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Entropy generation to predict irreversibilities in poroelastic film with multiple forces: spectral study

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Abstract

The present investigation is useful in medical engineering treatments, in which biothermal therapy is one of the popular treatments. The investigation of transport phenomena of fluid flow and heat in those applications requires multi-physical models featuring heat transfer and deformable porous media. In view of this, it is anticipated to study the influence of thermal buoyancy force and nonlinear radiation on the irreversibility, flow field, solid deformation, and heat transfer characteristics in viscous radiated fluid flow in a vertical deformable porous film. The combined phenomenon of the flow field movement and solid deformation in the porous medium is considered. The flow governing equations are non-dimensionalized and solved numerically by employing Chebyshev spectral method. The impact of important parameters on the fluid velocity, solid displacement, and fluid temperature profiles is depicted graphically and interpreted at length. In the deformable porous layer, it is perceived that the fluid velocity, solid displacement, and fluid temperature profiles decrease with an increase in suction/injection parameter values. The present physical model finds applications in geomechanics (Coussy in Mechanics of porous continua, Wiley, New York, 1995; Biot in J Appl Phys 12(2):155–164, 1941) and biomedical engineering (Mow et al. in J Biomech 17(5):377–394, 1984; Barry et al. in J Appl Math Phys 42:633–648, 1991; Lai et al. in J Biomech Eng 131:245-258, 1991).

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Abbreviations

Be:

Bejan number

Br:

Brinkman number

E G :

Entropy generation (W m−3 K−1)

E G,C :

Characteristic entropy generation

Fr:

Froud number

\(g,g_{x} ,g_{y}\) :

Gravitational acceleration (m2 s−1)

Gr:

Grashof number

h :

Channel height (m)

k :

Porous drag coefficient

\(k^{*}\) :

Mean absorption coefficient

k 0 :

Thermal conductivity (W m−1 K−1)

m :

Temperature parameter

Nr:

Radiation parameter

Ns:

Non-dimensional entropy generation

Nu1, Nu2 :

Nusselt numbers

\(\frac{\partial p}{\partial x},\frac{\partial p}{\partial y}\) :

Axial and transverse pressure gradients (Pa m−1)

q r :

Radiative heat flux (W m−2)

T 0 :

Reference temperature (K)

Re:

Reynolds number

T :

Temperature (K)

T 1 :

Temperature of left wall (K)

T w :

Temperature of right wall (K)

u :

Solid displacement (m)

v :

Fluid velocity (m s−1)

V :

Suction/injection velocity (m s−1)

U 0 :

Characteristic velocity (m s−1)

X, Y :

Space coordinates (m)

x, y :

Non-dimensional space coordinate

\(\beta\) :

Thermal expansion coefficient

\(\delta\) :

Viscous drag parameter

\(\phi\) :

Porous medium volume fraction

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\mu_{a}\) :

Lame constant

\(\rho\) :

Fluid density (kg m−3)

\(\sigma^{*}\) :

Stefan–Boltzmann constant (kg s−3 K−4)

\(\theta_{w}\) :

Temperature ratio parameter

\(\theta\) :

Non-dimensional temperature

\(\tau_{0} ,\tau_{1}\) :

Shear stress (kg m−1 s−2)

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Warangal, Telangana, 506004, India

    Srinivas Jangili

  2. Department of Mathematics, BMS College of Engineering (Affiliated to VTU), Bangalore, Karnataka, 560019, India

    B. Mallikarjuna

  3. Department of Mathematics, MLRITM, Hyderabad, 500043, India

    G. Gopi Krishna

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  1. Srinivas Jangili
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  2. B. Mallikarjuna
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  3. G. Gopi Krishna
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Correspondence to Srinivas Jangili.

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Jangili, S., Mallikarjuna, B. & Gopi Krishna, G. Entropy generation to predict irreversibilities in poroelastic film with multiple forces: spectral study. Indian J Phys 95, 2719–2732 (2021). https://doi.org/10.1007/s12648-020-01922-0

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