Applied Mathematics and Mechanics (English Edition)

Analysis of coupled flow-reaction with heat transfer in heap bioleaching processes

吴爱祥刘金枝尹升华王洪江

2010, 31(12): 1473-1480. doi:10.1007/s10483-010-1377-7

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A mathematical model for heap bioleaching is developed to analyze heat transfer, oxygen flow, target ion distribution and oxidation leaching rate in the heap. The model equations are solved with Comsol Multiphysics software. Numerical simulation results show the following facts: Concentration of oxygen is relatively high along the boundary of the slope, and low in the center part where leaching rate is slow. Temperature is relatively low along the slope and reaches the highest along the bottom region near the slope, with difference being more than 6?C. Concentration of target mental ions is the highest in the bottom region near the slope. Oxidation leaching rate is relatively large in the bottom and slope part with a fast reaction rate, and small in the other part with low oxygen concentration.

Soret and Dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation

S.R.VEMPATI A.B.LAXMI-NARAYANA-GARI

2010, 31(12): 1481-1496. doi:10.1007/s10483-010-1378-9

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The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour (diffusion thermo) and Soret (thermal diffusion) effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate (Gr > 0) and the externally heated plate (Gr < 0) to observe the effects of various parameters encountered in the equations.

Unsteady flow and heat transfer of porous media sandwiched between viscous fluids

J.C.UMAVATHI I.C.LIU J.PRATHAP-KUMAR D.SHAIK-MEERA

2010, 31(12): 1497-1516. doi:10.1007/s10483-010-1379-6

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The problem of unsteady oscillatory flow and heat transfer of porous media sandwiched between viscous fluids has been considered through a horizontal channel with isothermal wall temperatures. The flow in the porous medium is modeled using the Brinkman equation. The governing partial differential equations are transformed to ordinary differential equations by collecting the non-periodic and periodic terms. Closed-form solutions for each region are found after applying the boundary and interface conditions. The influence of physical parameters, such as the porous parameter, the frequency parameter, the periodic frequency parameter, the viscosity ratios, the conductivity ratios, and the Prandtl number, on the velocity and temperature fields is computed numerically and presented graphically. In addition, the numerical values of the Nusselt number at the top and bottom walls are derived and tabulated.

P.LOGANATHAN P.PUVI-ARASU R.KANDASAMY

2010, 31(12): 1517-1526. doi:10.1007/s10483-010-1380-8

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Combined heat and mass transfer on free, forced, and mixed convection flow along a porous wedge with magnetic effect in the presence of chemical reaction is investigated. The flow field characteristics are analyzed by the Runge-Kutta-Gill scheme with the shooting method as well as the local non-similarity method up to the third level of truncation, which are used to reduce the governing partial differential equations into nine ordinary differential equations. The governing boundary layer equations are converted to a dimensionless form by Falkner-Skan transformations. Because of the effect of suction/injection on the wall of the wedge with buoyancy force and variable wall temperature, the flow field is locally non-similar. Numerical calculations up to the third order level of truncation are carried out as a special case for different values of dimensionless parameters. Effects of the magnetic field strength in the presence of chemical reaction with variable wall temperature and concentration on the dimensionless velocity, temperature and concentration profiles are shown graphically.

High accuracy eigensolution and its extrapolation for potential equations

程攀黄晋曾光

2010, 31(12): 1527-1536. doi:10.1007/s10483-010-1381-x

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From the potential theorem, the fundamental boundary eigenproblems can be converted into boundary integral equations (BIEs) with the logarithmic singularity. In this paper, mechanical quadrature methods (MQMs) are presented to obtain the eigensolutions that are used to solve Laplace’s equations. The MQMs possess high accuracy and low computation complexity. The convergence and the stability are proved based on Anselone’s collective and asymptotical compact theory. An asymptotic expansion with odd powers of the errors is presented. By the h3-Richardson extrapolation algorithm(EA), the accuracy order of the approximation can be greatly improved, and an a posteriori error estimate can be obtained as the self-adaptive algorithms. The efficiency of the algorithm is illustrated by examples.

Nonconforming finite elements for the equation of planar elasticity

杨永琴肖留超陈绍春

2010, 31(12): 1537-1548. doi:10.1007/s10483-010-1382-7

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Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to λ. The energy norm and L² norm errors are proved to be O(h²) and O(h³), respectively. Numerical tests confirm the theoretical analysis.

Sensitivity analysis of composite laminated plates with bonding imperfection in Hamilton system

李顶河徐建新卿光辉

2010, 31(12): 1549-1560. doi:90C31

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Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method (RPIM) in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner (H-R) variational principle. The analytical method (AM), the semi-analytical method (SAM), and the finite difference method (FDM) are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

秦冰陈正汉方振东孙树国方祥位王驹

2010, 31(12): 1561-1576. doi:10.1007/s10483-010-1384-6

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This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive (or restriction) equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final governing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.

Soliton solution to generalized nonlinear disturbed Klein-Gordon equation

莫嘉琪

2010, 31(12): 1577-1584. doi:10.1007/s10483-010-1385-x

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A generalized nonlinear disturbed Klein-Gordon equation is studied. Using the homotopic mapping method, the corresponding homotopic mapping is constructed. A suitable initial approximation is selected, and an arbitrary-order approximate solution to the soliton is calculated. A weakly disturbed equation is also studied.

Modified domain decomposition method for Hamilton-Jacobi-Bellman equations

陈光华陈光明戴智华

2010, 31(12): 1585-1592. doi:10.1007/s10483-010-1386-8

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This paper presents a modified domain decomposition method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal control problems using diffusion models. A convergence theorem is established. Numerical results indicate the effectiveness and accuracy of the method.

Inexact Newton method via Lanczos decomposed technique for solving box-constrained nonlinear systems

张勇朱德通

2010, 31(12): 1593-1602. doi:10.1007/s10483-010-1387-x

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This paper proposes an inexact Newton method via the Lanczos decomposed technique for solving the box-constrained nonlinear systems. An iterative direction is obtained by solving an affine scaling quadratic model with the Lanczos decomposed technique. By using the interior backtracking line search technique, an acceptable trial step length is found along this direction. The global convergence and the fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the results of the numerical experiments show the effectiveness of the proposed algorithm.

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