An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: A multi-scale approach

Nanda Poddar, Subham Dhar, Bijoy Singha Mazumder, Kajal Kumar Mondal

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

The present paper explores an analytical solution to study the two-dimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei's homogenization technique is used to acquire the mean concentration distributions up to the second-order approximation and the transverse concentration distributions up to third order. An uneven form of the concentration cloud and the transverse variation of the concentration distribution in a hydromagnetic flow are illustrated for the initial stage. The rate of progress towards uniformity of a solute cloud seems much slower than that of normality. It is observed that the peak of the transverse mean concentration and transverse variation of the concentration distribution of the solute significantly decrease with the increase in the magnetic field for small dispersion times. This is because, with an increase in the magnetic field, the velocity profiles flatten at the central core region between the parallel plates. The research proposes a time scale of 10d 2 /D (where d is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

Original languageEnglish
Article number20200830
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume477
Issue number2248
DOIs
StatePublished - 7 Apr 2021
Externally publishedYes

Keywords

  • analytical method
  • dispersion
  • homogenization
  • multi-scale analysis
  • transverse concentration distribution
  • transverse uniformity

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy

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