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Electro-osmotic effect on the three-layer flow of Binary nanoliquid between two concentric cylinders

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Abstract

The three-layer flow of an immiscible nanoliquid in composite annulus with an electro-kinetic effect is analyzed using Buongiorno’s model. This model helps in analyzing the impact of two major phenomena, namely thermophoresis and Brownian motion. In this model, an interfacial layer is formed between the liquids due to the immiscibility of the base liquids. The use of a multilayer model especially in cooling systems brings more applications in many industries such as nuclear, biomedical, and solar. Different from the earlier studies on multilayer channel flow, this paper explains the three-layer flow between two concentric cylinders in the presence of cross-diffusion which makes the work unique. Further, the middle region is assumed to be porous and heat source or sink is applied to the entire system. Also, the flux conservation condition for nanoparticle volume fraction is considered. The equations governing the problem are simplified and are solved using the differential transform method. The results indicate that the electroosmotic parameter enhances the velocity but reduces the electrostatic potential. Further, the diffusion ratio improves the temperature and decreases the solute concentration of the fluid.

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Abbreviations

\(\bar{\psi }\) :

Electrostatic potentials

\(\delta\) :

Dimensionless internal heat source

\(\Gamma\) :

Non-dimensional pressure gradient

\(\psi\) :

Non-dimensional electrostatic potentials

\(\rho\) :

Density \((Kgm^{-3})\)

\(\sigma\) :

Porosity parameter

\(\theta\) :

Dimensionless temperature

\(\kappa\) :

Permeability of porous medium \((m^2)\)

\(\mu\) :

Dynamic viscosity \((Kgm^{-1}s^{-1})\)

\(\Phi\) :

Nanoparticle volume fraction

\(\phi\) :

Non-dimensional nanoparticle volume fraction

\(\lambda _{\text{c}}\) :

Modified mass Grashof number

\(\lambda _{\text{t}}\) :

Modified temperature Grashof number

C :

Solute concentration

\(C_{\text{{w}}_1}\), \(C_{\text{{w}}_2}\) :

Nanoparticle concentration at lower and upper wall

Cp :

Specific heat at constant pressure \((m^2s^{-2})\)

D :

Coefficient of mass diffusivity \((m^2s^{-1})\)

Ec :

Eckert number

g :

Gravitational acceleration \((ms^{-2})\)

\(Gr_{\text{c}}\) :

Local mass Grashof number

\(Gr_{\text{t}}\) :

Local temperature Grashof number

\(K_{\text{T}}\) :

Thermal diffusion ratio

P :

Pressure \((Kgm^{-1}s^{-2})\)

Pr :

Prandtl number

Re :

Reynolds number

S :

Non-dimensional solute concentration

T :

Temperature (K)

\(T_{\text{{w}}_1}\), \(T_{\text{{w}}_2}\) :

Temperature at lower and upper wall (K)

\(w_{\text{i}}\),:

Velocity component for r directions \((ms^{-1})\)

z, r :

Cartesian coordinates (m)

k:

Thermal conductivity \((WK^{-1}m^{-1})\)

1:

Nanoliquid

2:

Hybrid nanoliquid

f :

Base liquid

i :

Region I,II and III

np :

Nanoparticle

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Authors and Affiliations

  1. Department of Mathematics, CHRIST (Deemed to be University), Bangalore, India

    Anandika Rajeev

  2. Department of Sciences and Humanities, CHRIST (Deemed to be University), Bangalore, India

    S. Manjunatha

  3. Department of PG Studies, Government Science College, Chitrdurga, India

    C. S. Vishalakshi

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  1. Anandika Rajeev
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  2. S. Manjunatha
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  3. C. S. Vishalakshi
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Correspondence to S. Manjunatha.

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Rajeev, A., Manjunatha, S. & Vishalakshi, C.S. Electro-osmotic effect on the three-layer flow of Binary nanoliquid between two concentric cylinders. J Therm Anal Calorim 147, 15069–15081 (2022). https://doi.org/10.1007/s10973-022-11684-y

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