The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and s...The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and stationary,while the top plate is impermeable and moving.The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations.The Homotopy Perturbation Method(HPM)is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution.The analysis includes plotting the velocity profile for different Reynolds number values and temperature distribution curves for distinct physical parameters such as Reynolds number,Deborah number,magnetic parameter,porosity parameter,radiation parameter,and Prandtl number.In the case of injection,the temporal profile declines with an increase in radiation parameter as the plates move away from each other,and an opposite trend is observed as plates move towards each other.Furthermore,the skin friction coefficient and heat transfer rate are analysed for the impact of these parameters using HPM.The numerical values obtained using HPM are compared using the classical finite difference method.The results show good agreement between the semi-analytical and numerical solutions.展开更多
In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise...In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.展开更多
Based on the asynptotical perturbation method and the Galerkin Itechnique.thehybrid changeable basis Galerkin technique is presented for predicting the nonlinearresponse of structures. By the. idea of changeable basis...Based on the asynptotical perturbation method and the Galerkin Itechnique.thehybrid changeable basis Galerkin technique is presented for predicting the nonlinearresponse of structures. By the. idea of changeable basis functions first proposed, itgreatly reduces calculation and is easily used in other numerical diseretizationtechniques,such as finite element method etc.,It appears to have high potential forsolution of nonlinear srtyctyrak oribkrbts.Finally, the effectiveness of this technique isdemonstrate by means of two numerical examples: the large deflection of circularplates objected to uniform normal load and the large deflection of spherical caps undercentrally distributed pressures.展开更多
Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary con...Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.展开更多
文摘The study in this manuscript aims to analyse the impact of thermal radiation on the two-dimensional magnetohydrodynamic flow of upper convected Maxwell(UCM)fluid between parallel plates.The lower plate is porous and stationary,while the top plate is impermeable and moving.The equations that describe the flow are transformed into non-linear ordinary differential equations with boundary conditions by employing similarity transformations.The Homotopy Perturbation Method(HPM)is then employed to approach the obtained non-linear ordinary differential equations and get an approximate analytical solution.The analysis includes plotting the velocity profile for different Reynolds number values and temperature distribution curves for distinct physical parameters such as Reynolds number,Deborah number,magnetic parameter,porosity parameter,radiation parameter,and Prandtl number.In the case of injection,the temporal profile declines with an increase in radiation parameter as the plates move away from each other,and an opposite trend is observed as plates move towards each other.Furthermore,the skin friction coefficient and heat transfer rate are analysed for the impact of these parameters using HPM.The numerical values obtained using HPM are compared using the classical finite difference method.The results show good agreement between the semi-analytical and numerical solutions.
基金supported by the National Natural Science Foundation of China (11072107,91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20093218110003)
文摘In the present paper, the maximal Lyapunov ex- ponent is investigated for a co-dimension two bifurcation system that is on a three-dimensional central manifold and subjected to parametric excitation by a bounded noise. By using a perturbation method, the expressions of the invari- ant measure of a one-dimensional phase diffusion process are obtained for three cases, in which different forms of the matrix B, that is included in the noise excitation term, are assumed and then, as a result, all the three kinds of singular boundaries for one-dimensional phase diffusion process are analyzed. Via Monte-Carlo simulation, we find that the an- alytical expressions of the invariant measures meet well the numerical ones. And furthermore, the P-bifurcation behav- iors are investigated for the one-dimensional phase diffusion process. Finally, for the three cases of singular botmdaries for one-dimensional phase diffusion process, analytical ex- pressions of the maximal Lyapunov exponent are presented for the stochastic bifurcation system.
文摘Based on the asynptotical perturbation method and the Galerkin Itechnique.thehybrid changeable basis Galerkin technique is presented for predicting the nonlinearresponse of structures. By the. idea of changeable basis functions first proposed, itgreatly reduces calculation and is easily used in other numerical diseretizationtechniques,such as finite element method etc.,It appears to have high potential forsolution of nonlinear srtyctyrak oribkrbts.Finally, the effectiveness of this technique isdemonstrate by means of two numerical examples: the large deflection of circularplates objected to uniform normal load and the large deflection of spherical caps undercentrally distributed pressures.
基金supported by the National Special Fund for Major Research Instrument Development(Grant No.2011YQ140145)111 Project(Grant No.B07009)+1 种基金National Natural Science Foundation of China(Grant No.11002013)Defense Industrial Technology Development Program(Grant Nos.A2120110001 and B2120110011)
文摘Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.
