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Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts

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Abstract

The present investigative paper explores the hydromagnetic liberated convective along with oscillating flow of an optically thinner second grade fluid delimited during two parallel absorbent walls under the influences of an externally applied transverse magnetic field into a permeable medium. The radiative heat flux and radiation absorption effects are taking into account for considered problem. The leading equations are solved for the velocity, temperature, and concentration fields making utilization of Laplace transformation methodology. The impacts of a mixture of relevant flow parameters on concentration, temperature, and velocity distribution, in addition to the friction factor coefficients, Nusselt number, and Sherwood number, are found and explored using graphs along with tabular format. The magnitude of the velocity field is climbs by an augment in penetrability parameter, and enhances with increase in Hall and ion slip parameters and also skin friction factor coefficients uplift by mounting in Hartmann number.

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Abbreviations

\(u,\,\,v\) :

The velocity components along \(x\) and \(y\) directions respectively (m s−1)

\(B\) :

Magnetic induction vector (Tesla)

\(B_{0}\) :

Applied magnetic field (Tesla)

\(C\) :

Dimensional concentration (kg m−3)

\(C_{w}\) :

The uniform concentration of the fluid at the plate (kg m−3)

\(C_{\infty }\) :

The concentration of the fluid far away from the plate (kg m−3)

\(C_{p}\) :

The specific heat at constant pressure (Kelvin−1m2 s−2)

\(D\) :

Coefficient of mass diffusivity (m2s−1)

\(d\) :

Distance between the plates (m)

\(E\) :

Electric field vector (volts m−1)

Gm:

Mass Grashof number

Gr:

Thermal Grashof number

\(g\) :

Acceleration due to gravity (m s−2)

\(H\) :

Heat source parameter

\(J_{x} ,\,J_{y}\) :

Current densities along x and y directions

\(J\) :

Current density vector (A/m2)

\(k\) :

Permeability of porous medium (m2)

\(K\) :

Permeability parameter

Kr:

Chemical reaction rate constant

Kc:

Chemical reaction parameter

\(k_{1}\) :

Thermal conductivity (Wm−1 K−1)

\(m_{e}\) :

Hall parameter

\(m_{i}\) :

Ion slip parameter

\(M\) :

Hartmann number

N :

Radiation parameter

\(Nu\) :

Nusselt number

Pr :

Prandtl number

S :

Second grade fluid parameter

\(Q\) :

Radiation absorption parameter

\(Q_{0}\) :

Dimensional heat absorption coefficient

\(R\) :

Rotation parameter

Sc:

Schmidt number

\(Sh\) :

Sherwood number

\(t\) :

Time (s)

\(T_{w}\) :

The uniform temperature of the fluid at the plate (K)

\(T_{\infty }\) :

The temperature of the fluid far away from the plate (K)

\(w\) :

Slip velocity (m s−1)

\(w_{0}\) :

Scale of suction velocity

\(\alpha_{1}\) :

Normal stress moduli for second grade fluid

\(\beta\) :

Coefficient of thermal expansion of the fluid

\(\beta *\) :

Coefficient of mass expansion of the solid

\(\nu\) :

Kinematic viscosity of the fluid (m2 s−1)

\(\Omega\)  :

Angular velocity (s−1)

\(\omega_{e}\) :

Cyclotron frequency (Rad Sce−1)

\(\phi\) :

Non-dimensional concentration

\(\rho\) :

Fluid density (kg m−3)

\(\sigma\) :

Electrical conductivity (sm−1)

\(\theta\) :

Non-dimensional temperature

\(\tau\) :

Local skin friction coefficient

\(\tau_{e}\) :

Electron collision time (s)

\(\lambda\) :

Suction parameter

\(e\) :

Electrons

\(i\) :

Ions

\(\infty\) :

Free stream conditions

\(w\) :

Conditions on the wall

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Acknowledgements

The authors are grateful and express their sincere thanks to the editor, reviewers, and Team of Biomass Conversion and Biorefinery for giving suggestions and the improvement of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Rayalaseema University, Kurnool, Andhra Pradesh, 518007, India

    M. Veera Krishna

  2. Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816 – 1364, USA

    K Vajravelu

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Contributions

MVK carried out the problem designing, performed the computational analysis, participated in the sequence alignment, and drafted the manuscript. VK participated in its design and coordination and helped to draft the manuscript. The authors read and approved the final manuscript.

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Correspondence to M. Veera Krishna.

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Krishna, M., Vajravelu, K. Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts. Biomass Conv. Bioref. 14, 8745–8759 (2024). https://doi.org/10.1007/s13399-022-02802-9

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