Photothermoelastic Interactions in Silicon Microbeams Resting on Linear Pasternak Foundation Based on DPL Model

2021 ◽  
Author(s):  
Kadry Zakaria ◽  
Magdy A. Sirwah ◽  
Ahmed E. Abouelregal ◽  
Ali F. Rashid
Keyword(s):  
Photogenerated Electron ◽  
Approximation Technique ◽  
Winkler Foundation ◽  
Phase Lag ◽  
Two Phase ◽  
Special Cases ◽  
Elastic Process ◽  
Two Parameters ◽  
Foundation Parameters ◽  
Foundation Parameter

In this work, the photothermal interactions in semiconductor microbeams during the photo-thermo-elastic process have been investigated using the generalized photothermal theory. The proposed mathematical model is constructed based on the Euler–Bernoulli model, the heat equation with two-phase lag and coupled plasma wave equation that indicates the prediction of thermal, elastic and photovoltaic effects in the microbeam resonators. Based on the introduced model, the dynamic influence of thermoelastic photovoltaic microbeam resting on an elastic foundation medium with two parameters has been studied. The Winkler foundation parameter is one of these parameters while the second is the shear foundation parameter. In the field of Laplace transform, the governing equations have been solved while the inverse transforms are found numerically using a tried-and-true approximation technique based on Fourier transform series. The numerical calculations of thermophysical field variables have been discussed and graphically presented. The effects of the magnetic field, Winkler and shear foundation parameters, and lifetime of photogenerated electron have been investigated and studied in detail. Comparisons have been made between the proposed model and previous models that have been derived as special cases from the presented results.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

Formulation of a General Multiphase, Multicomponent Chemical Flood Model

1981 ◽  
Vol 21 (01) ◽  
pp. 63-76 ◽  
Author(s):  
Paul D. Fleming ◽  
Charles P. Thomas ◽  
William K. Winter
Keyword(s):  
Phase Equilibrium ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Field Tests ◽  
Reservoir Rock ◽  
Phase System ◽  
Surfactant Flooding ◽  
Two Phase ◽  
Special Cases ◽  
Flood Model

Abstract A general multiphase, multicomponent chemical flood model has been formulated. The set of mass conservation laws for each component in an isothermal system is closed by assuming local thermodynamic (phase) equilibrium, Darcy's law for multiphase flow through porous media, and Fick's law of diffusion. For the special case of binary, two-phase flow of nonmixing incompressible fluids, the equations reduce to those of Buckley and Leverett. The Buckley-Leverett equations also may be obtained for significant fractions of both components in the phases if the two phases are sufficiently incompressible. To illustrate the usefulness of the approach, a simple chemical flood model for a ternary, two-phase system is obtained which can be applied to surfactant flooding, polymer flooding, caustic flooding, etc. Introduction Field tests of various forms of surfactant flooding currently are under way or planned at a number of locations throughout the country.1 The chemical systems used have become quite complicated, often containing up to six components (water, oil, surfactant, alcohol, salt, and polymer). The interactions of these components with each other and with the reservoir rock and fluids are complex and have been the subject of many laboratory investigations.2–22 To aid in organizing and understanding laboratory work, as well as providing a means of extrapolating laboratory results to field situations, a mathematical description of the process is needed. Although it seems certain that mathematical simulations of such processes are being performed, models aimed specifically at the process have been reported only recently in the literature.23–31 It is likely that many such simulations are being performed on variants of immiscible, miscible, and compositional models that do not account for all the facets of a micellar/polymer process. To help put the many factors of such a process in proper perspective, a generalized model has been formulated incorporating an arbitrary number of components and an arbitrary number of phases. The development assumes isothermal conditions and local phase equilibrium. Darcy's law32,33 is assumed to apply to the flow of separate phases, and Fick's law34 of diffusion is applied to components within a phase. The general development also provides for mass transfer of all components between phases, the adsorption of components by the porous medium, compressibility, gravity segregation effects, and pressure differences between phases. With the proper simplifying assumptions, the general model is shown to degenerate into more familiar special cases. Numerical solutions of special cases of interest are presented elsewhere.35

Thermo-viscoelastic fractional model of rotating nanobeams with variable thermal conductivity due to mechanical and thermal loads

2021 ◽  
pp. 2150297
Author(s):  
Ahmed E. Abouelregal ◽  
Hijaz Ahmad ◽  
Taher A. Nofal ◽  
Hanaa Abu-Zinadah
Keyword(s):  
Thermal Conductivity ◽  
Fractional Derivative ◽  
Integral Transformation ◽  
Nonlocal Parameter ◽  
Dynamic Strength ◽  
Thermodynamic Temperature ◽  
Phase Lag ◽  
Euler Beam ◽  
Two Phase ◽  
Conduction Model

This paper analyzes the thermoelastic dynamic behavior of simply supported viscoelastic nanobeams of fractional derivative type due to a dynamic strength load. The viscoelastic Kelvin–Voigt model with fractional derivative with Bernoulli–Euler beam theory is introduced. The generalized thermoelastic heat conduction model with a two-phase lag is also used. It is assumed that the beam is rotating at a uniform angular velocity and that the thermal conductivity varies linearly depending on the temperature. Due to a variable harmonic heat and retreating time-dependent load, the nanobeam is excited. The Laplace integral transformation technique is used as the solution method. The thermodynamic temperature, deflection function, bending moment, and displacement are numerically calculated. Results of fractional and integer viscoelastic material models are compared. In the studied system, the effect of the nonlocal parameter, viscosity and varying load on the solutions is shown, and the temperature-dependence of the thermal conductivity is analyzed.

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.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

Double-Inclusion Model and Overall Moduli of Multi-Phase Composites

1994 ◽  
Vol 116 (3) ◽  
pp. 305-309 ◽  
Author(s):  
Muneo Hori ◽  
Sia Nemat-Nasser
Keyword(s):  
Ellipsoidal Inclusion ◽  
The Self ◽  
Average Field ◽  
Two Phase ◽  
Homogeneous Domain ◽  
Special Cases ◽  
Self Consistent ◽  
Inclusion Model ◽  
Exact Bounds ◽  
Multi Phase

The double-inclusion model consists of an ellipsoidal inclusion of arbitrary elasticity, containing another ellipsoidal heterogeneity of arbitrary elasticity, size, and orientation, which are embedded in an infinitely extended homogeneous domain of yet another arbitrary elasticity. Average field quantities for the double inclusion are obtained analytically, and used to estimate the overall moduli of two-phase composites. The technique includes the self-consistent and other related methods as special cases. Furthermore, exact bounds for the overall moduli are obtained on the basis of the double-inclusion model. The double-inclusion model has been generalized (Nemat-Nasser and Hori, 1993) to a multi-inclusion model, where, again, all the average field quantities are estimated analytically. The application of the multiinclusion model includes a composite containing inclusions with multi-layer coatings.

APPROXIMATION TO THE LATERAL VARIATION OF RESIDUAL GRAVITY DUE TO A FRUSTUM OF A VERTICAL CONE

Geophysics ◽  
1953 ◽  
Vol 18 (2) ◽  
pp. 401-415
Author(s):  
W. Raymond Griffin
Keyword(s):  
Gulf Coast ◽  
Lateral Variation ◽  
Vertical Cone ◽  
Salt Domes ◽  
Residual Gravity ◽  
Special Cases ◽  
Lateral Distance ◽  
Independent Variable ◽  
The Subject ◽  
Two Parameters

The equation for the subject title is presented in nondimensional form. The approximation consists of considering a frustum of a vertical cone in which the radii are small relative to the depth to its top. The dependent variable has been taken as being the ratio of the residual gravity (as defined in a previous publication by the author) to the maximum residual gravity. The independent variable was chosen as the ratio of the lateral distance (from the center line of the frustum to a given station) to the depth to the top of the frustum. The two parameters were chosen as being (a) The ratio of depth to the bottom of the frustum to that to its top, (b) The ratio of the bottom radius to that of the top radius. It is then shown that, for special values of the parameters, the equation gives the lateral variation of residual gravity due to cylinders, upright cones, and inverted cones as special cases. Tables of the principal functions, which occur in the equation, are given over practical ranges of values. Graphs of the equation are given. They cover the practical range for each of the variables and each of the parameters. Application of the equation is made to two Gulf Coast salt domes whose dimensions are rather well known from previous drilling. Graphs, showing the degree of correlation, are given. The conclusion is drawn that, despite the approximation involved in the derivation of the equation, and despite the departure of the ratio of the dimensions of the salt domes from that assumed, the correlation with the actual gravity values for two deep salt domes is remarkably close.

Compressibility and free convection

1966 ◽  
Vol 293 (1434) ◽  
pp. 395-407 ◽  
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Temperature Difference ◽  
Convection Boundary Layer ◽  
Relative Temperature ◽  
Specific Heats ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Basic Equations ◽  
Two Parameters

The basic equations of laminar compressible flow and heat transfer are applied to the free convection boundary layer along an isothermal plate. Solutions which include the effect of all the parameters involved are given. It is found that in the complete approach, the profiles can not be expressed in terms of one similarity variable and one parameter. The profiles, in dimensionless form, are dependent upon the coordinate along the wall, by means of a compressibility variable suitably defined. In addition to the Prandtl number, two parameters influence the profiles, namely the wall — ambient relative temperature difference and the ratio of specific heats. The effect of the compressibility variable is to increase the heat transfer rate at the wall, for small values of the relative temperature difference, and to decrease it for the large values. The skin friction, however, is always reduced. It is concluded, nevertheless, that as long as the compressibility parameter and the relative temperature difference are not of the same order of magnitude, all such compressibility effects may be neglected. The previous approaches to the free convection problem are shown to be special cases of the general formulation given.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (3) ◽  
pp. 714-716 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

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