the combined effect of non-newtonian rheology and irreversible boundary reaction on dispersion in a herschel-bulkley fluid through a conduit (pipe/channel) is studied by using generalized dispersion model. the study explains the development of dispersive transport following the injection of a tracer in terms of three effective transport coefficients namely exchange, convective and dispersion co...

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we develope...

The laminar flow of a number of fluids such as polymeric liquids, food products, paints, slurries, foams, and so forth cannot be adequately described by the help of the classical linearly viscous Newtonian model. Thus, there is a need to have at hand an arsenal of non-Newtonian fluid models and over the past several decades a variety of models have been developed. While the fluids of the differ...

We present new periodic, kink-like and soliton-like travelling wave solutions to the hyperbolic generalization of Burgers equation. To obtain them, we employ the classical and generalized symmetry methods and the ansatz-based approach

Some classes of the rational, periodic and solitary wave solutions for the Burgers hierarchy are presented. The solutions for this hierarchy are obtained by using the generalized Cole Hopf transformation.

We present an introductory overview of several challenging problems in the statistical characterisation of turbulence. We provide examples from fluid turbulence in three and two dimensions, from the turbulent advection of passive scalars, turbulence in the one-dimensional Burgers equation, and fluid turbulence in the presence of polymer additives.

The Burgers' model of compressible fluid dynamics in one dimension is extended to include the effects of pressure back-reaction. The system consists of two coupled equations: Burgers' equation with a pressure gradient (essentially the one-dimensional Navier-Stokes equation) and an advection-diffusion equation for the pressure field. It presents a minimal model of both adiabatic gas dynamics and...

Numerous applied mathematics and physical applications, such as the simulation of financial mathematics, gas dynamics, nonlinear phenomena in plasma physics, fluid mechanics, ocean engineering, utilize time-fractional generalized Burgers–Fisher equation (TF-GBFE). This describes concept dissipation illustrates how reaction systems can be coordinated with advection. To examine analyze present ev...