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Analysis of two-phase flow in the porous medium through a rectangular curved duct

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Abstract

The current work is primarily concerned with the analysis of an unsteady incompressible laminar two-phase flow in a porous medium through a rectangular curved duct. The Navier–Stokes equations and the level set equation with boundary conditions represent the corresponding governing equations. Fluid flow through curved rectangular ducts is influenced by the centrifugal action arising from duct curvature and has a unique behavior different from fluid flow through straight ducts. Centrifugal force-induced secondary flow vortices produce spiraling fluid motion within curved ducts. This paper shows the vector plot of the field flow, velocity contours, and fluid volume fractions graphically. The effect of curvature, Dean number, aspect ratio, porosity, and particle concentration on each fluid domain is also displayed. A comparison of the two-phase flow between different fluids is also shown. The results reveal that the unstable behavior of the flow is reduced with increased values of curvature, Dean number, and high viscosity flow.

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Abbreviations

c p :

Specific heat at constant pressure

d :

Width of the curved duct (m)

De :

Dean number

g :

Gravitational acceleration

h :

Height of the curved duct (m)

K :

Porosity

L :

Radius of curvature (m)

P :

Pressure

Re :

Reynolds number

t :

Dimensional time

u, v, w :

Velocity in X, Y, Z axis, respectively

x, y, z :

Cartesian coordinates

γ :

Re-initialization parameter

ε :

Thickness of interface

μ :

Dynamic viscosity of the fluid

ν :

Kinematic viscosity of the fluid

ρ :

Density of the fluid

φ :

Level set function

ϕ :

Particle concentration

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Acknowledgements

This work is done within the framework of the Ph.D. program of the first author under the Department of Mathematics, Bangladesh University of Engineering and Technology (BUET), Dhaka, Bangladesh. Financial support from the University Grant Commission (UGC), Bangladesh Fellowship program is acknowledged.

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Authors and Affiliations

  1. Department of Mathematics, Bangladesh Civil Service, Ministry of Education, Dhaka, 1000, Bangladesh

    Khalilur Rahman

  2. Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, 1000, Bangladesh

    Khalilur Rahman, Salma Parvin & Abdul Hakim Khan

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  1. Khalilur Rahman
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  2. Salma Parvin
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  3. Abdul Hakim Khan
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Correspondence to Khalilur Rahman.

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Rahman, K., Parvin, S. & Khan, A.H. Analysis of two-phase flow in the porous medium through a rectangular curved duct. Exp. Comput. Multiph. Flow 6, 67–83 (2024). https://doi.org/10.1007/s42757-023-0159-9

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  • DOI: https://doi.org/10.1007/s42757-023-0159-9

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