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Impacts of Variable Porosity and Variable Permeability on the Thermal Augmentation of Cu–H2O Nanofluid-Drenched Porous Trapezoidal Enclosure Considering Thermal Nonequilibrium Model

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Abstract

Our present work studies the impacts of variable porosity and variable permeability on the transient buoyancy-induced heat transmission flow of Cu–H2O nanofluid through a holey medium (glass bead, aluminum foam and sandstone) inside a right-angle trapezoidal cavity considering thermal nonequilibrium states amid the solid matrix and the nanofluid. We carried out numerical simulation by utilizing the Galerkin finite element method. We explored the impacts of the different model parameters on the thermal characteristics in details. The obtained numerical results confirm that the critical Rayleigh number, \( {\text{Ra}}_{\text{c}} \), determining the thermal nonequilibrium state increased by increasing the Nield number, whereas it is found to be diminished with the increase in the diameter of the beads constructing the porous medium as well as with the porosity parameter. Additionally, the average Nusselt number in a porous medium having variable porosity is found to be higher compared to the medium of the uniform porosity. Increasing the variable porosity can significantly (more than 500%) increase the rate of heat transfer of the nanofluid in a porous medium. The higher porosity of the medium enhances the thermal state of a system to make it thermal nonequilibrium from the thermal equilibrium state. Furthermore, nanofluid flow in glass bead porous medium provides maximum (5% and 14% increase compared to the sandstone and aluminum foam, respectively) heat transmission rate.

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Abbreviations

\( A_{1} \) :

Aspect ratio

\( A_{2} \) :

Aspect ratio

\( c_{1} \) :

Empirical constant

\( c_{2} \) :

Empirical constant

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

Specific heat (J/kg K)

Da:

Darcy number

\( d_{\text{p}} \) :

Solid particles diameter in the porous medium (m)

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

Dimensionless solid particles diameter in the porous medium

\( g \) :

Acceleration as a result of gravity (m/s2)

\( h \) :

Interface heat transmission coefficient among the nanofluid and solid matrix (kg/ms)

\( H \) :

Height of the cavity (m)

\( K \) :

Permeability (m2)

\( l \) :

Length of the upper wall (m)

\( L \) :

Length of the lowest wall (m)

Ni:

Nield number

Mu:

Nusselt number

\( p \) :

Dimensional pressure (Pa)

\( P \) :

Non-dimensional pressure

Ra:

Rayleigh number

\( {\text{Ra}}_{\text{c}} \) :

Critical Rayleigh number

\( t \) :

Dimensional time (s)

\( T \) :

Temperature (K)

\( T_{0} \) :

Reference temperature (K)

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

Temperature of the hot wall (K)

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

Temperature of the cold wall (K)

\( (u,v) \) :

Dimensional velocity components (m/s)

\( (U,V) \) :

Non-dimensional velocity components

\( (x,y) \) :

Dimensional coordinates (m)

\( (X,Y) \) :

Non-dimensional coordinates

\( \alpha \) :

Thermal diffusivity (m/s2)

\( \beta \) :

Coefficient of volume expansion (1/K)

\( \tau \) :

Nondimensional time

\( \rho \) :

Fluid density (kg/m3)

\( \mu \) :

Dynamic viscosity (Pa)

\( \upsilon \) :

Kinematic coefficient of viscosity (m/s2)

\( \theta \) :

Non-dimensional temperature

\( \phi \) :

Nanoparticle volume fraction

\( \kappa \) :

Thermal conductivity (W/m K)

\( \lambda \) :

Ratio of diffusivities

\( \varepsilon \), \( \varepsilon^{*} \) :

Porosity

\( \varepsilon_{\infty } \) :

Uniform porosity

\( \delta \) :

Ratio of conductivities

nf :

Nanofluid

\( bf \) :

Base fluid

\( sp \) :

Solid particles

\( s \) :

Solid matrix

\( t \), \( \tau \) :

Partial derivative w.r.t. \( t \), \( \tau \)

\( x \), \( X \) :

Partial derivative w.r.t. \( x \), \( X \)

\( y \), \( Y \) :

Partial derivative w.r.t. \( y \), Y

h :

Hot

c :

Cold

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Funding

This study was funded by the research Grant IG/SCI/DOMS/18/10.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Sultan Qaboos University, PO Box 36, 123, Al-Khod, Muscat, Sultanate of Oman

    Sheikha M. Al-Weheibi & M. M. Rahman

  2. Department of Industrial and Mechanical Engineering, Ryerson University, Toronto, Canada

    M. Z. Saghir

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  1. Sheikha M. Al-Weheibi
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Al-Weheibi, S.M., Rahman, M.M. & Saghir, M.Z. Impacts of Variable Porosity and Variable Permeability on the Thermal Augmentation of Cu–H2O Nanofluid-Drenched Porous Trapezoidal Enclosure Considering Thermal Nonequilibrium Model. Arab J Sci Eng 45, 1237–1251 (2020). https://doi.org/10.1007/s13369-019-04234-6

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