained. A linear correlation has been established between the maximum heat release rate inside the compartment and the ventilation factor. The latter is expressed as Q̇inmax=850AH. A linear relation between the maximum air flow rate ṁin and the ventilation factor AH was found, i.e. ṁinmax=0.46AH where A is the door surface area and H its height.

Bounded dissipation predicts finite asymptotic state of near-wall turbulence

Enormous efforts have been devoted to the prediction and control of turbulent wall flows. A primary consideration here is the Reynolds number scaling problem in which non-dimensional representations are sought that render the normalized variables of interest unchanged for varying Reynolds number. Relative to this objective and in contrast to the mean velocity, there remains a considerable lack of clarity associated with the apparent failure of inner normalization (i.e. using the friction velocity and kinematic viscosity) when applied to the statistical profiles of fluctuating quantities in the near-wall region. In their present work Chen & Sreenivasan (J. Fluid Mech., vol. 933, 2022, A20) generalize their earlier effort, Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, R3), and present a rational framework for characterizing and describing the evolution of turbulence quantities that either attain a near-wall peak or have non-zero wall values. Their analysis enjoys considerable empirical support. Physically, the asymptotic boundedness of the inner-normalized dissipation is used to reason that there is a limiting state of near-wall turbulence at asymptotically large Reynolds numbers. The law of bounded dissipation arguments put forth by Chen and Sreenivasan prescribe the recovery of inner scaling and suggest new possibilities regarding the physics of how wall turbulence matures to its asymptotic state.

Investigation of thermal evolution and fluid flow in the hot-end of a material extrusion 3D Printer using melting model

This work presents Computational Fluid Dynamics (CFD) simulations of the thermal evolution and fluid flow in the hot-end during material extrusion in fuse filament fabrication (FFF) additive manufacturing. The hot-end is the most fundamental and complex part of a FFF 3D printer. The fluid dynamics during material extrusion depend on the hot-end design while the printing speed depends on the speed at which the hot-end can melt the filament. In this work, a new melting model developed specifically for the FFF process is introduced. The CFD melting model incorporated the liquid fraction evolution to account for the presence of an air gap between the liquefier wall and the solid filament. For the first time, the thermal contact resistance was implemented using a melting model. The governing transport equations for the melting model were presented both in the dimensional primitive and non-dimensional primitive representations to understand the relevance of each term in a physical sense. The model equations were implemented with the aid of written user-defined function (UDF) codes coupled in the ANSYS Fluent. The grids were refined systematically to ensure that the influence of the mesh size on the computational results is minimized. The Richardson extrapolation technique was used to estimate the grid convergence index (GCI) and to quantify discretization error. The maximum discretization error is found to be 1.68%, which is an indication that the solution is in the asymptotic range. The thermal boundary conditions were implemented using simple liquid fraction-heat transfer coefficient relation and the results were validated using previously measured feeding force by Serdeczny et al. [1]. The predicted feeding force agrees reasonably with the measured feeding force. The model predicted a strong counter-clockwise recirculating vortex close to the barrel inlet. The further simulation revealed that the filament did not melt immediately at entry into the heated barrel, and variation in the barrel length indicates that the solid penetration depth ratio increases with an increase in the P é clet-number ( Pe ). Since high-speed 3D printing depends on the flow rate, an optimized thermal dissipation is desired in the hot-end. Our approach in presenting the model equations and subsequent results obtained should advance the understanding of the flow characteristics in the liquefier hot-end and thermal history within the barrel and the nozzle exit. Hence, the presented melt flow dynamics model would help in developing hot-end designs for 3D printers capable of melting filaments at an improved rate, by reducing the barrel length and printing at a higher liquefier temperature, while preheating the solid filament. • A new CFD melting model developed specifically for the FFF process is introduced. • Thermal contact resistance was implemented using the CFD melting model. • Effect of the air gap between the filament and the liquefier wall was implemented. • The true position of the melting front at the liquefier center was identified. • CFD Grid Sensitivity Analysis reveals solution is within the asymptotic limits.

Measurements of void fraction, liquid temperature and velocity under boiling two-phase flows using thermal-anemometry

Forced convective boiling is of great interest for several applications in the power and process industry, particularly in nuclear plants. Under certain nominal, incidental or accidental conditions, boiling crisis (considering Departure from Nucleate Boiling as well as Dry-Out) may lead to mechanical damage of the heated surface. An accurate prediction of the conditions leading to the occurrence of this phenomenon is then essential. It is believed that such an objective cannot be reached unless a good and accurate description of the associated two-phase flow is provided. In our work, we propose to use thermal anemometry for measuring the void fraction, the liquid temperature and liquid velocity for high pressure and high temperature Freon R134A boiling flow. Experiments have been conducted in a circular tube whose inner diameter and length are 19.2 mm and 3.5 m, respectively. The tube is heated by Joule effect. The sensor (hot-wire d5μm) has been operated with the Constant Current mode (CCA) and the multiple overheating method, which is classical for gas measurements but seems to be very innovative for liquid flows. This method, has been used to access simultaneously the liquid velocity and temperature. To consider for temperature effect on velocity calibration, a new non-dimensional representation of the calibration curve has been proposed. The frequency response of the probe has also been improved using a digital compensation method. The method has been first checked for single-phase flows and has shown that it was possible to get very accurate measurements of both mean and fluctuating liquid and temperature profiles. For boiling flows, a specific two-steps approach has been developed to first measure the void fraction where it is necessary to set a high overheat ratio leading to boiling on the wire surface and secondly to measure the liquid temperature and velocity for the case where boiling on the wire surface is not acceptable due to the multiple overheating method. An innovative method using probability density functions has been adapted from the pioneering work of Delhaye (1969).Some tests have been conducted for boiling flows and the experimental results have been compared to previous ones using thermocouples and optical probes for respectively the liquid temperature and the void fraction. The experimental uncertainties have been carefully analyzed and they are estimated to be close to 0.5 °C for the liquid temperature, ±2% for the void fraction (absolute uncertainty) and ± 5% for the liquid velocity (relative velocity). Those data aim to be used for NEPTUNE_CFD code validation.

Exact transcendental stiffness matrices of general beam-columns embedded in elastic mediums

Stiffness matrices of beams embedded in an elastic medium and subjected to axial forces are considered. Both the bending and the axial deformations have been incorporated. Two approaches for deriving the element stiffness matrix analytically have been proposed. The first approach is based on the direct force–displacement relationship, whereas the second approach exploits shape functions within the finite element framework. The displacement function within the beam is obtained from the solution of the governing differential equation with suitable boundary conditions. Both approaches result in identical expressions when the exact transcendental displacement functions are used. Exact closed-form expressions of the elements of the stiffness matrix have been derived for the bending and axial deformation. Depending on the nature of the axial force and stiffness of the elastic medium, seven different cases are proposed for the bending stiffness matrix. A unified approach to the non-dimensional representation of the stiffness matrix elements and system parameters that are consistent across all the cases has been developed. Through Taylor-series expansions of the stiffness matrix coefficients, it is shown that the classical stiffness matrices appear as an approximation when only the first few terms of the series are retained. Numerical results shown in the paper explicitly quantify the error in using the classical stiffness compared to the exact stiffness matrix derived in the paper. The expressions derived here gives the most comprehensive and consistent description of the stiffness coefficients, which can be directly used in the context of finite element analysis over a wide range of parameter values.

Development and Evaluation of an ODE Representation of 3D Subsurface Tile Drainage Flow Using the HLM Flood Forecasting System

AbstractWe developed a new ordinary differential equation (ODE) to represent subsurface flows from a hillslope with artificial subsurface drainage (tiling) into an adjacent channel. Our ODE is based on a derived storage‐discharge relationship from high‐resolutions HYDRUS3D simulations that solve 3D partial differential Richards' equations for a hillslope (plot scale) with internal drainage surfaces, variable soil depth, hydraulic conductivity, and varying slope in the direction of flow. The ODE does not capture the hysteresis in the storage‐drainage relation that can only be captured using partial differential equations (PDEs), however the simplification does not have major impacts on the modeled flows. The nondimensional representation of the equation is consistent with, and provides an explanation for, the empirical equation used in classical hydrological models such as the ARNO (Arno River) and Variable Infiltration Capacity (VIC) model to simulate subsurface flows, which removes the need for parameter calibration. Our equation captures the features not captured by other ODE simplifications such as DRAINMOD. The ODE can be coupled to the Hillslope Link Model (HLM) flood forecasting system allowing real‐time regional simulation of streamflow fluctuations and floods over large domains. We show that (i) the new equation improves the capability to model watershed scale hydrograph recessions and to better capture the timing above flood thresholds for multiple spatial scales from 0.1 to 18,000 km2; (ii)using realistic values of slope combined with typical values of tile separation and soil depth provides good predictive power at gauged basin outlets; and (iii) parameters can be derived for particular situations using the 3D PDE framework.

Simultaneous measurements of liquid velocity and temperature for high pressure and high temperature liquid single phase flows

Forced convective boiling is of great interest for several applications in the power and process industry, particularly in nuclear plants. Under certain nominal, incidental or accidental conditions, boiling crisis (Departure from Nucleate Boiling) may occur resulting in the melting of the heated surface. An accurate prediction of the conditions leading to the occurrence of this phenomenon is then essential. We believe that such an objective unreachable unless one provides a good and accurate description of the associated two-phase flow. To achieve this goal, local parameters e.g. void fraction, vapor and liquid velocities, liquid temperature…, need to be measured within the range of interest, which mainly concerns the high pressure and high temperature convective boiling flows. In this work, we only focus on the liquid velocity and temperature measurements and we propose to use thermal anemometry for performing such measurements. However, due to the high complexity of those flows, we have developed a two-steps strategy. Indeed, before using such an experimental technic for boiling flows, we need first to check the feasibility of this method for characterizing single-phase heated flows. Measurements for boiling flows will be performed in a second step, which is beyond the scope of the present paper. We applied the multiple overheating method for simultaneous measurement of the liquid velocity and the liquid temperature using a single sensor. If this methodology has already been used for gas flows measurements (Bestion et al., 1983; Barre et al., 1992, 1994), as far as we know, this work is the first attempt for liquid flows. We conducted experiments in a circular heated tube whose inner diameter and length are 19.2 mm and 3.5 m, respectively. The sensor (hot wire d~5 µm) has been operated with the Constant Current mode (CCA). To consider for temperature effect on velocity calibration, we proposed a new non-dimensional representation of the calibration curve. We also improve the frequency response of the probe using a digital compensation method. Preliminary tests for single-phase flows confirmed that it was possible to get very accurate measurements of mean and fluctuating liquid velocity profiles as well as mean temperature profiles. We have carefully analyzed the experimental uncertainties, which are close to 0.5 °C for the liquid temperature and ±5% for the liquid velocity.

Has the iPhone cannibalized the iPad? An asymmetric competition model

AbstractProduct cannibalization is a well‐known phenomenon in marketing, describing the case when a new product steals sales from another product under the same brand. A special case of cannibalization may occur when the older product reacts to the competitive strength of the newer one, absorbing the corresponding market shares. We show that such cannibalization occurred between two Apple products, the iPhone and the iPad, and the first has succeeded at the expense of the second. We propose an innovation diffusion model for asymmetric competition, Lotka‐Volterra with asymmetric competition, allow to test the presence and the extent of the inverse cannibalization phenomenon. A nondimensional representation of the model helps showing the effects of cannibalization on life cycle length.

Visualization of Hydraulic Cylinder Dynamics by a Structure Preserving Nondimensionalization

This paper reveals a new simplicity of a nominal hydraulic cylinder model whose original representation suffers from too many physical parameters. The eight-dimensional (8-D) parameter space in the original representation is reduced to a 3-D parameter space in the proposed nondimensional representation while preserving the parametric structure. To clarify comprehensive relations between the nonlinear dynamics and many physical parameters, an advanced direct search approach is suggested. More precisely, we can repeat the fast computation of the nonlinear dynamics and the updates of only three parameters without verifying any new simulator. The efficient visualization of the numerical solutions presents the best possible result corresponding to the analytical solution.

Further results on the fast computation of a class of hydro-mechanical systems

This paper updates the fast computation method for a class of hydro-mechanical systems. First, a Casimir based simplified representation and a structure preserving nondimensional representation are introduced. Second, based on the two representations, a new Casimir based nondimensional representation is proposed. Finally, in comparison with other representations, the validity of the proposed representation is confirmed with respect to the computation time

Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach

This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.