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Effect of Magnetic Field on Mixed Convection Flow in a Porous Enclosure Using Nanofluids

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Abstract

Two dimensional combined free-forced convection of Cu-water nanofluid in a square enclosure filled with fluid saturated porous medium subjected to uniform magnetic field has been numerically analyzed in the present work. The mathematical formulation consists of Darcy–Brinkman Forchheimer extended momentum equation with the enclosure having adiabatic top and bottom walls and isothermally cooled vertical side walls. Study has been performed over various ranges of governing parameters like Richardson number, Darcy number, Hartmann number and solid volume fraction. The results are presented in the form of hydrodynamic and temperature fields, average Nusselt number, velocity graphs and they are discussed to expound the effects of the physical parameters in the solution.

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Abbreviations

\(\hbox {B}_{0}\) :

Magnetic field (T)

\(\hbox {c}_{\mathrm{p}}\) :

Fluid specific heat [(J/(kg K)]

Da:

Darcy number (\({=}\kappa /L^{2}\))

g:

Gravitational acceleration (\(\hbox {m}/\hbox {s}^{2})\)

Gr:

Grashof number (\({=}g\beta (T_{h}-T_{c})L^{3}/\nu _{f}^{2}\))

H:

Height of the enclosure (m)

Ha:

Hartmann number (\({=}B_0 L\surd \sigma _{nf} /\rho _{nf} \nu _f\))

K:

Thermal conductivity (W/m K)

L:

Width of the enclosure (m)

Nu:

Local Nusselt number

\(\overline{Nu}\) :

Average Nusselt number

p:

Pressure (\(\hbox {N}/\hbox {m}^{2})\)

P:

Dimensionless pressure

Pr:

Prandtl number (\({=}\nu _f /\alpha _f\))

Re:

Reynolds number (\({=}U_{0}L/\nu _f\))

Ri:

Richardson number (\({=}Gr/Re^{2}\))

t:

time (s)

T:

Dimensionless temperature (K)

\(\hbox {U}_{0}\) :

Lid velocity (m/s)

u,v:

Velocity components (m/s)

U,V:

Dimensionless velocity components

x,y:

Cartesian coordinates (m)

X,Y:

Dimensionless Cartesian coordinates

\(\upalpha \) :

Thermal diffusivity (\(\hbox {m}^{2}/\hbox {s}\))

\(\upbeta \) :

Coefficient of thermal expansion (1/K)

\(\upchi \) :

Specific heat ratio

\(\upphi \) :

Phase deviation

\(\upkappa \) :

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

\(\upmu \) :

Dynamic viscosity (\(\hbox {Ns}/\hbox {m}^{2})\)

\(\upnu \) :

Kinematic viscosity (\(\hbox {m}^{2}/\hbox {s}\))

\(\uptheta \) :

Temperature

\(\uprho \) :

Density of the working fluid (\(\hbox {kg}/\hbox {m}^{3})\)

\(\upsigma \) :

Electrical conductivity (s/m)

\(\uptau \) :

Dimensionless time

c:

Cold

f:

Fluid

h:

Hot

0:

Reference state

P:

Solid particle

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Acknowledgements

The author A.SHAMADHANI BEGUM gratefully acknowledges for the financial support from the UGC, New Delhi for BSR-JRF Fellowship.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

    N. Nithyadevi & A. Shamadhani Begum

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  1. N. Nithyadevi
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Correspondence to A. Shamadhani Begum.

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Nithyadevi, N., Begum, A.S. Effect of Magnetic Field on Mixed Convection Flow in a Porous Enclosure Using Nanofluids. Int. J. Appl. Comput. Math 3, 3433–3442 (2017). https://doi.org/10.1007/s40819-017-0305-9

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