Aspect ratio effect on natural convection in a square enclosure with a sinusoidal active thermal wall using a thermal non-equilibrium model

ABSTRACT

A numerical investigation of the aspect ratio effect on natural convection in a square enclosure is carried out by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic, the left vertical wall is partially heated and cooled by the sinusoidal thermal boundary condition, and the right vertical wall is maintained at uniform thermal boundary condition. The results show the value of periodicity parameter increasing. The streamlines vary in different patterns, rotating clockwise and counterclockwise simultaneously when N > 1, and the number of clockwise and counterclockwise rotating cells increases with the increase of N and equals the value of N. The sinusoidal local Nusselt number profiles are observed and the wave amplitude of local Nusselt number decreases with the increase of aspect ratio, and the absolute values of average Nusselt number at left wall of porous cavity reach maximum when Ar = 1. The absolute value of solid-to-fluid temperature differences decreases as the inter-phase heat transfer coefficient (H) increases and it increases as the value of aspect ratio increases. The total heat transfer of porous cavity can be enhanced by increasing the aspect ratio and the thermal conductivity ratio.

Nomenclature

Ar	=	[—] aspect ratio
cp	=	[J/kg · K] specific heat at constant pressure
CF	=	[—] Forchheimer coefficient
Da	=	[—] Darcy number
g	=	[m/s2] gravitational acceleration
h	=	[W/m3 · K] volumetric heat transfer coefficient between the solid and fluid phases
H	=	[—] inter-phase heat transfer coefficient
k	=	[W/m · K] thermal conductivity
K	=	[m2] permeability of the porous medium
L	=	[m] enclosure width
M	=	[m] enclosure height
Nu	=	[—] average Nusselt number
Nufy	=	[—] local Nusselt numbers for the fluid phases
Nusy	=	[—] local Nusselt numbers for the solid phases
P	=	[Pa] pressure
P	=	[—] dimensionless pressure
Pr	=	[—] Prandtl number
Q	=	[—] dimensionless total heat transfer rate
	=	[W/m3] rate of volumetric heat generation in solid phase
Ra	=	[—] Rayleigh number
T	=	[K] temperature
u, v	=	[m/s] velocity components along x and y axes
U, V	=	[—] non-dimensional velocity components
x, y	=	[m] Cartesian coordinates
X, Y	=	[—] non-dimensional Cartesian coordinates
α	=	[m2/s] thermal diffusivity
β	=	[K−1] coefficient of volume expansion
γ	=	[—] thermal conductivity ratio
ϵ	=	[—] porosity
θ	=	[—] non-dimensional temperature
νf	=	[m2/s] fluid kinematic viscosity
ρ	=	[kg/m3] density
ψ	=	[—] dimensionless stream function
Subscripts	=
f	=	[—] fluid
s	=	[—] solid

Nomenclature

Ar	=	[—] aspect ratio
cp	=	[J/kg · K] specific heat at constant pressure
CF	=	[—] Forchheimer coefficient
Da	=	[—] Darcy number
g	=	[m/s2] gravitational acceleration
h	=	[W/m3 · K] volumetric heat transfer coefficient between the solid and fluid phases
H	=	[—] inter-phase heat transfer coefficient
k	=	[W/m · K] thermal conductivity
K	=	[m2] permeability of the porous medium
L	=	[m] enclosure width
M	=	[m] enclosure height
Nu	=	[—] average Nusselt number
Nufy	=	[—] local Nusselt numbers for the fluid phases
Nusy	=	[—] local Nusselt numbers for the solid phases
P	=	[Pa] pressure
P	=	[—] dimensionless pressure
Pr	=	[—] Prandtl number
Q	=	[—] dimensionless total heat transfer rate
	=	[W/m3] rate of volumetric heat generation in solid phase
Ra	=	[—] Rayleigh number
T	=	[K] temperature
u, v	=	[m/s] velocity components along x and y axes
U, V	=	[—] non-dimensional velocity components
x, y	=	[m] Cartesian coordinates
X, Y	=	[—] non-dimensional Cartesian coordinates
α	=	[m2/s] thermal diffusivity
β	=	[K−1] coefficient of volume expansion
γ	=	[—] thermal conductivity ratio
ϵ	=	[—] porosity
θ	=	[—] non-dimensional temperature
νf	=	[m2/s] fluid kinematic viscosity
ρ	=	[kg/m3] density
ψ	=	[—] dimensionless stream function
Subscripts	=
f	=	[—] fluid
s	=	[—] solid

Additional information

Funding

This work is supported by National Science Foundation of China (grant number 21476181), China Postdoctoral Science special Foundation (grant number 2015T81048), and China Postdoctoral Science Foundation funded project (grant number 2013M540768).