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1.
Amin Moosaie 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(8):679-694
The non-Fourier axisymmetric (2+1)-dimensional temperature field within a hollow sphere is analytically investigated by the
solution of the well-known Cattaneo–Vernotte hyperbolic heat conduction equation. The material is assumed to be homogeneous
and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables
method. General linear time-independent boundary conditions are considered. Ultimately, the presented solution is applied
to a (1+1)—as well as a (2+1)—dimensional problem, and their respective non-Fourier thermal behavior is studied. The present
solution can be reduced to special cases of interest by choosing appropriate boundary conditions parameters.
Dedicated to Prof. Gholamali Atefi, with appreciation and admiration on the occasion of his 65th birthday. 相似文献
2.
Antonio Barletta Eugenia Rossi di Schio Leiv Storesletten 《Transport in Porous Media》2010,81(3):461-477
The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries
are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations
with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only
on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution
due to the forced convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution
is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number
and of the Darcy–Rayleigh number are determined numerically by the fourth-order Runge–Kutta method. It is shown that, although
generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy–Rayleigh number for
downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary
temperature difference is discussed. 相似文献
3.
An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature. 相似文献
4.
The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different
boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and
collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of
ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization
and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions
of several types are presented
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 74–85, October 2008. 相似文献
5.
Hyperbolic heat conduction in a plane slab, infinitely long solid cylinder and solid sphere with a time dependent boundary
heat flux is analytically studied. The solution is based on the separation of variables method and Duhamel’s principle. The
temperature distribution, the propagation and reflection of the temperature wave and the effect of geometry on the shape of
the wave front are studied for the case of a rectangular pulsed boundary heat flux. Comparisons with the solution obtained
for Fourier heat conduction are performed by considering the limit of a vanishing thermal relaxation time. 相似文献
6.
Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy–Boussinesq
model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with
fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the
case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall
temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general
analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the
radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature,
and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower
than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its
maximum, no axisymmetric solutions exist.
E. Magyari is on leave from the Institute of Building Technology, ETH—Zürich. 相似文献
7.
A. Ya. Voronov 《Fluid Dynamics》1998,33(3):450-458
An asymptotic representation for the solution of the problem of the radial structure of the internal boundary (transition)
layer and the radial distribution of the basic physical plasma characteristics of the column of a free-burning low-pressure
electric are in He is constructed.
Sarov. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–195, May–June, 1998. 相似文献
8.
A. Ya. Grigorenko O. V. Vovkodav S. N. Yaremchenko 《International Applied Mechanics》2012,48(1):80-93
The stress–strain state of an orthotropic spherical shell with thickness varying in two coordinate directions is analyzed.
Different boundary conditions are considered, and a refined problem statement is used. A numerical analytic method based on
spline-approximation and discrete orthogonalization is developed. The stress–strain state of spherical orthotropic shells
with variable thickness is studied 相似文献
9.
The effects of thermal radiation on laminar-forced and free convection along the wavy surface are studied. The optically thick
limit approximation for the radiation flux is assumed. A modified form for the entropy generation equation is derived. The
effect of geometry (e.g. flat surface, wavy surface), fluid friction and heat transfer (e.g. convection and radiation effects)
are all included in the modified entropy generation form. Prandtl’s transposition theorem is used to stretch the ordinary
coordinate system in certain directions. The wavy surface can be transformed into a calculable planar coordinate system. The
governing equations are derived from the complete Navier–Stokes equations. A simple transformation is proposed to transform
the governing equations into boundary layer equations for solution by the cubic spline collocation method. 相似文献
10.
We study free oscillations of a viscous incompressible fluid with free boundary in a hemispherical tank. We determine four
systems of coordinate functions that satisfy the equations of the problem inside the domain and possess the properties of
the required solution. Then, using these systems, we construct a coordinate system that satisfies all but one boundary condition
of the problem. This system is used for the solution of the problem by a projection method. We compute the eigenfrequencies
and logarithmic decrements of oscillations of the fluid. The results obtained are compared with asymptotic and empirical formulas.
Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 439–461, October–December, 2008. 相似文献
11.
Mohammad Reza Talaee Gholamali Atefi 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(12):1793-1806
Analytical solution of the non-Fourier axisymmetric temperature field within a finite hollow cylinder exposed to a periodic
boundary heat flux is investigated. The problem studied considering the Cattaneo–Vernotte (CV) constitutive heat flux relation.
The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method
of separation of variables is used for solving the problem with time-independent boundary conditions, and the Duhamel integral
is used for applying the time dependency. The solution is applied for the special cases of harmonic uniform heat flux and
an exponentially pulsed heat flux with Gaussian distribution in outer surface for modeling a laser pulse, and their respective
non-Fourier thermal behavior is studied. 相似文献
12.
Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries 总被引:3,自引:0,他引:3
This paper analyzes the convective heat transfer enhancement mechanism of microencapsulated phase change material slurries based on the analogy between convective heat transfer and thermal conduction with thermal sources. The influence of each factor affecting the heat transfer enhancement for laminar flow in a circular tube with constant wall temperature is analyzed using an effective specific heat capacity model. The model is validated with results available in the literature. The analysis and the results clarify the heat transfer enhancement mechanism and the main factors influencing the heat transfer. In addition, the conventional Nusselt number definition of phase change slurries for internal flow is modified to describe the degree of heat transfer enhancement of microencapsulated phase change material slurries. The modification is also consistent evaluation of the convective heat transfer of internal and external flows.c volumetric concentration of microcapsules - cm mass concentration of microcapsules - cp specific heat, kJ kg–1 K–1 - hfs phase change material heat of fusion, kJ kg–1 - hm* modified convective heat transfer coefficient, W m–2 K–1 - k thermal conductivity, W m–1 K–1 - ke effective thermal conductivity of slurry, W m–1 K–1 - kb slurry bulk thermal conductivity, W m–1 K–1 - ML dimensionless initial subcooling - Mr dimensionless phase change temperature range - Nu conventional Nusselt number - Nu* improved Nusselt number - qwn wall heat flux, Wm–2 - Pe Peclet number - Pr Prandtl number - Re Reynolds number - r radial coordinate, m - r0 duct radius, m - r1 dimensionless radial coordinate - Ste Stefan number - T temperature, K - T1 lower phase change temperature limit, K - T2 upper phase change temperature limit, K - Ti slurry inlet temperature, K - u axial velocity, m/s - v radial velocity, m/s - x axial coordinate, m - x1 dimensionless axial coordinate - thermal diffusivity, m2/s - dimensionless temperature - dynamic viscosity, N·s/m2 - kinematic viscosity, m2/s - t width of thermal boundary, m - degree of heat transfer enhancement, = hm*/(hm*)single - b bulk fluid (slurry) - b0 slurry without phase change - l liquid - m mean - s solid - f suspending fluid - p microcapsule particles - w wall - single single-phase fluid 相似文献
13.
A. A. Shutov A. A. Zakhar'yan 《Journal of Applied Mechanics and Technical Physics》1998,39(4):489-492
The problem of the jet flow of an incompressible liquid with free boundaries in an electric field is solved in the approximation
of a laminar boundary layer. An exact solution for a round jet is found in the class of self-similar solutions. In the case
of a flat slit jet, a solution is constructed in the form of a series in powers of the coordinate transverse to the plane
of symmetry. The dependence of the radius (half-width) on the longitudinal coordinate is given.
Branch of the Karpov Physicochemistry Institute, State Science Center, Obninsk 249020. Karpov Physicochemistry Institute,
State Science Center, Moscow 115523. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 12–16,
July–August, 1998. 相似文献
14.
IntroductionInrecentyears,theresearchesoncavitationandcatastropheofacavityhavesuppliedanewmethodforinvestigatingthemechanicso... 相似文献
15.
B. A. Lugovtsov 《Journal of Applied Mechanics and Technical Physics》2000,41(5):870-878
The stability of steady axisymmetricMHD flows of an inviscid, incompressible, perfectly conducting fluid with respect to swirling—perturbations of the azimuthal
components of the velocity field—is studied in a linear approximation. It is shown that for flows similar to a magnetohydrodynamic
Hill-Shafranov vortex, the problem reduces to a one-dimensional problem on a closed streamline of the unperturbed flow (the
arc length of the streamline is the spatial coordinate). A spectral boundary-value eigenvalue problem is formulated for a
system of two ordinary differential equations with periodic coefficients and periodic boundary conditions. Sufficient conditions
under which swirling is impossible are obtained. Numerical solution of the characteristic equation shows that, under certain
conditions, for each streamline there is a real eigenvalue that yields monotonic exponential growth of the initial perturbations.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 120–129, September–October, 2000. 相似文献
16.
W. Q. Chen Y. Lu G. R. Ye J. B. Cai 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(1):39-51
Summary The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The
functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement
and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing
the laminate model, the two state equations are transformed into ones with constant variables from which the state variable
solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces
are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces.
Received 28 February 2001; accepted for publication 26 June 2001 相似文献
17.
N. H. Abu-Hamdeh 《Heat and Mass Transfer》2002,38(7-8):687-693
The analytical solutions of equations describing the dynamics of distributed parameter systems are usually complicated in
form and derivations and inconvenient to use for simulation and control system design. The liquid–liquid counter flow heat
exchanger is an example of these disturbed parameter systems. An analytical solution of the dynamics of a symmetrically operated
counter flow heat exchanger in the form of transfer function matrix is investigated in open-loop and close-loop conditions.
The resulting non-linear model was linearized using perturbation approach. A feed-forward path controller to counteract at
any disturbances in the boundary temperature and a non-interactive controller to decouple the outputs were implemented.
Received on 22 February 2001 / Published online: 29 November 2001 相似文献
18.
The paper proposes a method to analyze the behavior of a mechanical system consisting of an infinite thin cylindrical shell
filled with a flowing compressible liquid and containing a pulsating spherical inclusion. This coupled problem is solved using
linear potential flow theory and the theory of thin elastic shells based on the Kirchhoff–Love hypotheses. Use is made of
the possibility to represent the general solutions of equations of mathematical physics in different coordinate systems. This
makes it possible to satisfy the boundary conditions on both spherical and cylindrical surfaces and to obtain a solution in
the form of a Fourier series. Some numerical results are given 相似文献
19.
A formulation of the problem, a method of solution, and calculated results are considered for flow past the windward side
of a sphere under conditions of an aerodynamic facility (a wind tunnel) with magnetohydrodynamic (MHD) acceleration of the
air flow and the corresponding full-scale flight conditions in the Earth's atmosphere. Calculations were performed on the
basis of numerical solution of Navier-Stokes equations taking into account thermochemical nonequilibrium of air and catalytic
properties of the body surface. Results of the mathematical simulation of flow around a sphere in an MHD-acceleration wind
tunnel are compared with experimental data obtained at the Central Aerohydrodynamic Institute (TsAGI). The problem of recalculation
of experimental data for full-scale conditions is analyzed.
Central Aerohydrodynamic Institute, Zhukovskii 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol.
39, No. 2, pp. 91–102, March–April, 1998. 相似文献
20.
This paper discusses the behavior of g-jitter induced free convection in microgravity under the influence of a transverse
magnetic field and in the presence of heat generation or absorption effects for a simple system consisting of two parallel
impermeable infinite plates held at four different thermal boundary conditions. The governing equations for this problem are
derived on the basis of the balance laws of mass, linear momentum, and energy modified to include the effects of thermal buoyancy,
magnetic field and heat generation or absorption as well as Maxwell's equations. The fluid is assumed to be viscous, Newtonian
and have constant properties except the density in the body force of the balance of linear momentum equation. The governing
equations are solved analytically for the induced velocity and temperature distributions as well as for the electric field
and total current for electrically-conducting and insulating walls. This is done for isothermal–isothermal, isoflux–isothermal,
isothermal–isoflux and isoflux–isoflux thermal boundary conditions. Graphical results for the velocity amplitude and distribution
are presented and discussed for various parametric physical conditions. 相似文献