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Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients

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Abstract

A numerical study of three-dimensional incompressible viscous flow inside a cubical lid-driven cavity is presented. The flow is governed by two mechanisms: (1) the sliding of the upper surface of the cavity at a constant velocity and (2) the creation of an external gradient for temperature and solutal fields. Extensive numerical results of the three-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely Reynolds number, Grashof number and the ratio of buoyancy forces. The preceding numerical results obtained have a good agreement with the available numerical results and the experimental observations. The deviation of the flow characteristics from its two-dimensional form is emphasized. The changes in main characteristics of the flow due to variation of Reynolds number are elaborated. The effective difference between the two-dimensional and three-dimensional results for average Nusselt number and Sherwood number at high Reynolds numbers along the heated wall is analyzed. It has been observed that the substantial transverse velocity that occurs at a higher range of Reynolds number disturbs the two-dimensional nature of the flow.

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Abbreviations

B :

Buoyancy ratio

C :

Dimensionless species concentration

C H :

Concentration at the hot wall (K)

C L :

Concentration at the cold wall (K)

D :

Mass diffusivity

g :

Acceleration due to gravity (m/s2)

Gr :

Grashof number

Le :

Lewis number

Nu :

Nusselt number

\({\overline{Nu}}\) :

Average Nusselt number

\({\overline{p}}\) :

Dimensional pressure (= kg/ms2)

p :

Dimensionless pressure

Pr :

Prandtl number

Re :

Reynolds number

Ri :

Richardson number (= Gr/Re 2)

Sc :

Schmidt number

Sh :

Sherwood number

\({\overline{Sh}}\) :

Average Sherwood number

T :

Dimensionless temperature

T H :

Temperature at the hot wall (K)

T L :

Temperature at the cold wall (K)

u :

Dimensionless x-component of velocity

v :

Dimensionless y-component of velocity

w :

Dimensionless z-component of velocity

β :

Volumetric coefficient of thermal expansion

β*:

Volumetric coefficient of solutal expansion

ν :

Kinematic viscosity

μ :

Dynamic viscosity

θ :

Dimensionless temperature

κ :

Thermal diffusivity

β T :

Volumetric coefficient of thermal expansion

β C :

Volumetric coefficient of solutal expansion

ρ :

Fluid density

ρ 0 :

Fluid density at zero temperature (Reference density)

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    A. K. Nayak & S. Bhattacharyya

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  1. A. K. Nayak
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  2. S. Bhattacharyya
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Correspondence to A. K. Nayak.

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Communicated by Zang.

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Nayak, A.K., Bhattacharyya, S. Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients. Theor. Comput. Fluid Dyn. 26, 565–581 (2012). https://doi.org/10.1007/s00162-011-0246-6

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