Double-diffusive convection in Jeffery–Hamel flow

Abstract

In this paper, double-diffusive convection in flow of viscous fluid is investigated inside a horizontal channel. It has heated, inclined and rectangular plane walls. The upper wall has non-uniform temperature and variable species concentration. Note that the Jeffery–Hamel flow depends upon the radial component of velocity, whereas, the peripheral velocity is taken zero. However, the current simulation has been accomplished in view of new procedures and we dealt with two non-zero components of velocity. The problem has been described in a set of four PDEs and the relevant BCs, whereas, the whole set of BVP is taken in Cartesian Coordinates. A set of proper transformation is formed, which reduces the system of PDEs into a new system of ODEs. The system of ODEs is solved with the help of several methods in order to check the validity of the solution. An approximate analytical solution is provided for small values of inclination parameter. An accurate numerical solution of the modelled equations is also given. Moreover, skin friction, rate of the two diffusions are investigated for all different cases of assisting (opposing) and converging (diverging) flows. Thus, the current modelled problem perfectly describes the physical problems of real world in such special circumstances.