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Modeling and Prediction of Effects of Time-Periodic Heating Zone on Mixed Convection in a Lid-Driven Cavity Filled with Fluid-Saturated Porous Media

  • Research Article - Mechanical Engineering
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Abstract

In this study, the effects of time-dependent temperature boundary condition on the fluid flow and heat transfer characteristic in a lid-driven square cavity filled with fluid-saturated porous media were numerically investigated. The top horizontal wall of the cavity is moving with constant speed and maintained at constant cold temperature, while the bottom wall is at hot temperature with a sinusoidally varying time-dependent part. On the other walls of the cavity, adiabatic boundary conditions are assumed. The governing equations of mass, momentum and energy were solved with a commercial solver using finite element method. Numerical simulations were performed for various values of the Richardson number from 0.1 to 50, Darcy number from 10−4 to 10−2, Prandtl number from 0.05 to 10, amplitude from 0.2 to 0.8 and non-dimensional frequency from 0.01 to 1 of the time-periodic heating zone. It is observed that increasing the Darcy number and Prandtl number enhances the heat transfer and flow strength, while the effect is opposite for Richardson number. Compared to steady case, there is negligible influence of periodic heating zone on the heat transfer enhancement for all values of Darcy number and Richardson numbers less than 1, Prandtl number less than 1.4 and non-dimensional frequency less than 0.5. It is observed that the fluid flow and temperature field within the cavity can be controlled with frequency and amplitude of time-dependent boundary condition. Furthermore, a reduced-order model of the system with nine modes and with dynamic boundary condition explicitly written based on proper orthogonal decomposition is proposed to predict the thermal performance of the system. This approach gives satisfactory results in terms of local and averaged Nusselt numbers.

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Abbreviations

A :

Amplitude

Da :

Darcy number

f :

Frequency (s−1)

g :

Gravitational acceleration (m s−2)

h :

Local heat transfer coefficient (Wm−2K −1)

k :

Thermal conductivity (Wm−1 K−1)

H :

Length of the enclosure (m)

n :

Unit normal vector

Nu:

Nusselt number

p :

Pressure (Pa)

Pr :

Prandtl number

Re :

Reynolds number

Ri :

Richardson number

St :

Strouhal number

t :

Time (s)

T :

Temperature (K)

u, v :

x–y velocity components (m s−1)

x, y :

Cartesian coordinates (m)

\({\alpha}\) :

Thermal diffusivity (m2 s−1)

\({\beta}\) :

Thermal expansion coefficient (K−1)

\({\theta}\) :

Non-dimensional temperature

\({\nu}\) :

Kinematic viscosity (m2 s−1)

\({\rho}\) :

Density (kg m−3)

\({\tau}\) :

Period (s)

c:

Cold

h:

Hot

m:

Average

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Authors and Affiliations

  1. Department of Mechanical Engineering, Celal Bayar University, 45140, Manisa, Turkey

    Fatih Selimefendigil

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  1. Fatih Selimefendigil
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Correspondence to Fatih Selimefendigil.

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Selimefendigil, F. Modeling and Prediction of Effects of Time-Periodic Heating Zone on Mixed Convection in a Lid-Driven Cavity Filled with Fluid-Saturated Porous Media. Arab J Sci Eng 41, 4701–4718 (2016). https://doi.org/10.1007/s13369-016-2239-7

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  • DOI: https://doi.org/10.1007/s13369-016-2239-7

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