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Natural Convection of Cold Water Near Its Density Maximum in a Porous Wavy Cavity

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Flow and Transport in Subsurface Environment

Abstract

The aim of the present numerical study is to investigate the buoyant convective flow and heat transfer of cold water near its density maximum in a wavy porous square cavity. The vertical left wall of the cavity is heated, while the wavy right wall is cooled at a constant temperature. The top and bottom walls are taken to be adiabatic. The Darcy model is adapted for fluid flow through the porous medium inside the cavity. The governing equations are solved numerically using the finite volume method over a range of wavy wall’s amplitude and a number of undulation, density inversion parameter, and Darcy–Rayleigh numbers. The waviness of the cavity enhances the heat transfer. The density maximum leaves a strong effect on fluid flow and temperature distribution inside the cavity.

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Abbreviations

A :

Amplitude

g :

Gravitational acceleration (m s−2)

L :

Enclosure length (m)

K :

Permeability of the porous medium (m2)

Nu loc :

Local Nusselt number

\( \overline{Nu}_{\text{h}} \) :

Average Nusselt number

P :

Pressure (Pa)

Ra D :

Darcy–Rayleigh number

T :

Temperature (K)

u, v:

Velocity components in x- and y-directions (m s−1)

x, y:

Cartesian coordinates (m)

X, Y:

Dimensionless Cartesian coordinates

α :

Thermal diffusivity (m2 s−1)

β :

Volumetric coefficient of thermal expansion (K−1)

λ :

Number of undulations

μ :

Dynamic viscosity (m2 s−1)

ν :

Kinematic viscosity, (kg m−1 s−1)

ψ :

Stream function (m2 s−1)

Ψ:

Dimensionless stream function

Θ:

Dimensionless temperature

c:

Cold

h:

Hot

m:

At density maximum

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Authors and Affiliations

  1. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. Sivasankaran

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  1. S. Sivasankaran
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Correspondence to S. Sivasankaran .

Editor information

Editors and Affiliations

  1. Department of Civil engineering, Dr. Mahalingam College of Engineering and Technology, Pollachi, Tamil Nadu, India

    Natarajan Narayanan

  2. Department of Civil Engineering, National Institute of Technology, Arunachal Pradesh, Yupia, Arunachal Pradesh, India

    Berlin Mohanadhas

  3. Department of Civil Engineering, Bannari Amman Institute of Technology, Sathyamangalam, Tamil Nadu, India

    Vasudevan Mangottiri

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Sivasankaran, S. (2018). Natural Convection of Cold Water Near Its Density Maximum in a Porous Wavy Cavity. In: Narayanan, N., Mohanadhas, B., Mangottiri, V. (eds) Flow and Transport in Subsurface Environment. Springer Transactions in Civil and Environmental Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-8773-8_10

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  • DOI: https://doi.org/10.1007/978-981-10-8773-8_10

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  • Online ISBN: 978-981-10-8773-8

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