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Hydromagnetic solid–liquid pulsatile flow through concentric cylinders in a porous medium

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Abstract

The current research is reported about the hydromagnetic solid–liquid flow in an annulus between two concentric circular cylinders embedded in a porous media. The impact of joule heating is also accounted for. Unlike the usually applied constant pressure gradient, the pulsatile pressure gradient is employed. The flow problem is first modeled and then tackled by Runge–Kutta–Fehlberg fourth–fifth-order (RKF45) numerical scheme along with shooting algorithm. The impacts of emerging parameters namely magnetic field parameter and porosity parameter on velocity and temperature distributions are displayed through graphs and briefly addressed.

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Abbreviations

A:

A constant with a unit of pressure gradient (Pam−1)

θ f, θ s :

Dimensionless temperature of fluid and particle phase (−)

u *f , u *s :

Dimensionless velocity for fluid and solid phase (−)

Ec :

Eckert number (−)

u f, u s :

Fluid phase and solid phase velocity (ms−1)

B 0 :

Magnetic field strength (T)

M :

Magnetic parameter (−)

N 1 :

Particles number density (kgm−3)

k * :

Permeability of porous medium (m2)

K :

Porosity parameter (−)

Pr :

Prandtl number (−)

p :

Pressure (Pa)

r s :

Radius of spherical particles (m)

f 1 :

Ratio of densities of particle to fluid (−)

U :

Reference velocity (ms−1)

Re :

Reynolds number (−)

c f, c s :

Specific heat of fluid and solid particles (m2s−2K−1)

S :

Stokes drag coefficient (−)

T a, T b :

Temperature at surface of inner and outer cylinder (K)

T f, T s :

Temperature for fluid and solid particle (K)

k :

Thermal conductivity (Wm−1K−1)

r, z :

Variables representing r and z directions (m)

C :

Volume fraction of particles (kgm−3)

f:

Fluid (−)

s:

Solid particles (−)

λ :

Aspect ratio (−)

ρ :

Density (kgm−3)

ɛ :

Dimensionless small quantity (−)

α :

Dust parameter (−)

μ :

Dynamic viscosity (kgm−1s−1)

σ :

Electrical conductivity (kg−1m−3s3A2)

ω :

Frequency of oscillation (Hz or s−1)

β 1 :

Frequency parameter (−)

ν :

Kinematic viscosity [m2s−1]

γ :

Ratio of specific heat of particle to fluid (−)

ξ, η :

Similarity variables (−)

τ T :

Thermal equilibrium time (s)

τ v :

Velocity relaxation time (s)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, FBAS, International Islamic University, Islamabad, Pakistan

    Muhammad Muddassar Maskeen & Ahmad Zeeshan

  2. Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantonment, 47040, Pakistan

    Obaid Ullah Mehmood

Authors
  1. Muhammad Muddassar Maskeen
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  2. Obaid Ullah Mehmood
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  3. Ahmad Zeeshan
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Correspondence to Obaid Ullah Mehmood.

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Maskeen, M.M., Mehmood, O.U. & Zeeshan, A. Hydromagnetic solid–liquid pulsatile flow through concentric cylinders in a porous medium. J Vis 21, 407–419 (2018). https://doi.org/10.1007/s12650-017-0468-9

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