Table of Content

15 July 2013, Volume 34 Issue 8

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Articles

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

S. ABBASBANDY;T. HAYAT;H. R. GHEHSAREH;A.ALSAEDI

2013, 34(8):  921-930.  doi:10.1007/s10483-013-1717-7

Abstract ( 881 )   PDF (230KB) ( 957 )  

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The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An efficient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

Zhi-qiang LUO;Zhi-min CHEN

2013, 34(8):  931-944.  doi:10.1007/s10483-013-1718-7

Abstract ( 862 )   PDF (18543KB) ( 794 )  

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A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equations with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equations of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

Stretching surface in rotating viscoelastic fluid

K. ZAIMI;A. ISHAK;I. POP

2013, 34(8):  945-952.  doi:10.1007/s10483-013-1719-9

Abstract ( 824 )   PDF (229KB) ( 992 )  

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The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thoroughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter increase. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase.

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

Gang CHEN;Min-fu FENG;Yin-nian HE

2013, 34(8):  953-970.  doi:10.1007/s10483-013-1720-9

Abstract ( 907 )   PDF (250KB) ( 632 )  

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A unified analysis is presented for the stabilized methods including the pressure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equations. The existence and uniqueness of the solution and the optimal error estimates are proved.

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

J. A. ESFAHANI;M. MODIRKHAZENI;S. MOHAMMADI

2013, 34(8):  971-984.  doi:10.1007/s10483-013-1721-8

Abstract ( 808 )   PDF (303KB) ( 736 )  

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The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence of geometry on the entropy generation rate is studied, and the distribution of volumetric local entropy generation rate for the selected geometries is drawn.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

H. P. RANI;G. J. REDDY;C. N. KIM

2013, 34(8):  985-1000.  doi:10.1007/s10483-013-1722-6

Abstract ( 842 )   PDF (566KB) ( 702 )  

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The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases.
The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

Zhan-fang LIU;Shi-jun YAN;Zhi FU

2013, 34(8):  1001-1016.  doi:10.1007/s10483-013-1723-8

Abstract ( 913 )   PDF (621KB) ( 889 )  

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The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kinematics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their increments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motiondeformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

Wei-bin WEN;Kai-lin JIAN;Shao-ming LUO

2013, 34(8):  1017-1030.  doi:10.1007/s10483-013-1724-x

Abstract ( 879 )   PDF (519KB) ( 689 )  

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A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conventional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the principle
of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

Equivalent method for accurate solution to linear interval equations

Chong WANG;Zhi-ping QIU

2013, 34(8):  1031-1042.  doi:10.1007/s10483-013-1725-6

Abstract ( 824 )   PDF (234KB) ( 654 )  

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Based on linear interval equations, an accurate interval finite element method for solving structural static problems with uncertain parameters in terms of optimization is discussed. On the premise of ensuring the consistency of solution sets, the original interval equations are equivalently transformed into some deterministic inequations. On this basis, calculating the structural displacement response with interval parameters is
predigested to a number of deterministic linear optimization problems. The results are proved to be accurate to the interval governing equations. Finally, a numerical example is given to demonstrate the feasibility and efficiency of the proposed method.