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Thermal analysis of electroosmotic flow in a vertical ciliated tube with viscous dissipation and heat source effects

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Abstract

Thermal analysis of electroosmotic flow of Newtonian fluid in the presence of viscous dissipation and heat source in a vertical ciliated tube is discussed. Three different cases of electroosmotic flow with heat source, viscous dissipation and buoyancy effects are presented, and their solutions are calculated analytically. Exact solutions for velocity and temperature field are calculated for the first case (presence of heat source and buoyancy force) and second case (presence of viscous dissipation), but the approximate solution is calculated by the Adomian decomposition method for the third case (presence of buoyancy force and viscous dissipation). The modeled equations of electroosmotic flow are reduced into simple equations by the long wavelength and low Reynolds number approximation. Influences of physical parameters are graphically computed for axial velocity, temperature profile, pressure gradient and stream function. It is observed that electroosmosis shows the significant effect on velocity and temperature profile in the presence of viscous dissipation and buoyancy force. This mathematical model gives a deep understanding to describe the thermal analysis in biomimetic ciliary flow and for the efficient flow of highly viscous fluid due to artificial cilia on glass tube used in laboratory.

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Abbreviations

\(w,\,u\) :

Axial and radial velocity in wave frame

T:

Temperature profile

\(\varOmega\) :

Potential function

\(\zeta\) :

Zeta potential

P :

Pressure

\({\varvec{\upvarepsilon}}\) :

Cilia length

\(\psi\) :

Stream function

\(Gr\) :

Grashof number

\(c\) :

Wave speed

\(k\) :

Electroosmotic parameter

\(Br\) :

Brinkman number

\(a\) :

Mean radius of the tube

\(Uhs\) :

Helmholtz–Smoluchowski velocity

\(\eta\) :

Heat source

\(\lambda\) :

Wavelength

\(\rho_{\text {e}}\) :

Electric charge density

\(\nu \;\) :

Dielectric permittivity of the medium

n0 :

Number density

e:

Proton charge

\(t\) :

Valence of elementary charge

kb :

Boltzmann constant

T0 :

Absolute temperature

\(\rho_{f}\) :

Fluid density

\(\mu\) :

Viscosity coefficient

g:

Acceleration of gravity

cp :

Heat capacity

m:

Thermal conductivity

\(\varphi\) :

Dimensionless temperature

\(\alpha\) :

Eccentricity of ellipse

\(\beta\) :

Wave number

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Authors and Affiliations

  1. Department of Mathematics & Statistics, International Islamic University, Islamabad, 44000, Pakistan

    F. Gul & K. Maqbool

  2. Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Near Zero Point, G-7/1, Islamabad, 44000, Pakistan

    A. B. Mann

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  1. F. Gul
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Gul, F., Maqbool, K. & Mann, A.B. Thermal analysis of electroosmotic flow in a vertical ciliated tube with viscous dissipation and heat source effects. J Therm Anal Calorim 143, 2111–2123 (2021). https://doi.org/10.1007/s10973-020-09702-y

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