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Mixed convection in a triangular cavity permeated with micropolar nanofluid-saturated porous medium under the impact of MHD

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Abstract

This article contains numerical results for mixed convection through an isosceles triangular cavity enclosing micropolar nanofluid when a uniform magnetic field is applied along the x-axis. Heat is provided uniformly through inclined side walls of the enclosure where the bottom wall of the enclosure is cold and moves with constant speed. The finite element method has been adopted to compute the numerical simulations for a wide range of pertinent flow parameters, including Grashof number (\(10^{4} \le {\text{Gr}} \le 10^{5}\)), Hartman number (\(0 \le {\text{Ha}} \le 60\)), Darcy number (\(10^{ - 3} \le {\text{Da}} \le 10^{ - 1}\)), Prandtl numbers (\(0.72 \le { \Pr } \le 6.2\)), viscosity parameter (\(0 \le K_{1} \le 10\)) and solid volume fraction (\(0 \le \phi \le 0.1\)). It is observed through this investigation that introducing nano-sized copper particles amplifies the conductivity of the fluid where augmentation in the strength of the magnetic field attenuates the heat transfer rate in the enclosure. Furthermore, larger values of Darcy number escalate the flow strength in the cavity, and increase in solid volume fraction increases the average Nusselt number.

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Abbreviations

B 0 :

Magnetic induction, Tesla N/Am2

c p :

Specific heat, J/kg K

Da:

Darcy number

g :

Acceleration of gravity, m2/s

Gr:

Grashof number

Ha:

Hartmann number

j :

Micro-inertia, m2

K 1 :

Dimensionless viscosity parameter

K 2 :

Permeability, m2

k :

Thermal conductivity, W/m K

L :

Cavity width, m

N :

Microrotation, m

Nu:

Nusselt number

p :

Pressure, N/m2

P :

Dimensionless pressure, P = pL2/ρ nf α 2f

Pr:

Prandtl number

R :

Residue

Re:

Reynolds number

T :

Local temperature, K

T c :

Cold wall temperature, K

T h :

Hot wall temperature, K

u :

Velocity component in x direction

U :

Dimensionless velocity component in X direction

U o :

Velocity of moving wall

v :

Velocity component in y direction

V :

Dimensionless velocity component in X direction

x, y :

Dimensional coordinates

X, Y :

Dimensionless coordinates

α :

Thermal diffusivity, m2/s

β :

Coefficient of thermal expansion, K−1

γ :

Penalty parameter

γ 1 :

Spin-gradient viscosity, kg/ms

ΔT :

Temperature difference, T h − T c, K

\(\varepsilon\) :

Perturbation parameter

\(\theta\) :

Dimensionless temperature (T − T c)/(T h−T c)

\(\kappa\) :

Vortex viscosity

\(\mu\) :

Dynamic viscosity, kg/m s

\(\nu\) :

Kinematic viscosity, m2/s

\(\rho\) :

Local density, kg/m3

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

Characteristic density, kg/m3

\(\sigma\) :

Electrical conductivity, Am/V

\(\sigma_{1}\) :

Eigenvalues

\(\sigma_{\text{r}}\) :

Real part of eigenvalues

\(\sigma_{\text{i}}\) :

Imaginary part of eigenvalues

\(\phi\) :

Solid volume fraction

\(\phi_{\text{i}}\) :

Base functions

\(\psi\) :

Dimensionless stream function

\(\varOmega\) :

Internal domain

f :

Base fluid

nf:

Nanofluid

s :

Nanoparticle

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Acknowledgements

The authors acknowledge the support of Higher Education Commission of Pakistan under the scheme “National Research Program for Universities” through Project Number 3713. Furthermore, the authors are grateful to the editor and the anonymous reviewers for the insightful comments and suggestions which improved the quality of the manuscript.

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Authors and Affiliations

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

    Tariq Javed, Ziafat Mehmood & Muhammad Arshad Siddiqui

Authors
  1. Tariq Javed
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  2. Ziafat Mehmood
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  3. Muhammad Arshad Siddiqui
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Correspondence to Ziafat Mehmood.

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Technical Editor: Jader Barbosa Jr.

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Javed, T., Mehmood, Z. & Siddiqui, M.A. Mixed convection in a triangular cavity permeated with micropolar nanofluid-saturated porous medium under the impact of MHD. J Braz. Soc. Mech. Sci. Eng. 39, 3897–3909 (2017). https://doi.org/10.1007/s40430-017-0850-5

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