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Chemically reactive magnetohydrodynamic mixed convective nanofluid flow inside a square porous enclosure with viscous dissipation and Ohmic heating

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Abstract

The characteristics of the mixed convection nanofluid flow inside a square enclosure saturated with porous medium are numerically investigated. The present analysis incorporates the impact of chemical reaction, Joule heating (Ohmic heating), magnetic field, and viscous dissipation. The horizontal walls of the cavity are considered as adiabatic walls. The right and left walls of the cavity are considered as cold and hot walls, respectively. The Buongiorno mathematical model is adopted to characterize the nanoliquid, and the impact of thermophoresis and Brownian motion is accounted in the present model. The equations in the non-dimensional form are solved by using the Marker-And-Cell (MAC) technique, and the outcomes are illustrated graphically. The results conclude that the magnitude of the streamline profiles decreases as the Hartmann number rises. The free convection is more dominant than forced and mixed convections. The growing values of chemical reaction parameter slightly increase the fluid flow and having a significant change in the mass transfer profiles.

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Data Availability Statement

The data will be made available on reasonable request. This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

Abbreviations

x, y :

Dimensional Cartesian coordinates (m)

u, v :

Dimensional velocity components in \(x,\;y\) directions \(\left( {\mathrm{{m}}\,{\mathrm{{s}}^{\mathrm{{ - 1}}}}} \right)\)

g :

Acceleration due to gravity \((\text{m}\,\,\text{s}^{-2})\)

L :

Length of the enclosure (m)

K :

Permeability of the porous medium \((\text{m}^{2})\)

\(B_0\) :

Magnetic field’s strength \((\text{kg}\,\,\text{s}^{-2}\,\,\text{A}^{-1})\)

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

Thermophoresis diffusion coefficient \((\text{m}^{2}\,\text{s}^{-1})\)

p :

Dimensional pressure (Pa)

\(U_0\) :

Constant reference velocity \(\left( {\text{m}\,{\text{s}^{{{ - 1}}}}} \right)\)

\(D_{\text {B}}\) :

Brownian diffusion coefficient \((\text{m}^{2}\,\text{s}^{-1})\)

\(C_{\text {h}}\) :

High concentration \((\text{kg}\,\text{m}^{-3})\)

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

Low concentration \((\text{kg}\,\text{m}^{-3})\)

C :

Dimensional concentration of the fluid \((\text{kg}\,\text{m}^{-3})\)

U, V :

Dimensionless velocities along X and Y directions (–)

\(T_{\text {h}}\) :

Hot wall temperature (K)

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

Cold wall temperature (K)

\(t^*\) :

Dimensional time (s)

T :

Dimensional temperature (K)

X, Y :

Dimensionless Cartesian coordinate system (–)

P :

Dimensionless pressure (–)

Nu:

Nusselt number (–)

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

Thermophoresis parameter (–)

Re:

Reynolds number (–)

Kr :

Chemical reaction parameter (–)

Pr:

Prandtl number (–)

Le:

Lewis number (–)

Ec:

Eckert number (–)

\(N_{\text {B}}\) :

Brownian motion parameter (–)

Da:

Darcy parameter (–)

Ri:

Richardson number (–)

Gr:

Grashof number (–)

Ha:

Hartmann number (–)

Nr :

Buoyancy ratio parameter (–)

R :

Dimensional chemical reaction parameter (–)

\(\mu _{\text {f}}\) :

Dynamic viscosity of the fluid \((\text{kg}\,\text{m}^{-3} \text{s}^{-1})\)

\(\rho _{\text {f}}\) :

Fluid density \((\text{kg}\,\text{m}^{-3})\)

\(\rho _{\text {p}}\) :

Density of the nanoparticle \((\text{kg}\,\text{m}^{-3})\)

\(\sigma _{\text {f}}\) :

Electrical conductivity \((\text{S}\,\text{m}^{-1})\)

\(\beta _{\text {f}}\) :

Thermal diffusivity of the fluid \((\text{K}^{-1})\)

\(\nu _{\text {f}}\) :

Kinematic viscosity of the fluid \((\text{m}^{2}\text{s}^{-1})\)

\(\alpha _{\text {f}}\) :

Thermal diffusivity of the fluid \((\text{m}^{2}\text{s}^{-1})\)

\(\theta\) :

Dimensionless temperature (–)

\(\phi\) :

Dimensionless concentration (–)

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Acknowledgements

The second author (R. Sivaraj) is thankful to the Ministry of Education, United Arab Emirates, for the financial assistance to complete this research work through the Collaborative Research Program Grant 2019 (CRPG 2019) with the Fund No. 21S107.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India

    A. Sumithra & R. Sivaraj

  2. Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates

    R. Sivaraj

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  1. A. Sumithra
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Sumithra, A., Sivaraj, R. Chemically reactive magnetohydrodynamic mixed convective nanofluid flow inside a square porous enclosure with viscous dissipation and Ohmic heating. Eur. Phys. J. Plus 137, 1193 (2022). https://doi.org/10.1140/epjp/s13360-022-03409-9

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