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1.
Toupin-Berdichevskii Theorem can't be considered as a mathematical expression of Saint-Venant's Principle 总被引:1,自引:0,他引:1
赵建中 《应用数学和力学(英文版)》1986,7(10):971-974
In this paper the condition and the conclusion of Toupin-Berdichevskii Theorem is examined, whereby it is explained and demonstrated with an example that the theorem can't be considered as a mathematical expression of Saint-Venant's Principle in Elasticity. 相似文献
2.
M. ASHRAF N. JAMEEL K. ALI 《应用数学和力学(英文版)》2013,34(10):1263-1276
A study is presented for magnetohydrodynamics (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing. 相似文献
3.
In this paper, the steady boundary layer flow and heat transfer of a micropolar fluid on an isothermal continuously moving plane surface is studied analytically. It is assumed that the microinertia density is variable and the viscous dissipation effect is taken into account. The system of nonlinear ordinary differential equations is solved analytically using the homotopy analysis method (HAM) and the results are obtained for various flow and heat transfer characteristics. By using HAM, accurate analytic series solutions are obtained in the whole spatial region. Also, a new suggestion for choosing the proper value of the auxiliary parameter ? in the convergence region is proposed. It is observed that the present solutions have higher accuracy when the residual error is obtained. The present results show that this algorithm is effective and can be similarly applied to other nonlinear equations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, the unsteady three‐dimensional boundary layer flow due to a stretching surface in a viscous and incompressible micropolar fluid is considered. The partial differential equations governing the unsteady laminar boundary layer flow are solved numerically using an implicit finite‐difference scheme. The numerical solutions are obtained which are uniformly valid for all dimensionless time from initial unsteady‐state flow to final steady‐state flow in the whole spatial region. The equations for the initial unsteady‐state flow are also solved analytically. It is found that there is a smooth transition from the small‐time solution to the large‐time solution. The features of the flow for different values of the governing parameters are analyzed and discussed. The solutions of interest for the skin friction coefficient with various values of the stretching parameter c and material parameter K are presented. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
5.
In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields. 相似文献
7.
The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case,the homotopy analysis method (HAM) is used. to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu's model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects. 相似文献
8.
Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Hiickel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the mi- crocapillary, while the couple stress tensor is uniform across the cross-section. 相似文献
9.
Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical mi... 相似文献
10.
The present paper investigates the steady flow of an Oldroyd-B fluid. The fluid flow is induced by an exponentially stretched surface. Suitable transformations reduce a system of nonlinear partial differential equations to a system of ordinary differential equations. Convergence of series solution is discussed explicitly by a homotopy analysis method (HAM). Velocity, temperature and heat transfer rates are examined for different involved parameters through graphs. It is revealed that for a larger retardation time constant, the velocity is enhanced and the temperature is lowered. It is noted that relaxation time constant and the Prandtl number enhance the heat transfer rate. 相似文献
11.
Summary A Theoretical analysis is carried out to study the boundary-layer flow over a continuously moving surface through an otherwise
quiescent micropolar fluid. The transformed boundary-layer equations are solved numerically for a power-law surface velocity
using the Keller-box method. The effects of the micropolar K and exponent m parameters on the velocity and microrotation field as well as on the skin-friction group are discussed in a detailed manner.
It is shown that there is a near-similarity solution of this problem. The accuracy of the present solution is also discussed.
Accepted for publication 1 April 1996 相似文献
12.
This paper examines the magnetohydrodynamic boundary layer flow of Jeffrey fluid due to a rotating disk. The governing partial differential equations are first transformed into the coupled system of ordinary differential equations and then solved by using the homotopy analysis method. The influence of various involved physical parameters on the dimensionless radial and azimuthal velocities is sketched and analyzed. The variation of skin friction coefficients in radial and azimuthal directions is studied for various values of pertinent parameters. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
13.
This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically. 相似文献
14.
I. A. Hassanien H. M. El-Hawary M. A. A. Mahmoud R. G. Abdel-Rahman A. S. Elfeshawey 《应用数学和力学(英文版)》2013,34(6):703-720
The aim of this paper is to study the thermal radiation effects on the flow and heat transfer of an unsteady magnetohydrodynamic (MHD) micropolar fluid over a vertical heated nonisothermal stretching surface in the presence of a strong nonuniform magnetic field. The symmetries of the governing partial differential equations are de- termined by the two-parameter group method. One of the resulting systems of reduced nonlinear ordinary differential equations are solved numerically by the Chebyshev spec- tral method. The effects of various parameters on the velocity, the angular velocity, and the temperature profiles as well as the skin-friction coefficient, the wall couple stress co- efficient, and the Nusselt number are studied. 相似文献
15.
In this paper, we reconsider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. The resulting boundary‐value problem is solved analytically by the homotopy analysis method. The accuracy of the present solution is found to be in excellent agreement with the solutions of Cheng (Int. Commun. Heat Mass Transfer 2006; 33 :627–635). Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
16.
An analytical solution to the famous Falkner-Skan equation for the magnetohydrodynamic (MHD) flow is obtained for a special
case, namely, the sink flow with a velocity power index of −1. The solution is given in a closed form. Multiple solution branches
are obtained. The effects of the magnetic parameter and the wall stretching parameter are analyzed. Interesting velocity profiles
are observed with reversal flow regions even for a stationary wall. These solutions provide a rare case of the Falkner-Skan
MHD flow with an analytical closed form formula. They greatly enrich the analytical solution for the celebrated Falkner-Skan
equation and provide better understanding of this equation. 相似文献
17.
T.HAYAT.MUSTAFA.A.HENDI 《应用数学和力学(英文版)》2011,2(32):167-178
This article studies the three-dimensional boundary layer flow of an elasticoviscous luid over a stretching surface. Velocity of the stretching sheet is assumed to be ime-dependent. Effect of mass transfer with higher order chemical reaction is further onsidered. Computations are made by the homptopy analysis method (HAM). Convergence f the obtained series solutions is explicitly analyzed. Variations of embedding arameters on the velocity and concentration are graphically discussed. Numerical computations f surface mass transfer are reported. Comparison of the present results with he numerical solutions is also given. 相似文献
18.
This article studies the three-dimensional boundary layer flow of an elasticoviscous fluid over a stretching surface. Velocity
of the stretching sheet is assumed to be time-dependent. Effect of mass transfer with higher order chemical reaction is further
considered. Computations are made by the homptopy analysis method (HAM). Convergence of the obtained series solutions is explicitly
analyzed. Variations of embedding parameters on the velocity and concentration are graphically discussed. Numerical computations
of surface mass transfer are reported. Comparison of the present results with the numerical solutions is also given. 相似文献
19.
An analysis is carried out to study the unsteady magnetohydrodynamic (MHD) two-dimensional boundary layer flow of a second grade viscoelastic fluid over an oscillatory stretching surface. The flow is induced due to an infinite elastic sheet which is stretched back and forth in its own plane. For the investigated problem, the governing equations are reduced to a non-linear partial differential equation by means of similarity transformations. This equation is solved both by a newly developed analytic technique, namely homotopy analysis method (HAM) and by a numerical method employing the finite difference scheme, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The results obtained by means of both methods are then compared and show an excellent agreement. The effects of various parameters like visco-elastic parameter, the Hartman number and the relative frequency amplitude of the oscillatory sheet to the stretching rate on the velocity field are graphically illustrated and analysed. The values of wall shear stress for these parameters are also tabulated and discussed. 相似文献
20.
A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through von Karman’s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing. 相似文献