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Effects of Prandtl Number on Natural Convection in a Cavity Filled with Silver/Water Nanofluid-Saturated Porous Medium and Non-Newtonian Fluid Layers Separated by Sinusoidal Vertical Interface

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Abstract

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6 < n < 1.4), Darcy number (10−5 < Da < 10−1), volume fraction (0 < ∅ < 0.2), and undulation number (1 < N < 4) on the thermal performance of the cavity for Prandtl numbers (Pr) ranging from 0.015 to 13.4 and Rayleigh number (Ra) equal to 105. Results showed that increasing Prandtl and Darcy numbers raised the average Nusselt number. However, increasing the power-law index reduced the average Nusselt number. When the non-Newtonian fluid behaves as a shear-thinning fluid (n = 0.7) and Pr = 13.4, the effect of the undulations number of the sinusoidal vertical interface on average Nu is not evident for a given range of volume fraction.

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Abbreviations

C p :

Specific heat at constant pressure (KJ/kg K)

D :

Rate of strain-tensor

g :

Gravitational acceleration (m/s2)

k :

Thermal conductivity (W/m K)

L :

Dimensionless Length and Height of the cavity

P :

Dimensionless pressure

p :

Pressure (Pa)

Pr :

Prandtl number (νf/αf)

Ra :

Rayleigh number (gβfL3 ∆T/νfαf)

T :

Temperature (K)

Da :

Darcy numbers

N :

Number of undulation

Nu :

Nusselt number

n :

Power-law index

U :

Dimensionless velocity component in x-direction

u :

Velocity component in x-direction (m/s)

V :

Dimensionless velocity component in y-direction

v :

Velocity component in y-direction (m/s)

X :

Dimensionless coordinate in horizontal direction

x :

Cartesian coordinates in horizontal direction (m)

Y :

Dimensionless coordinate in vertical direction

y :

Cartesian coordinate in vertical direction (m)

θ :

Dimensionless temperature (T − Tc/ΔT)

Ψ :

Dimensional stream function (m2/s)

ψ :

Dimensionless stream function

μ :

Dynamic viscosity (kg s/m)

ν :

Kinematic viscosity (μ/ρ)(Pa s)

α :

Thermal diffusivity coefficient (m2/s)

∅ :

Nanoparticle volume fraction (%)

ε :

Permeability of porous medium

β :

Volumetric coefficient of thermal expansion (K−1)

ρ :

Density (kg/m3)

β :

Thermal expansion (1/K)

σ :

The consistency coefficient

c:

Cold

fl:

Base fluid

h:

Hot

pn:

Porous-nanofluid

nN:

non-Newtonian fluid

sn:

Solid-nanoparticle

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Authors and Affiliations

  1. Department of Mechanical Engineering, College of Engineering, University of Babylon, Babylon, Iraq

    Qusay R. Al-Amir, Saba Y. Ahmed, Hameed K. Hamzah & Farooq H. Ali

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  1. Qusay R. Al-Amir
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  2. Saba Y. Ahmed
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  3. Hameed K. Hamzah
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  4. Farooq H. Ali
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Correspondence to Saba Y. Ahmed.

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Al-Amir, Q.R., Ahmed, S.Y., Hamzah, H.K. et al. Effects of Prandtl Number on Natural Convection in a Cavity Filled with Silver/Water Nanofluid-Saturated Porous Medium and Non-Newtonian Fluid Layers Separated by Sinusoidal Vertical Interface. Arab J Sci Eng 44, 10339–10354 (2019). https://doi.org/10.1007/s13369-019-04115-y

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