应用数学和力学

2010 Vol. 31, No. 12

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Analysis of Coupled Flow-Reaction With Heat Transfer in Heap Bioleaching Processes

WU Ai-xiang, LIU Jin-zhi, YIN Sheng-hua, WANG Hong-jiang

2010, 31(12): 1393-1400. doi: 10.3879/j.issn.1000-0887.2010.12.001

Abstract(1715) PDF(973)

Abstract:
A mathem aticalmodel for heap bioleaching was developed to analyze heat transfer,oxygen flow,targetions distribution and oxidation leaching rate in the heap,and the model equations were solved by Comsol Multiphysics software.The numerical simulation results show:the concentration of oxygen is comparatively higher along the boundary of the slope,and lower in the center part where leaching rate is slow;the temperature is comparatively low along the slope and the highest along the bottom region near the slope,and the difference is more than 6℃;the concentration of target mentalions is highest in the bottom region near the slope;the oxidation leaching rate is bigger in the bottom and slope part with quicker reaction rate,and comparatively smaller in the restpart with lower oxygen concen tration.

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): 1401-1414. doi: 10.3879/j.issn.1000-0887.2010.12.002

Abstract(2010) PDF(926)

Abstract:
The objectives of the present study are to investigate the effect of flow parameters on free convection and mass transfer unsteady magnetohydrodynamic flow of an electrically conducting,viscous,in compressible fluid pastan infinite vertical porous plate under oscillatory suction velocity and thermal radiation by taking into account the Dufour (diffusion thermo) and Soret (thermal diffusion) effects.The problem is solved numerically by using finite element method for velocity,temperature and concentration field and also the expression for skin friction,rate of heat and mass transfer have been obtained.The results obtained have been presented numerically through graphs and tables for externally cooled plate (Gr>0) and externally heated plate (Gr<0) to observe the effects of various param eters 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): 1415-1434. doi: 10.3879/j.issn.1000-0887.2010.12.003

Abstract(1904) PDF(872)

Abstract:
The problem of unsteady oscillatory flow and heat transfer of porousmedia sandwiched between viscous fluids through a horizontal channel with isothermal wall temperatures was considered.The flow in the porous medium was modeled using Brinkm an equation.The governing partial differential equations were transformed to ordinary differential equations by collecting the non-periodic and periodic terms and closed-formsolutions for each region were found after applying the boundary and interface conditions.The influence of physical parameters such as porous parameter,frequency parameter,periodic frequency parameter,viscosity ratios,conductivity ratios and Prandtl number on the velocity and tem perature fields were computed numerically and presented graphically.In addition,the numerical values of the heat transfer rate at the top and bottom walls are derived and were tabulated.

P. Loganathan, P. Puviarasu, R. Kandasamy

2010, 31(12): 1435-1444. doi: 10.3879/j.issn.1000-0887.2010.12.004

Abstract(1727) PDF(796)

Abstract:
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 was investigated.The flow field characteristics were analyzed using the Runge-Kutta Gillwith shooting method as well as the local non-similarity method up to thirdlevel of truncation was used toreduce the governing partial differential equations into nineord inary differential equations.The governing boundary layer equations were written into a dimensionless form by Falkner-Skan transform ations.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 nonsimilar.Numerical calculations up to thirdorder level of truncation are carried out for different values of dmiension less param eters as a special case.Effects of the strength of magnetic field in the presence of chemical reaction with variable wall temperature and concentration on the dimensionless velocity,temperature and concen tration profiles are shown graphically.

High Accuracy Eigensolution and Its Extrapolation for Potential Equations

CHENG Pan, HUANG Jin, ZENG Guang

2010, 31(12): 1445-1453. doi: 10.3879/j.issn.1000-0887.2010.12.005

Abstract(1840) PDF(877)

Abstract:
By the potential theorem,fundamental boundary eigenproblems were converted into boundary in tegral equations (BIE) with logarithmic singularity.Mechanical quadrature methods (MQMs) were presented to obtain eigen solutions which were used to solve Laplace's equations.And the MQMs possess high accuracies and low computing complexities.The convergence and stability were proved based on Anselone's collective compact and asymptotical compact theory.Furthermore,an asymptotic expansion with odd powers of the errors is presented.Using h³-Richardson extrapolation algorithm (EA),the accuracy order of the approximation can be greatly improved,and a posterior error estmiate 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

YANG Yong-qin, XIAO Liu-chao, CHEN Shao-chun

2010, 31(12): 1454-1464. doi: 10.3879/j.issn.1000-0887.2010.12.006

Abstract(1815) PDF(970)

Abstract:
Two new locking-free nonconforming finite elements for the pure displacement planarela sticity problem were presented.Convergen cerates of the elements were uniformly optimal with respect to K.T he energy norm and L² norm errors were proved to be O (h²) and O (h³),respectively.La stly,numerical tests are carried out,which coincide with the theoretical analysis.

Sensitivity Analysis of Composite Laminated Plates With Bonding Imperfection in Hamilton System

LI Ding-he, XU Jian-xin, QING Guang-hui

2010, 31(12): 1465-1475. doi: 10.3879/j.issn.1000-0887.2010.12.007

Abstract(1751) PDF(934)

Abstract:
The sensitivity analysis of composite laminated plates with bonding interfacial imperfection was investigated based on the radial point interpolation method (RPMI) in Hamilton system.A hybrid governing equations of the response and sensitivity quantities was reduced by the spring-layer model and modified Hellinger-Reissner (H-R) variational principle.The analy ticalmethod (AM),semi-analy ticalmethod (SA) and the finite difference method (FD) were given for the sensitivity analysis approach which is based on this reduced hybrid governing-equation.One of the main advantages of the hybrid governing equation is that the convoluted algorithm is avoided in sensitivity analysis.In addition,the sensitivity analysis method using this hybrid governing equation not only obtains the response values and the sensitivity coefficients smiultaneity,butalso accounts for the bonding interfacial imperfections of composite laminated plates.

Analysis of Coupled Thermo-Hydro-Mechanical Behavior of Unsaturated Soils Based on Theory of Mixtures Ⅰ

QIN Bing, CHEN Zheng-han, FANG Zhen-dong, SUN Shu-guo, FANG Xiang-wei, WANG Ju

2010, 31(12): 1476-1488. doi: 10.3879/j.issn.1000-0887.2010.12.008

Abstract(1673) PDF(1215)

Abstract:
An analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils was presented based on theory of mixtures.Unsaturated soilw as considered as amixture composed of soil skeleton,liquidwater,vapor,dry air and dissolved air.In addition to mass and momentum conservation equations of each component and energy conservation equation of the mixture,the system was closed using other 37 constitutive (or restriction) equations.In virtue of the requirement that the change in water chemical potential was identical with the change in vapor chemical potential,a therm odynamic restriction relationship for phase transition between pore water and pore vapor was formulated,in which the impact of the change in gas pressure on the phase transition was taken into account.Six final governing equations were given in incremental form in term of six prmiary variables,i.e.three displacement components of soil skeleton,water pressure,gas pressure and temperature.The processes involved in the coupled model included the rmal expansions of soil skeleton and soil particle,Soret effec,tphase transition between water and vapor,air dissolution in pore water,deformation of soil skeleton,etc.

Soliton Solution to Nonlinear Generalized Disturbed Klein-Gordon Equation

MO Jia-qi

2010, 31(12): 1489-1495. doi: 10.3879/j.issn.1000-0887.2010.12.009

Abstract(1532) PDF(1018)

Abstract:
Ageneralized nonlinear disturbed Klein-Gordon equation was considered.By using the homotopic mapping method,firstly,the corresponding homotopic mapping was constructed.Then the suitable in itial approx miation was selected,and the arbitrary order approx imate solution of the soliton was calculated.At one time,a weakly disturbed equation was studied.

Modified Domain Decomposition Method for Hamilton-Jacobi-Bellman Equations

CHEN Guang-hua, CHEN Guang-ming, DAI Zhi-hua

2010, 31(12): 1496-1502. doi: 10.3879/j.issn.1000-0887.2010.12.010

Abstract(2090) PDF(1083)

Abstract:
Amodified domain decom position method for the numerical solution of discrete Hamilton-Jacobi-Bellman equations arising from a class of optimal controls with diffusion models.The convergence theorem was estab lished.Numerical results indicate the efficiency and accuracy of the method.

Inexact Newton Method via Lanczos Decomposed Technique for Solving Box-Constrained Nonlinear Systems

ZHANG Yong, ZHU De-tong

2010, 31(12): 1504-1512. doi: 10.3879/j.issn.1000-0887.2010.12.011

Abstract(1429) PDF(744)

Abstract:
An in exact Newton methodvia Lanczos decomposed technique was proposed for solving the box-constrained nonlinear systems.The iterative direction was obtained by solving an affine scaling quadratic modelwith Lanczos decom posed technique.By using the in terior backtracking line search technique,the acceptable trial steplength a long this direction will be found.The global convergence and fastlocal convergence rate of the proposed algorithm were established under some reasonable conditions.Furthermore,the results of the numerical expermients are reported to show the effectiveness of the proposed a lgorithm.