We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a nu...We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.展开更多
In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both ...In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.展开更多
文摘We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.
文摘In this paper we analyze the influence of free convection on nonlinear peristaltic transport of a Jeffrey fluid in a finite vertical porous stratum using the Brinkman model. Heat is generated within the fluid by both viscous and Darcy dissipations. The coupled nonlinear governing equations are solved analytically. The expressions for the temperature, the axial velocity, the local wall shear stress and the pressure gradient are obtained. The effects of various physical parameters such as the Jeffrey parameter λ1, the permeability parameter σ and the heat source/sink parameter β are analyzed through graphs, and the results are discussed in detail. It is observed that the velocity field increases with increasing values of the Jeffrey parameter but it decreases with increasing values of the permeability parameter. It is found that the pressure rise increases with decreasing Jeffrey parameter and increasing permeability parameter. We notice that the effect of the permeability parameter a is the strongest on the bolus trapping phenomenon. For λ1 = 0, N =0, the results of the present study reduce to the results of Tripathi [Math. Comput.Modelling 57 （2013） 1270-1283]. Further the effect of viscous and Darcy dissipations is to reduce the rate of heat transfer in the finite vertical porous channel under peristalsis.
