On dispersion of solute in a hydromagnetic flow between two parallel plates with boundary absorption

2021 ◽  
Vol 33 (8) ◽  
pp. 083609
Author(s):  
Subham Dhar ◽  
Nanda Poddar ◽  
Kajal Kumar Mondal ◽  
Bijoy Singha Mazumder
Keyword(s):  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Boundary Absorption

A linear theory of rotating, thermally stratified, hydromagnetic flow

1975 ◽  
Vol 72 (1) ◽  
pp. 1-16 ◽  
Author(s):  
David E. Loper
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Constant Heat Flux ◽  
Ekman Pumping ◽  
Parallel Plates ◽  
Axially Symmetric ◽  
Hydromagnetic Flow ◽  
Thermal Boundary Conditions ◽  
Fluid Diffusion

The hydromagnetic flow of a thermally stratified fluid confined between two rotating parallel plates is studied. The flow is assumed to be linear, steady and axially symmetric. The flow is driven both mechanically and thermally and general thermal boundary conditions are applied. Attention is focused upon the mechanism controlling the interior fluid (diffusion, Ekman pumping or hydro-magnetic forces) and upon the conditions under which laminated flow (∂v/∂z ≠ 0) may occur. It is found that the occurrence of laminated flow is very sensitive to the thermal boundary conditions and is suppressed by hydromagnetic effects. For mixed boundary conditions, hydromagnetic forces control the interior and laminated flow is suppressed if α [ges ] O(1), where α2 represents the ratio of hydro-magnetic to Coriolis forces. For a constant heat flux, this occurs for a much weaker magnetic field: if α [ges ] O(E¼). For a restricted range of the parameters, a new boundary layer, called the thermomagnetic layer, in which Coriolis, thermal and hydromagnetic forces balance may occur.

An Exact Periodic Solution of a Hydromagnetic Flow of an Oldroyd Fluid in a Channel

1999 ◽  
Vol 66 (4) ◽  
pp. 974-977 ◽  
Author(s):  
R. N. Ray ◽  
A. Samad ◽  
T. K. Chaudhury
Keyword(s):  
Periodic Solution ◽  
Unsteady Flow ◽  
Velocity Gradient ◽  
Separation Of Variables ◽  
The Other ◽  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Mean Velocity ◽  
Oldroyd Fluid ◽  
Viscoelastic Parameters

The unsteady flow of a conducting Oldroyd fluid between two parallel plates, one of which is at rest and the other oscillating in its own plane with a constant mean velocity, has been investigated. Using separation of variables an exact periodic solution for the problem is obtained. Effects of viscoelastic parameters on velocity gradient, skin friction amplitude, and phase angle of the flow are discussed with graphs.

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

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Nanda Poddar ◽  
Subham Dhar ◽  
Bijoy Singha Mazumder ◽  
Kajal Kumar Mondal
Keyword(s):  
Magnetic Field ◽  
Concentration Distribution ◽  
Order Approximation ◽  
Transverse Magnetic ◽  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Molecular Diffusivity ◽  
The Magnetic Field ◽  
Mean Concentration ◽  
Transverse Variation

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 10 δ 2 / D (where δ is half the distance between two parallel plates and D is the molecular diffusivity) to characterize the dispersion process to approach the transverse uniformity.

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