Table of Content

01 November 2014, Volume 35 Issue 11

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Articles

Self-similar behavior for multicomponent coagulation

Man-li YANG;Zhi-ming LU;Yu-lu LIU

2014, 35(11):  1353-1360.  doi:10.1007/s10483-014-1872-7

Abstract ( 453 )   HTML   PDF (177KB) ( 232 )  

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Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.

Assessment of shock capturing schemes for discontinuous Galerkin method

Jian YU;Chao YAN;Rui ZHAO

2014, 35(11):  1361-1374.  doi:10.1007/s10483-014-1875-7

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This paper carries out systematical investigations on the performance of several typical shock-capturing schemes for the discontinuous Galerkin (DG) method, including the total variation bounded (TVB) limiter and three artificial diffusivity schemes (the basis function-based (BF) scheme, the face residual-based (FR) scheme, and the element residual-based (ER) scheme). Shock-dominated flows (the Sod problem, the Shu- Osher problem, the double Mach reflection problem, and the transonic NACA0012 flow) are considered, addressing the issues of accuracy, non-oscillatory property, dependence on user-specified constants, resolution of discontinuities, and capability for steady solutions. Numerical results indicate that the TVB limiter is more efficient and robust, while the artificial diffusivity schemes are able to preserve small-scale flow structures better. In high order cases, the artificial diffusivity schemes have demonstrated superior performance over the TVB limiter.

Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

A. A. AFIFY;M. J. UDDIN;M. FERDOWS

2014, 35(11):  1375-1386.  doi:10.1007/s10483-014-1873-7

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Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic (MHD) flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation

M. M. KHADER;A. M. MEGAHED

2014, 35(11):  1387-1400.  doi:10.1007/s10483-014-1870-7

Abstract ( 457 )   HTML   PDF (331KB) ( 156 )  

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This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations (PDEs) are transformed into a system of coupled non-linear ordinary differential equations (ODEs) with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method (DTM). The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.

Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions

S. MANSUR;A. ISHAK;I.POP

2014, 35(11):  1401-1410.  doi:10.1007/s10483-014-1878-7

Abstract ( 402 )   HTML   PDF (313KB) ( 221 )  

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The boundary layer flow of a nanofluid past a stretching/shrinking sheet with hydrodynamic and thermal slip boundary conditions is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the skin friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and concentration profiles for some values of the velocity slip parameter, thermal slip parameter, stretching/shrinking parameter, thermophoresis parameter, and Brownian motion parameter. The results show that the local Nusselt number, which represents the heat transfer rate, is lower for higher values of thermal slip parameter, thermophoresis parameter, and Brownian motion parameter.

Dynamic release process of pollutants during suspended sediment transport in aquatic system

Hong-wei ZHU;Dao-zeng WANG;Peng-da CHENG

2014, 35(11):  1411-1420.  doi:10.1007/s10483-014-1876-7

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Pollutants release is highly consistent with suspended sediment concentration (SSC) in water column, especially during re-suspension and transport events. The present research focuses on pollutant dynamic release from re-suspended sediment, especially the vertical distribution relationship between them. The sediment erosion experiments on a series of uniform flow are conducted in a circulate flume. Reactive tracer (phosphorus) is used as the contaminant in fine-grained sediments to identify the release characteristic length and time. Experimental results show that the flow condition near-bed depends on the sediment surface roughness. The region with high turbulent intensities corresponds to a high concentration sediment layer. In addition, the SSC decreases with the distance, water depth, and particle grain size. The sediment in a smaller grain size takes much more time to reach equilibrium concentration. Total phosphorus (TP) concentration changes along the water depth as SSC in the initial re-suspension stage, appearing in two obvious concentration regimes: the upper low-concentration layer and the high-concentration near-bottom layer. This layered phenomenon remains for about 3 hours until SSC distribution tends to be uniform. Longitudinal desorption plays an important role in long-way transport to reduce the amount of suspended sediment in water column.

Dynamic response of axially moving Timoshenko beams: integral transform solution

Chen AN;Jian SU

2014, 35(11):  1421-1436.  doi:10.1007/s10483-014-1879-7

Abstract ( 662 )   HTML   PDF (751KB) ( 146 )  

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The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.

Analysis and simulation for tensile behavior of anisotropic open-cell elastic foams

Zi-xing LU;Qiang LIU;Xin CHEN

2014, 35(11):  1437-1446.  doi:10.1007/s10483-014-1874-7

Abstract ( 414 )   HTML   PDF (330KB) ( 159 )  

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Based on the elongated Kelvin model, a simplified periodic structural cell is obtained to investigate the tensile behavior of anisotropic open-cell elastic foams due to Kelvin model's periodicity and symmetry in the whole space. The half-strut element and elastic deflection theory are used to analyze the tensile response as done in the previous studies. This study produces theoretical expressions for the tensile stress-strain curve in the rise and transverse directions. In addition, the theoretical results are examined with finite element simulation using an existing formula. The results indicate that the theoretical analysis agrees with the finite element simulation when the strain is not too high, and the present model is better. At the same time, the anisotropy ratio has a significant effect on the mechanical properties of foams. As the anisotropy ratio increases, the tensile stress is improved in the rising direction but drops in the transverse direction under the same strain.

Power transmission through double-walled laminated composite panels considering porous layer-air gap insulation

M. H. SHOJAEIFARD;R. TALEBITOOTI;B. RANJBAR;R. AHMADI

2014, 35(11):  1447-1466.  doi:10.1007/s10483-014-1877-7

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The acoustic behavior of double-walled laminated composite panels consisting of two porous and air gap middle layers is studied within the classical laminated plate theory (CLPT). Thus, viscous and inertia coupling in a dynamic equation, as well as stress transfer, thermal and elastic coupling of porous material are based on the Biot theory. In addition, the wave equations are extracted according to the vibration equation of composite layers. The transmission loss (TL) of the structure is then calculated by solving these equations simultaneously. Statistical energy analysis (SEA) is developed to divide the structure into specific subsystems, and power transmission is extracted with balancing power flow equations of the subsystems. Comparison between the present work and the results reported elsewhere shows excellent agreement. The results also indicate that, although favorable enhancement is seen in noise control particularly at high frequencies, the corresponding parameters associated with fluid phase and solid phase of the porous layer are important on TL according to the boundary condition interfaces. Finally, the influence of composite material and stacking sequence on power transmission is discussed.

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

He ZHANG;Ji-qing JIANG;Zhi-cheng ZHANG

2014, 35(11):  1467-1478.  doi:10.1007/s10483-014-1871-7

Abstract ( 385 )   HTML   PDF (454KB) ( 132 )  

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Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model (ALM) is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.