scholarly journals Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

2020 ◽  
Vol 9 (1) ◽  
pp. 156-168
Author(s):  
Seyed Mahdi Mousavi ◽  
Saeed Dinarvand ◽  
Mohammad Eftekhari Yazdi
Keyword(s):  
Boundary Layer ◽  
Equilibrium Model ◽  
Second Order ◽  
Model Parameters ◽  
Slip Parameter ◽  
Two Phase ◽  
Convective Boundary ◽  
First Order ◽  
Special Cases ◽  
Two Component

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

Derivation of Turbulent Kinetic Energy from a First-Order Nonlocal Planetary Boundary Layer Parameterization

2013 ◽  
Vol 70 (6) ◽  
pp. 1795-1805 ◽  
Author(s):  
Hyeyum Hailey Shin ◽  
Song-You Hong ◽  
Yign Noh ◽  
Jimy Dudhia
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Planetary Boundary Layer ◽  
Water Cycle ◽  
Convective Boundary ◽  
First Order ◽  
Eddy Simulation ◽  
Pbl Parameterization ◽  
Planetary Boundary Layer Parameterization

Abstract Turbulent kinetic energy (TKE) is derived from a first-order planetary boundary layer (PBL) parameterization for convective boundary layers: the nonlocal K-profile Yonsei University (YSU) PBL. A parameterization for the TKE equation is developed to calculate TKE based on meteorological profiles given by the YSU PBL model. For this purpose buoyancy- and shear-generation terms are formulated consistently with the YSU scheme—that is, the combination of local, nonlocal, and explicit entrainment fluxes. The vertical transport term is also formulated in a similar fashion. A length scale consistent with the K profile is suggested for parameterization of dissipation. Single-column model (SCM) simulations are conducted for a period in the second Global Energy and Water Cycle Experiment (GEWEX) Atmospheric Boundary Layer Study (GABLS2) intercomparison case. Results from the SCM simulations are compared with large-eddy simulation (LES) results. The daytime evolution of the vertical structure of TKE matches well with mixed-layer development. The TKE profile is shaped like a typical vertical velocity (w) variance, and its maximum is comparable to that from the LES. By varying the dissipation length from −23% to +13% the TKE maximum is changed from about −15% to +7%. After normalization, the change does not exceed the variability among previous studies. The location of TKE maximum is too low without the effects of the nonlocal TKE transport.

Global energetics of fast magnetic reconnection

1988 ◽  
Vol 40 (3) ◽  
pp. 505-515 ◽  
Author(s):  
M. Jardine ◽  
E. R. Priest
Keyword(s):  
Steady State ◽  
Total Energy ◽  
Second Order ◽  
Weakly Nonlinear ◽  
First Order ◽  
Weakly Nonlinear Theory ◽  
Special Cases ◽  
Pile Up ◽  
Different Types ◽  
Converging Flow

We examine the global energetics of a recent weakly nonlinear theory of fast steady-state reconnection in an incompressible plasma (Jardine & Priest 1988). This is itself an extension to second order of the Priest & Forbes (1986) family of models, of which Petschek-like and Sonnerup-like solutions are special cases. While to first order we find that the energy conversion is insensitive to the type of solution (such as slow compression or flux pile-up), to second order not only does the total energy converted vary but so also does the ratio of the thermal to kinetic energies produced. For a slow compression with a strongly converging flow, the amount of energy converted is greatest and is dominated by the thermal contribution, while for a flux pile-up with a strongly diverging flow, the amount of energy converted is smallest and is dominated by the kinetic contribution. We also find that the total energy flowing out of the downstream region can be increased either by increasing the external magnetic Mach number Me or the external plasma beta βe Increasing Me also enhances the variations between different types of solutions.

scholarly journals Development of FOPDT and SOPDT model from arbitrary process identification data using the properties of orthonormal basis function

2018 ◽  
Vol 7 (2.21) ◽  
pp. 77 ◽  
Author(s):  
Lalu Seban ◽  
Namita Boruah ◽  
Binoy K. Roy
Keyword(s):  
Basis Function ◽  
Delay Time ◽  
Orthonormal Basis ◽  
Control Point ◽  
Second Order ◽  
Step Test ◽  
Step Response ◽  
Order System ◽  
Model Parameters ◽  
First Order

Most of industrial process can be approximately represented as first-order plus delay time (FOPDT) model or second-order plus delay time (FOPDT) model. From a control point of view, it is important to estimate the FOPDT or SOPDT model parameters from arbitrary process input as groomed test like step test is not always feasible. Orthonormal basis function (OBF) are class of model structure having many advantages, and its parameters can be estimated from arbitrary input data. The OBF model filters are functions of poles and hence accuracy of the model depends on the accuracy of the poles. In this paper, a simple and standard particle swarm optimisation technique is first employed to estimate the dominant discrete poles from arbitrary input and corresponding process output. Time constant of first order system or period of oscillation and damping ratio of second order system is calculated from the dominant poles. From the step response of the developed OBF model, time delay and steady state gain are estimated. The parameter accuracy is improved by employing an iterative scheme. Numerical examples are provided to show the accuracy of the proposed method. 

scholarly journals Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 306 ◽  
Author(s):  
Juan Liang ◽  
Linke Hou ◽  
Xiaowu Li ◽  
Feng Pan ◽  
Taixia Cheng ◽  
...  
Keyword(s):  
Euclidean Space ◽  
Orthogonal Projection ◽  
Second Order ◽  
Dimensional Euclidean Space ◽  
Order Method ◽  
Order Convergence ◽  
Initial Value ◽  
Parametric Curve ◽  
First Order ◽  
Special Cases

Orthogonal projection a point onto a parametric curve, three classic first order algorithms have been presented by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, H-H-H method). In this research, we give a proof of the approach’s first order convergence and its non-dependence on the initial value. For some special cases of divergence for the H-H-H method, we combine it with Newton’s second order method (hereafter, Newton’s method) to create the hybrid second order method for orthogonal projection onto parametric curve in an n-dimensional Euclidean space (hereafter, our method). Our method essentially utilizes hybrid iteration, so it converges faster than current methods with a second order convergence and remains independent from the initial value. We provide some numerical examples to confirm robustness and high efficiency of the method.

Reflection and transmission approximations for monoclinic media with a horizontal symmetry plane

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. C13-C36 ◽  
Author(s):  
Song Jin ◽  
Alexey Stovas
Keyword(s):  
Order Approximation ◽  
Symmetry Plane ◽  
Second Order ◽  
Model Parameters ◽  
Reflection And Transmission ◽  
Model Parameter ◽  
First Order ◽  
Background Medium ◽  
Horizontal Symmetry ◽  
Parametric Analyses

We have considered a horizontal plane interface bounded by two monoclinic half-spaces to approximate the reflection and transmission (R/T) responses normalized by the vertical energy flux. We assume the monoclinic media have a horizontal symmetry plane, and the exact R/T coefficients can be analytically obtained for P-, S1-, and S2-waves. The exact R/T coefficients depend on the absolute model parameters of both half-spaces, whereas the R/T responses indicate the heterogeneity at the interface and, thus, can be characterized with model parameter contrasts across the interface. Compared with the exact R/T solutions, appropriate approximations with desirable accuracy can be determined by fewer model parameter contrasts and facilitate the parametric analyses and inversions. We first consider the weak-contrast assumption and use the perturbation method to obtain first-order approximations based on the homogeneous monoclinic background medium. To accommodate the strong-contrast interface, the published second-order approximations are then revised for the monoclinic media. For weakly anisotropic media, the first- and second-order approximations are proposed based on the isotropic background medium. Two pseudowaves are introduced as intermediate waves to legitimize our approximations for S1, S2, and converted waves in the applications. The derived approximations are verified on monoclinic models numerically. The second-order approximation method based on the monoclinic background medium is proven to have the overall best accuracy.

The Flow of a Laminar, Incompressible Jet Along a Parabola

1972 ◽  
Vol 39 (1) ◽  
pp. 13-17 ◽  
Author(s):  
A. Plotkin
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
External Flow ◽  
Boundary Layer Theory ◽  
Second Order ◽  
Wall Jet ◽  
Governing Equations ◽  
Displacement Effect ◽  
First Order ◽  
External Stream

The flow of a laminar, incompressible jet along a parabola in the absence of an external stream is analyzed using the techniques of second-order boundary-layer theory. The first-order solution is the Glauert wall-jet solution. Second-order corrections in the jet due to the effects of curvature and displacement are obtained numerically after the external flow is corrected to account for the displacement effect. The shear stress at the wall is calculated and it appears that for values of the Reynolds number at which the governing equations are valid the jet does not separate from the parabola.

Non-similar solution of free convective flow of power law nanofluids in porous medium along a vertical cone and plate with thermal and mass convective boundary conditions

2015 ◽  
Vol 93 (10) ◽  
pp. 1144-1155 ◽  
Author(s):  
W.A. Khan ◽  
M. Jashim Uddin ◽  
A.I.M. Ismail
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Power Law ◽  
Similar Solution ◽  
Convective Boundary Conditions ◽  
Concentration Increase ◽  
Vertical Cone ◽  
Convective Boundary ◽  
Special Cases

This paper investigates non-similar solution of free convective boundary layer flow of a viscous incompressible fluid along a vertical cone and plate embedded in a Darcian porous medium filled with power law non-Newtonian nanofluids. The effects of the thermal and mass convective boundary conditions are taken into account, which makes the present analysis practically applicable. The governing boundary layer equations are converted into a system of non-similar differential equations by using suitable transformations before being solved numerically. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, and the local Nusselt and Sherwood numbers are reported. It is found that the velocity, temperature, and concentration increase with mass transfer velocity for both the vertical plate and cone. Further, the velocity reduces whilst the temperature and concentration increase with increasing buoyancy ratio parameter for all three types of nanofluids in the case of both geometries. The local Nusselt and the local Sherwood numbers are found to be higher for dilatant nanofluids than pseudoplastic nanofluids and Newtonian fluids in each case. The numerical results for special cases are compared with the published data and an excellent agreement has been found.

scholarly journals Dark holograms and gravitational waves

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Francesco Bigazzi ◽  
Alessio Caddeo ◽  
Aldo L. Cotrone ◽  
Angel Paredes
Keyword(s):  
Phase Transitions ◽  
Gravitational Waves ◽  
Chiral Symmetry Breaking ◽  
Power Spectra ◽  
Model Parameters ◽  
Sound Waves ◽  
Critical Temperatures ◽  
Two Phase ◽  
First Order ◽  
First Order Phase

Abstract Spectra of stochastic gravitational waves (GW) generated in cosmological first-order phase transitions are computed within strongly correlated theories with a dual holographic description. The theories are mostly used as models of dark sectors. In particular, we consider the so-called Witten-Sakai-Sugimoto model, a SU(N) gauge theory coupled to different matter fields in both the fundamental and the adjoint representations. The model has a well-known top-down holographic dual description which allows us to perform reliable calculations in the strongly coupled regime. We consider the GW spectra from bubble collisions and sound waves arising from two different kinds of first-order phase transitions: a confinement/deconfinement one and a chiral symmetry breaking/restoration one. Depending on the model parameters, we find that the GW spectra may fall within the sensibility region of ground-based and space-based interferometers, as well as of Pulsar Timing Arrays. In the latter case, the signal could be compatible with the recent potential observation by NANOGrav. When the two phase transitions happen at different critical temperatures, characteristic spectra with double frequency peaks show up. Moreover, in this case we explicitly show how to correct the redshift factors appearing in the formulae for the GW power spectra to account for the fact that adiabatic expansion from the first transition to the present times cannot be assumed anymore.

scholarly journals Omnibus Modeling of Listeria monocytogenes Growth Rates at Low Temperatures

Foods ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 1099
Author(s):  
Vincenzo Pennone ◽  
Ursula Gonzales Barron ◽  
Kevin Hunt ◽  
Vasco Cadavez ◽  
Olivia McAuliffe ◽  
...  
Keyword(s):  
Growth Rate ◽  
Listeria Monocytogenes ◽  
Case Fatality ◽  
Second Order ◽  
Lag Phase ◽  
Model Parameters ◽  
Growth Data ◽  
Temperature Growth ◽  
First Order ◽  
Primary Model

Listeria monocytogenes is a pathogen of considerable public health importance with a high case fatality. L. monocytogenes can grow at refrigeration temperatures and is of particular concern for ready-to-eat foods that require refrigeration. There is substantial interest in conducting and modeling shelf-life studies on L. monocytogenes, especially relating to storage temperature. Growth model parameters are generally estimated from constant-temperature growth experiments. Traditionally, first-order and second-order modeling (or primary and secondary) of growth data has been done sequentially. However, omnibus modeling, using a mixed-effects nonlinear regression approach, can model a full dataset covering all experimental conditions in one step. This study compared omnibus modeling to conventional sequential first-order/second-order modeling of growth data for five strains of L. monocytogenes. The omnibus model coupled a Huang primary model for growth with secondary models for growth rate and lag phase duration. First-order modeling indicated there were small significant differences in growth rate depending on the strain at all temperatures. Omnibus modeling indicated smaller differences. Overall, there was broad agreement between the estimates of growth rate obtained by the first-order and omnibus modeling. Through an appropriate choice of fixed and random effects incorporated in the omnibus model, potential errors in a dataset from one environmental condition can be identified and explored.

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