377 research outputs found

    Numerical Simulation for Solute Transport in Fractal Porous Media

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    A modified Fokker-Planck equation with continuous source for solute transport in fractal porous media is considered. The dispersion term of the governing equation uses a fractional-order derivative and the diffusion coefficient can be time and scale dependent. In this paper, numerical solution of the modified Fokker-Planck equation is proposed. The effects of different fractional orders and fractional power functions of time and distance are numerically investigated. The results show that motions with a heavy tailed marginal distribution can be modelled by equations that use fractional-order derivatives and/or time and scale dependent dispersivity

    Anomalous diffusion in rotating Casson fluid through a porous medium

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    This paper investigates the space-fractional anomalous diffusion in unsteady Casson fluid through a porous medium, based on an uncoupled continuous time random walk. The influences of binary chemical reaction and activation energy between two horizontal rotating parallel plates are taken into account. The governing equations of motion are reduced to a set of nonlinear differential equations by time derivatives discretization and generalized transformation, which are solved by bvp4c and implicit finite difference method (IFDM). Stability and convergence of IFDM are proved and some numerical comparisons to the previous study are presented with excellent agreement. The effects of involved physical parameters such as fractional derivative parameter, rotation parameter and time parameter are presented and analyzed through graphs. Results indicate that the increase of fractional derivative parameter triggers concentration increase near the lower plate, while it causes a reduction near the upper plate. It is worth mentioning that the decrease of heat transfer rate on the plate is observed with the higher time parameter.</p

    Numerical Investigation of a Two-Phase Nanofluid Model for Boundary Layer Flow Past a Variable Thickness Sheet

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    Abstract This paper investigates heat and mass transfer of nanofluid over a stretching sheet with variable thickness. The techniques of similarity transformation and homotopy analysis method are used to find solutions. Velocity, temperature, and concentration fields are examined with the variations of governing parameters. Local Nusselt number and Sherwood number are compared for different values of variable thickness parameter. The results show that there exists a critical value of thickness parameter Ī² c (Ī² c ā‰ˆ0.7) where the Sherwood number achieves its maximum at the critical value Ī² c . For Ī²&gt;Ī² c , the distribution of nanoparticle volume fraction decreases near the surface but exhibits an opposite trend far from the surface.</jats:p

    Effects of fractional mass transfer and chemical reaction on MHD flow in a heterogeneous porous medium

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    This paper presents a study on space fractional anomalous convective-diffusion and chemical reaction in the magneto-hydrodynamic fluid over an unsteady stretching sheet. The fractional diffusion model is derived from decoupled continuous time random walks in a heterogeneous porous medium. A novel transformation which features time finite difference is introduced to reduce the governing equations into ordinary differential ones in each time level. Numerical solutions are established by an implicit finite difference scheme. The stability and convergence of the method are analyzed. Results show that increasing fractional derivative parameter enhances concentration near the surface while an opposite phenomenon occurs far away from the wall. There is a reduction of mass transfer rate on the sheet with an increase in the fractional derivative parameter. Moreover, the numerical solutions are compared with exact solutions and good agreement has been observed.</p

    Beam Performance Optimization of Multibeam Imaging Sonar Based on the Hybrid Algorithm of Binary Particle Swarm Optimization and Convex Optimization

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    It should be noted that the peak sidelobe level (PSLL) significantly influences the performance of the multibeam imaging sonar. Although a great amount of work has been done to suppress the PSLL of the array, one can verify that these methods do not provide optimal results when applied to the case of multiple patterns. In order to suppress the PSLL for multibeam imaging sonar array, a hybrid algorithm of binary particle swarm optimization (BPSO) and convex optimization is proposed in this paper. In this algorithm, the PSLL of multiple patterns is taken as the optimization objective. BPSO is considered as a global optimization algorithm to determine best common elementsā€™ positions and convex optimization is considered as a local optimization algorithm to optimize elementsā€™ weights, which guarantees the complete match of the two factors. At last, simulations are carried out to illustrate the effectiveness of the proposed algorithm in this paper. Results show that, for a sparse semicircular array with multiple patterns, the hybrid algorithm can obtain a lower PSLL compared with existing methods and it consumes less calculation time in comparison with other hybrid algorithms
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