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1.
This paper introduces a new model for the Fourier law of heat conduction with the time-fractional order to the generalized Maxwell fluid. The flow is influenced by magnetic field, radiation heat, and heat source. A fractional calculus approach is used to establish the constitutive relationship coupling model of a viscoelastic fluid. We use the Laplace transform and solve ordinary differential equations with a matrix form to obtain the velocity and temperature in the Laplace domain. To obtain solutions from the Laplace space back to the original space, the numerical inversion of the Laplace transform is used. According to the results and graphs, a new theory can be constructed. Comparisons of the associated parameters and the corresponding flow and heat transfer characteristics are presented and analyzed in detail. 相似文献
2.
A model of the equations of a generalized thermoelasticity (GT) with relaxation times for a saturated porous medium is given
in this article. The formulation can be applied to the GT theories: Lord–Shulman theory, Green–Lindsay theory, and Coupled
theory for the porous medium. A two-dimensional thermoelastic problem that is subjected to a time-dependent thermal/mechanical
source is investigated with the model of the generalized porous thermoelasticity. By using the Laplace transform and the Fourier
transform technique, solutions for the displacement, temperature, pore pressure, and stresses are obtained with a semi-analytical
approach in the transform domain. Numerical results are also performed for portraying the nature of variations of the field
variables. In addition, comparisons are presented with the corresponding four theories. 相似文献
3.
岩土介质非稳态热固结耦合问题的热源函数法 总被引:9,自引:1,他引:9
考虑耦合效应的饱和土体热固结问题控制方程,利用Fourier变换、Laplace变换给出其在变换域上的解,将初始温度场分布视为虚拟的热源或者将热源等价为特定的初始温度分布,利用热源函数法给出瞬时线热源非稳态温度场、应力场和位移场的解析求解方法,通过在时间域和空间域上进行积分,给出有初始温度场分布以及有分布内热源存在且热源强度随时间变化条件下的热固结问题计算方法。对一无限大物体内存在有平面矩形域热源情况下周围介质的温度、孔隙水压力以及位移等的变化特征进行分析。研究表明,热源函数法可有效地求解一系列复杂情况下的热固结问题。 相似文献
4.
M. A. Ezzat A. A. El-Bary A. S. Hatem 《Journal of Applied Mechanics and Technical Physics》2014,55(4):660-671
A technique of the state space approach and the inversion of the Laplace transform method are applied to dimensionless equations of an unsteady one-dimensional boundary-layer flow due to heat and mass transfer through a porous medium saturated with a viscoelastic fluid bounded by an infinite vertical plate in the presence of a uniform magnetic field is described. Complete analytical solutions for the temperature, concentration, velocity, and induced magnetic and electric fields are presented. The inversion of the Laplace transforms is carried out by using a numerical approach. The proposed method is used to solve two problems: boundary-layer flow in a viscoelastic fluid near a vertical wall subjected to the initial conditions of a stepwise temperature and concentration and viscoelastic fluid flow between two vertical walls. The solutions are found to be dependent on the governing parameters including the Prandtl number, the Schmidt number, the Grashof number, reaction rate coefficient, viscoelastic parameter, and permeability of the porous medium. Effects of these major parameters on the transport behavior are investigated methodically, and typical results are illustrated to reveal the tendency of the solutions. Representative results are presented for the velocity, temperature, concentration, and induced magnetic and electric field distributions, as well as the local skin-friction coefficient and the local Nusselt and Sherwood numbers. 相似文献
5.
AbstractEnlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added. 相似文献
6.
The thermopiezoelectricity problem of a one-dimensional (1-D), finite length, functionally graded medium excited by a moving
heat source is investigated in this paper. The Lord and Shulman theory of generalized coupled thermoelasticity is employed
to account for both the finite speed of thermal waves and coupling of temperature field with displacement and electric fields.
Except thermal relaxation time and specific heat, which are taken to be constant for simplicity, all other properties are
assumed to vary exponentially along the length through an arbitrary non-homogeneity index. Laplace transform has been used
to eliminate the time effect, and three coupled fields, namely, displacement, temperature, and electric fields are obtained
analytically in the Laplace domain. The solutions are then inverted to time domain using a numerical Laplace inversion method.
Numerical examples are displayed to illustrate the effects of non-homogeneity index, length and thermal relaxation time on
the results. When the medium is homogeneous, the results of the current paper are reduced to exactly the same results available
in the literature. 相似文献
7.
Horizontal well pressure analysis in box-bounded reservoirs 总被引:1,自引:0,他引:1
8.
9.
An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate
channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the
lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum
equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain
temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower
and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers
and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the
values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between
the lower or upper walls while the fluid is flowing in the channel. 相似文献
10.
This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method. 相似文献
11.
This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted. 相似文献
12.
M. F. Selivanov 《International Applied Mechanics》2010,46(7):799-805
The time variation in the stresses around an elliptic hole in a composite plate is studied. Solutions that characterize the
effect of the time dependence of the relaxation moduli of the composite components on stresses are obtained. The solutions
in the time domain are obtained from the elastic–viscoelastic analogy and the corresponding elastic solutions for the effective
moduli of the composite and the stress field around an elliptic hole in an anisotropic plate. The inverse Laplace transformation
is carried out by an effective numerical method 相似文献
13.
Exact analytical solutions for an equation describing advection, dispersion, first-order decay, and rate-limited sorption
of a solute in a steady, hemispherical or spherically symmetric, divergent flow field are presented for constant concentration
and constant flux boundary conditions in a porous medium. The partial differential equation describing transport is a confluent
hypergeometric equation that may be solved with variable substitution and Laplace transform, and the solutions are expressed
by parabolic cylindrical functions. The novel solutions derived here may be applied to predict concentration distributions
in space and time for porous media transport in a spherically symmetric flow field or for the special case where injection
is just below a confining layer (hemispherical flow). The analytical solutions can be used to simulate wastewater injection
from short-screened wells into thick formations or to analyze tracer tests that use short-screened wells to create approximately
spherical flow fields in thick formations. 相似文献
14.
Behrouz Gatmiri Pooneh Maghoul Denis Duhamel 《International Journal of Solids and Structures》2010,47(5):595-610
In this paper, the closed form two-dimensional fundamental solutions for a non-isothermal unsaturated deformable porous medium have been derived for a symmetric polar domain in both Laplace transform and time domains. The governing differential equations of the non-isothermal unsaturated soil consist of equilibrium, moisture, air and heat transfer equations including the suction effect, temperature effect and dissolved air in water. The derived fundamental solution has been verified mathematically by comparison with the previously presented corresponding fundamental solutions in three limiting cases including the steady-state thermo-hydro-mechanical, steady-state hydro-mechanical and elastostatic fundamental solutions. Also these 2D kernel functions are tested in comparison with a finite element method (FEM). 相似文献
15.
Combined heat and mass transfer in free, forced, and mixed convection flows along a porous wedge with a magnetic effect in
the presence of a chemical reaction is investigated. The flow field characteristics are analyzed with the Runge—Kutta—Gill
method in conjunction with the shooting method, and local nonsimilarity method. The governing boundary-layer equations are
written in a dimensionless form with the use of the Falkner—Skan transformations. Owing to the effect of the buoyancy force,
the power law of temperature and concentration, and suction/injection on the wall of the wedge, the flow field is locally
nonsimilar. Numerical calculations up to the third-order level of truncation are carried out for different values of dimensionless
parameters as a special case. Effects of the magnetic field strength in the presence of a chemical reaction with a variable
wall temperature and concentration on the dimensionless velocity, temperature, and concentration profiles are shown graphically.
Comparisons with previously published works are performed, and excellent agreement between the results is obtained. 相似文献
16.
An analysis has been made which describes the moisture migration in an unsaturated semi-infinite porous medium under the influence of periodic variation of the surface temperature. For the case of constant transport properties, this combined heat and mass transfer problem is governed by only one dimensionless group — the Luikov number K/αs. Numerical solutions of the energy and moisture conservation equations yielded temperature and moisture fields. The presentation of results provides the distributions of the dimensionless moisture content as a function of dimensionless distance measured from the surface of the semi-infinite medium and time with the Luikov number as a parameter. This parameter was varied in the range of 0.1 to .004. Because of an error in the pictorial presentation of the temperature field in the literature, these results were reproduced. It was found that the moisture fluctuations penetrate to a considerably smaller depth in the porous material than the temperature fluctuations, and that this penetration depth increases with increasing value of the Luikov number. An example demonstrates that the annual temperature fluctuations cause only small fluctuations of the moisture content in a sandy soil. The penetration depth of the moisture is also smaller than that of the temperature. 相似文献
17.
Theoretical investigations were performed on the developed laminar flow and convective heat transfer characteristics for incompressible
gases flow through rectanglar micropassages with constant wall heat flux. Mathematical models were proposed for considering
the change in viscosity and thermal conductivity of gas in the wall-adjacent region from the kinetic theory. The dimensionless
velocity distribution and corresponding pressure drop, the dimensionless temperature distribution and corresponding heat transfer
characteristics were both simulated numerically, and the results were compared to other report simulations [10–12] with brief
discussions. 相似文献
18.
In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration
of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are
proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using
Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established. 相似文献
19.
A new method for solving Biot's consolidation of a finite soil layer in the cylindrical coordinate system 总被引:3,自引:0,他引:3
A new method is developed to solve Biot's consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot's consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface (z = 0) and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms. 相似文献
20.
The article describes the unsteady motion of viscoelastic fluid for a Maxwell model with fractional derivatives. The flow is produced by cylinder, considering time dependent quadratic shear stress ft2 on Maxwell fluid with fractional derivatives. The fractional calculus approach is used in the constitutive relationship of Maxwell model. By applying Laplace transform with respect to time t and modified Bessel functions, semianalytical solutions for velocity function and tangential shear stress are obtained. The obtained semianalytical results are presented in transform domain, satisfy both initial and boundary conditions. Our solutions particularized to Newtonian and Maxwell fluids having typical derivatives. The inverse Laplace transform has been calculated numerically. The numerical results for velocity function are shown in Table by using MATLAB program and compared them with two other algorithms in order to provide validation of obtained results. The influence of fractional parameters and material constants on the velocity field and tangential stress is analyzed by graphs. 相似文献