Effect of Rayleigh number on transport of solute in a hydromagnetic natural convective flow through a vertical channel with chemical reaction

Abstract

In the present research, the transport of solute in a hydromagnetic natural convective flow through a vertical channel under the impact of bulk chemical reaction is investigated for the first time using Mei's multi-scale homogenization method. The purpose of this research is to obtain an analytical solution of a physical model for a vertical flow. A uniformly variable axial temperature is considered at both walls. Analytical expressions of Taylor dispersivity, multi-dimensional concentration distributions i.e. horizontal concentration, vertical mean and real concentration distributions are obtained together in the present article. One of the major fact of the present study is to highlight the influence of Rayleigh number (Ra) on mass transfer phenomena in the above mentioned flow. It is observed that both the velocity and Taylor dispersivity reduce due to the increment of the Hartmann and Rayleigh numbers. The Rayleigh number imposes the horizontal uniformity throughout the vertical channel and with the increment of Ra, the variation of horizontal distribution of concentration reduces but it remains tri-modal. It is important to note that, when the Rayleigh number reaches to 275, the non-uniform variation of horizontal concentration distribution becomes bimodal. It is significant to note that a critical value of the Rayleigh number is suggested where the horizontal variation curve becomes bimodal from tri-modal. The outcomes of this study may have a wide range of industrial applications, including metal casting, crystal growth and liquid metal cooling blankets for fusion reactors.