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Influence of Electroosmosis Mechanism and Chemical Reaction on Convective Flow Over an Exponentially Accelerated Plate

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Abstract

This article is primarily attained to study the electric double layer (EDL) phenomena and chemical reaction effects on unsteady natural convection flow through exponentially accelerated plate. The Poisson Boltzmann equation is used to derive the electroosmosis mechanism. The special effect of Lorentz and Darcy forces are considered in the proposed mathematical model. Governing equations of proposed model is linearized through Debye-Hückel linearization and dimensionless analysis. The system of nonlinear partial differential equations are solved with the help of Laplace transform technique. Further, the Nusselt number and Sherwood number are also derived. The graphical outcomes for velocity, temperature, concentration, Nusselt number and Sherwood number are illustrated with the help of Matlab software. Validation of the present solution is obtained by Laplace transform method which is compared with numerical solution obtained by finite difference with the help of MATLAB code. It is seen that the velocity profile is unequivocally reliance with attractive field and EDL thickness. It is also found that chemical reaction parameter significantly pretends on temperature distribution. This idea can be equipped for being applied in different complex frameworks where the electroosmosis stream can be moved by CPUs gadget.

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Abbreviations

\(B_{0}\) :

Uniform magnetic field,

\(C^{\prime}\) :

Concentration,

\(C^{\prime}_{w}\) :

Concentration of the plate,

\(C_{\infty }^{\prime}\) :

Concentration of the fluid far away from the plate,

\(C_{p} \) :

Specific heat at constant pressure,

\(g\) :

Acceleration due to gravity,

\(q_{r}\) :

Radiative heat fluxes in the -direction,

\(D\) :

Mass diffusivity,

\(T^{\prime}\) :

Fluid temperature,

\(T^{\prime}_{w}\) :

Temperature of the plate,

\(T^{\prime}_{\infty }\) :

Temperature of the fluid far away from the plate,

\(t^{\prime}\) :

Time,

\(u^{\prime}\) :

Velocity of the fluid in the direction,

\(y^{\prime}\) :

Coordinate axis normal to the plate,

\(\bar{\kappa }\) :

Thermal conductivity of the fluid,

\(\beta\) :

Volumetric coefficient of thermal expansion,

\(\beta _{1}\) :

Volumetric coefficient of expansion with concentration,

\(u_{0}\) :

Velocity of the plate,

\(\mu\) :

Coefficient of viscosity,

\(\nu\) :

Kinematic viscosity,

\(\rho\) :

Density of the fluid,

\(\sigma\) :

Electric conductivity,

\(\sigma ^{*}\) :

Stefan-Boltzmann constant,

\(a*\) :

Absorption coefficient,

\(\alpha ^{\prime}\) :

Accelerate parameter

\(u\) :

Velocity,

\(\theta\) :

Fluid temperature,

\(C\) :

Concentration,

\(y\) :

Coordinate axis normal to the plate,

\(t\) :

Time,

\(M\) :

Hartmann number,

\(k_{1}\) :

Permeability parameter (porous),

\(k_{2}\) :

Chemical reaction coefficient,

\(Gr\) :

Thermal Grashof number,

\(Gm\) :

Mass Grashof number,

\(Uhs\) :

Helmholtz-Smoluchowski velocity,

\(\kappa\) :

Electroosmosis parameter,

\(\Pr\) :

Prandtl number,

\(R\) :

Thermal radiation,

\(Sc\) :

Schmidt number

\(\alpha\) :

Exponential accelerate parameter.

\(Nu\) :

Nusselt number

\(Sh\) :

Sherwood number

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Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellor, Tamilnadu, 632115, India

    R. Vijayaragavan

  2. Department of Mathematics, Adhiparasakthi College of Arts and Science (Autonomous), Kalavai, Tamilnadu, 632506, India

    V. Bharathi

  3. Department of Mathematics Avvaiyar Government College for Women, U.T of Puducherry, Karaikal, 609 602, India

    J. Prakash

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Appendix

Appendix

$$ \begin{aligned} & a_{1} = \frac{R}{{\Pr }},a_{2} = \frac{{\left( {M{\mkern 1mu} k_{1} + 1} \right)}}{{k_{1} }},a_{3} = \frac{{Gm}}{{1 - Sc}},a_{4} = \frac{{Sc{\mkern 1mu} k_{2} - a_{2} }}{{Sc - 1}},a_{5} = \frac{{a_{3} }}{{a_{4} }},a_{6} = \frac{{G_{r} }}{{1 - \Pr }},\\ a_{7} &= \frac{{R - a_{2} }}{{\Pr - 1}},a_{8} = \frac{{a_{6} }}{{a_{7} }}, \hfill \\ a_{9} & = \kappa ^{2} {\mkern 1mu} Uhs,a_{{10}} = \kappa ^{2} - a_{2} ,a_{{11}} = \frac{{a_{9} }}{{a_{{10}} }},a_{{12}} = a_{5} + a_{8} + a_{{11}} ,\eta = \frac{y}{{2\sqrt t }}, \hfill \\ \end{aligned} $$

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Vijayaragavan, R., Bharathi, V. & Prakash, J. Influence of Electroosmosis Mechanism and Chemical Reaction on Convective Flow Over an Exponentially Accelerated Plate. Int. J. Appl. Comput. Math 7, 124 (2021). https://doi.org/10.1007/s40819-021-01063-w

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