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Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel

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Abstract

A numerical study of pulsatile flow and mass transfer of an electrically conducting Newtonian biofluid via a channel containing porous medium is considered. The conservation equations are transformed and solved under boundary conditions prescribed at both walls of the channel, using a finite element method with two-noded line elements. The influence of magnetic field on the flow is studied using the dimensionless hydromagnetic number, Nm, which defines the ratio of magnetic (Lorentz) retarding force to the viscous hydrodynamic force. A Darcian linear impedance for low Reynolds numbers is incorporated in the transformed momentum equation and a second order drag force term for inertial (Forchheimer) effects. Velocity and concentration profiles across the channel width are plotted for various values of the Reynolds number (Re), Darcy parameter (λ), Forchheimer parameter (Nf), hydro-magnetic number (Nm), Schmidt number (Sc) and also with dimensionless time (T). Profiles of velocity varying in space and time are also provided. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. Increasing the hydromagnetic number (Nm) from 1 to 15 considerably depresses biofluid velocity (U) indicating that a magnetic field can be used as a flow control mechanism in, for example, medical applications. A rise in Nf from 1 to 20 strongly retards the flow development and decreases the velocity, U, across the width of the channel. The effects of other parameters on the flowfield are also discussed at length. The flow model also has applications in the analysis of electrically conducting haemotological fluids flowing through filtration media, diffusion of drug species in pharmaceutical hydromechanics, and also in general fluid dynamics of pulsatile systems.

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Abbreviations

Dimensional:

 

x,y:

Coordinates parallel and transverse to channel walls

t :

Time variable

V i :

Velocity vector

J i :

Current density vector

B k :

Magnetic field vector

P :

Hydrodynamic pressure

τij :

Shear stress tensor

ρ:

Density of bio-fluid

\(\varepsilon\) ijk :

Permutation symbol

ν:

Kinematic viscosity of bio-fluid

b :

Forchheimer geometric parameter

C :

Concentration of species (e.g. Oxygen)

D :

Coefficient of mass diffusivity of species

\(\frac{d}{dt}\) :

Differential with respect to time following the material particle

H :

Width of channel

B 0 :

y-direction component of magnetic field vector

X :

Transformed coordinate parallel to channel walls

Y :

Transformed coordinate transverse to channel walls

U :

Transformed velocity component in X direction

V 0 :

Transpiration velocity

σ:

Electrical conductivity of haemo-fluid

P * :

Transformed hydrodynamic pressure (* dropped for convenience in analysis)

K :

Permeability of the porous medium

T :

Dimensionless time

Φ:

Dimensionless mass transfer (species concentration) function

Re :

Reynolds number

Nm :

Hydromagnetic number

λ:

Darcian porous parameter

Nf :

Forchheimer porous inertial parameter

Sc :

Schmidt number

()s :

Steady component

()o :

Oscillating component

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Authors and Affiliations

  1. Mathematics Department, Indian Institute of Technology, Roorkee, Uttaranchal, 247667, India

    R. Bhargava & S. Rawat

  2. Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M5 1GD, UK

    H. S. Takhar

  3. Fire Safety Engineering Program, Leeds College of Building/Leeds Metropolitan University, North Street, Leeds, LS2 7QT, UK

    O. Anwar Bég

Authors
  1. R. Bhargava
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  2. S. Rawat
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  3. H. S. Takhar
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  4. O. Anwar Bég
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Correspondence to O. Anwar Bég.

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Bhargava, R., Rawat, S., Takhar, H.S. et al. Pulsatile magneto-biofluid flow and mass transfer in a non-Darcian porous medium channel. Meccanica 42, 247–262 (2007). https://doi.org/10.1007/s11012-007-9052-z

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