Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction
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Mathematical model on magneto-hydrodynamic dispersion in a porous medium under the influence of bulk chemical reaction Ashis Kumar Roy1,*, Apu Kumar Saha2, R. Ponalagusamy3 and Sudip Debnath4 Department of Science & Humanities, Tripura Institute of Technology, Agartala, Tripura-799009, India 2 Department of Mathematics, National Institute of Technology, Agartala, 799046, Tripura, India 3 Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620015, Tamil Nadu, India 4 Center for Theoretical Studies, Indian Institute of Technology Kharagpur, 721302, West Bengal, India (Received May 15, 2020; final revision received July 26, 2020; accepted September 21, 2020) 1
The mathematical model of hydrodynamic dispersion through a porous medium is developed in the presence of transversely applied magnetic fields and axial harmonic pressure gradient. The solute introduce into the flow is experienced a first-order chemical reaction with flowing liquid. The dispersion coefficient is numerically determined using Aris’s moment equation of solute concentration. The numerical technique employed here is a finite difference implicit scheme. Dispersion coefficient behavior with Darcy number, Hartmann number and bulk flow reaction parameter is investigated. This study highlighted that the dependency of Hartmann number and Darcy number on dispersion shows different natures in different ranges of these parameters. Keywords: Darcy number, Hartmann number, Taylor-Aris dispersion, bulk flow reaction
1. Introduction In fluid dynamics, dispersive mass transfer is the movement of mass through convection and molecular diffusion from high concentrated region to a less concentrated region. For non-uniform velocity, the tracer material induces a concentration gradient in the transverse direction that leads to a transverse diffusion along with axial diffusion and convection, and the spreading of the tracer as a result of all these three factors is termed as TaylorAris dispersion. This theory was discovered by Taylor (1953), who calculated the effective diffusion coefficient of a passive solute injected into a laminar flow through a straight capillary tube, followed by Aris (1956), who developed a new methodology viz., method of moment to study the same. Ananthakrishnan (1965) studied the Taylor-Aris dispersion numerically and found that the theory provides a good explanation of the dispersion mechanism after 0.5(a 2 / D) times of solute injection, where a denotes radius of the conduct and D is the constant molecular diffusivity of the solute. Barton (1983) overcame this limitation of Taylor-Aris dispersion by resolving technical difficulties in Aris methodology. By devolving a new technique (General dispersion model) to estimate the effective dispersion coefficient, Sankarasubramanian and Gill published a series of articles (1971, 1972, 1973). The authors also considered a first-order reaction at the wall (1973) for which a new transport coefficient appeared for the first time through their investigati
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