A new traffic model with a lane-changing viscosity term

In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a ＂force＂ that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.

Flow, thermal criticality and transition of a reactive third-grade fluid in a pipe with Reynolds' model viscosity

Neglecting the consumption of the material, a steady incompressible flow of an exothermic reacting third-grade fluid with viscous heating in a circular cylindrical pipe is numerically studied for both cases of constant viscosity and Reynolds＇ viscosity model. The coupled ordinary differential equations governing the flow in cylindrical coordinates, are transformed into dimensionless forms using appropriate transformations, and then solved numerically. Solutions using Maple are presented in tabular form and given in terms of dimensionless central fluid velocity and temperature, skin friction and heat transfer rate for three parametric values in the Reynolds＇ case. The numerical results for the velocity and temperature fields are also presented through graphs. Bifurcations are discussed using shooting method. Comparisons are also made between the present results and those of previous work, and thus verify the validity of the provided numerical solutions. Important properties of thermal criticality are provided for variable viscosity parameter and reaction order. Further numerical results are presented in the form of tables and graphs for transition of physical parameters, while varying certain flow and fluid material parameters. Also, the flow behaviour of the reactive fluid of third-grade is compared with those of the Newtonian reactive fluid.