In this paper, we present a review of featured works in the field of hydrodynamics with the
main aim to clarify the ways of understanding the algorithms for solving the Navier–Stokes …

The present review analyzes classes of exact solutions for the convection and thermal
diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck …

We present a new exact solution of the thermal diffusion equations for steady-state shear
flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale …

The current study deals with the exact solutions of nonlinear confirmable time fractional
Sobolev type equations. Such equations have applications in thermodynamics, the flow of …

In this paper, a new method based on neural network is developed for obtaining the solution
of the Navier–Stokes equations in an analytical function form. The solution procedure is …

In fluid mechanics, a lot of authors have been reporting analytical solutions of Euler and
Navier-Stokes equations. But there is an essential deficiency of non-stationary solutions …

The nonlinear convective acceleration term in fluids performs a strong obstacle against the
analytical solutions of Navier-Stokes equations up to date. The obtained solutions are valid …

New further integrability conditions of the Riccati equation dy/dx= a (x)+ b (x) y+ c (x) y2 are
presented. The first case corresponds to fixed functional forms of the coefficients a (x) and c …

In this paper, the unsteady and nonlinear Navier-Stokes equations in three Cartesian
coordinates are converted to the linear diffusion equations based on the concept of linear …

Abstract Soliton solutions of a (2+ 1)-dimensional reaction–diffusion problem are derived in
the present work using the generalized Riccati equation map** method. The model …