Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation-now called the Boltzmann equation-for the phase space density of the molecules of a dilute fluid. He showed that the Second law of thermodynamics emerges from Newton's equations of motion. Ho...

Solute transport in soils is commonly simulated with the advective-dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil. Recently, a new model has been suggested that results in a solute transport equation with fractional spatial derivatives, or FADE. We have assembled a database on published solute...

Flow over a downstream-facing step is predicted using the F.E.M. A two-equation model of turbulence is employed where the transport of turbulence kinetic energy and dissipation rate are depicted using transport-type equations, i.e. the two-equation model of turbulence. The results obtained are compared with other models and experimental results. Generally, the model was found to be under-predic...

A new approach based on the method of characteristics (MOC) and Rosenbrock method is developed to solve the timedependent transport equation in one-dimensional (1D) geometry without any approximation and considering delayed neutrons. Within the MOC methodology, the leakage term in time-dependent transport equation can be simplified to spatial derivative of the angular flux along the characteris...

cohesive sediment transport remains a complicated subject that hydraulic engineers are frequently faced with in water-related engineering problems. this is primarily affected by the macroscopic aspects of water-sediment system characteristics. in this paper a 1-d mathematical model was developed to be employed in predicting the cohesive sediment transport under simultaneous conditions of erosio...

Peristaltic transport of an incompressible electrically conducting viscous fluid in an inclined planar asymmetric channel is studied. The asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude and phase. The closed form solutions of momentum and energy equation in presence of viscous dissipation term are obtained for long wave length and low Reynol...

In this paper, we perform a systematic multiscale analysis for convection dominated transport equations with a weak diffusion and a highly oscillatory velocity field. The paper primarily focuses on upscaling linear transport equations. But we also discuss briefly how to upscale two-phase miscible flows, in which case the concentration equation is coupled to the pressure equation in a nonlinear ...

A re®ned three-dimensional layer-integrated model to predict accurately salt and cohesive sediment transport in estuarine waters is described herein. A splitting algorithm has been used to split the three-dimensional transport equation into a horizontal twodimensional equation and a vertical one-dimensional equation due to the di€erent length scales. An additional source term associated with th...

The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solu...