TY - JOUR
T1 - An exact analysis of scalar transport in hydromagnetic flow between two parallel plates
T2 - A multi-scale approach
AU - Poddar, Nanda
AU - Dhar, Subham
AU - Mazumder, Bijoy Singha
AU - Mondal, Kajal Kumar
N1 - Funding Information:
Data accessibility. The present study has no experimental data. Analytical expressions of this study are plotted in Matlab [34]. Analytical expressions of this study are plotted in Matlab and can be accessed via figshare (https://doi.org/10.6084/m9.figshare.13103516.v3). Authors’ contributions. N.P.: designed the study, conceived of the study, coordinated the study and helped draft the manuscript. S.D.: participated in data analysis, participated in the design of the study and drafted the manuscript, coordinated the study and helped draft the manuscript. B.S.M.: carried out the statistical analyses and critically revised the manuscript. K.K.M.: coordinated the study and helped draft the manuscript, collected field data and critically revised the manuscript. All authors gave their final approval for publication. Competing interests. We declare that we have no competing interests. Funding. N.P. and S.D. have received research grants from the University Grants Commission (UGC) (grant no. 1164/(CSIR-UGC NET DEC. 2017)), India and the Council of Scientific and Industrial Research (CSIR) (grant no. 09/1219(0002)/2019-EMR-I), India for pursuing PhD theses. Acknowledgements. The authors would like to express their sincere thanks to Dr Zi Wu, Tsinghua University, for his helpful suggestion of this study. The authors are very grateful to the anonymous reviewers for critical observations and valuable suggestions that helped to improve the manuscript.
Publisher Copyright:
© 2021 The Author(s).
PY - 2021/4/7
Y1 - 2021/4/7
N2 - 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.
AB - 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.
KW - analytical method
KW - dispersion
KW - homogenization
KW - multi-scale analysis
KW - transverse concentration distribution
KW - transverse uniformity
UR - http://www.scopus.com/inward/record.url?scp=85106604474&partnerID=8YFLogxK
U2 - 10.1098/rspa.2020.0830
DO - 10.1098/rspa.2020.0830
M3 - Article
AN - SCOPUS:85106604474
SN - 1364-5021
VL - 477
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2248
M1 - 20200830
ER -