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Effect of finite size of ions on entropy generation characteristics for electroosmotic flow through microchannel considering interfacial slip

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Abstract

A theoretical model for entropy generation for an electroosmotic flow through a rectangular microchannel considering the finite size of ions and interfacial slip has been developed in this work to offer physical insights into the contributors of entropy generation. We use the Navier-slip model to represent interfacial slip and the modified Poisson–Boltzmann equation to describe the finite size of ions on the electric double-layer potential distribution without Debye–Huckel linearization. The modified Poisson–Boltzmann and the conservation of mass, momentum, and energy equations have been numerically solved using a finite element method-based solver. The numerical model is extensively validated with the reported experimental and numerical works. Results are presented for different viscous dissipation, Joule heating, Debye parameter, thermal Peclet number values, steric factor, and slip coefficient. It reveals that the effect of the finite size of ions on entropy generation with the consideration of interfacial slip strongly depends on the strength of the viscous and Joule heating. The average total entropy generation decreases with the slip coefficient, while it increases with the steric factor for lower values of thermal Peclet number (Pe). In contrast, the effect is opposite at higher values of Pe. For Pe = 0.1, the decrements in average total entropy generation are found as 45.25%, 38.42%, 34.89%, and 32.45%, respectively, for the steric factor of 0, 0.1, 0.2, and 0.3 with a slip coefficient of 0.1 as compared to without slip and point ion charge. For Pe = 2, the corresponding increments in average total entropy generation are found as 39.72%, 27.26%, 22.55%, and 19.69%, respectively.

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Abbreviations

Be:

Bejan number

Br:

Brinkman number

c p :

Specific heat (J kg−1 K−1)

e :

Electron charge (C)

\({\vec{\mathbf{E}}}\) :

External electric field (V m−1)

\({\vec{\text{F}}}_{{\text{b}}}\) :

Dimensionless body force

G :

Joule heating parameter

H :

Half channel height (m)

k :

Thermal conductivity (Wm−1 K1)

k B :

Boltzmann constant

L :

Channel length (m)

n 0 :

Bulk-ion concentration (1 m−3)

N″:

Normalized local entropy generation

N :

Normalized average entropy generation

\(\overline{{{\text{Nu}}}}\) :

Average Nusselt number

p :

Pressure (N m−2)

P :

Normalized pressure

Pe:

Thermal Peclet number

q s :

Wall heat flux (W m−2)

Re:

Reynolds number

S″:

Local entropy generation rate (W K−1 m−3)

T :

Temperature (K)

\({\vec{\mathbf{V}}}\) :

Velocity field (m s−1)

\({\overline{\text{u}}}\) :

Dimensionless velocity field

U HS :

Helmholtz–Smoluchowski velocity (m s−1)

u,v :

x- and y-velocity component (m s−1)

U,V:

Dimensionless x and y velocity

X,Y:

Dimensionless coordinate

Z:

Valence

β :

Slip length (m)

β :

Slip coefficient

ε :

Permittivity of the medium (C V−1 m−1)

λ D :

Debye length (m)

κ :

Debye parameter

μ :

Dynamic viscosity (kg/m s)

θ :

Dimensionless temperature

Θ:

Dimensionless parameter

ρ f :

Fluid density (kg m−3)

ρ e :

Surface charge density (C m−2)

σ :

Fluid electrical conductivity (S m−1)

υ :

Steric factor

ψ :

EDL potential (V)

\(\overline{\psi }\) :

Dimensionless EDL potential

ζ*:

Zeta potential (V)

ζ :

Normalized zeta potential

avg:

Average

i:

Inlet

r:

Reference

s:

Surface

t:

Total

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  1. Department of Mechanical Engineering, National Institute of Technology Silchar, Silchar, Assam, 788010, India

    T. Sujith, Sumit Kumar Mehta & Sukumar Pati

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  1. T. Sujith
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Sujith, T., Mehta, S.K. & Pati, S. Effect of finite size of ions on entropy generation characteristics for electroosmotic flow through microchannel considering interfacial slip. J Therm Anal Calorim 148, 489–503 (2023). https://doi.org/10.1007/s10973-022-11731-8

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