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Natural convection of nanofluids in solar energy collectors based on a two-phase lattice Boltzmann model

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Abstract

In order to improve the photothermal conversion efficiency of solar energy collectors, the laminar convection of nanofluids in five types of solar energy collectors was numerically studied with a two-phase lattice Boltzmann model. In the current simulation, Cu–water nanofluids (volume fraction φ = 0.3%) were chosen. The equilibrium distribution function with D2Q9 model and the boundary conditions of nonequilibrium extrapolation scheme were applied to establish the lattice Boltzmann model. The effects of different Rayleigh numbers (Ra = 104–106), structures (rectangle cavity, trapezoid cavity and parallelogram cavity) and aspect ratios (A = 2:1, 4:3 and 1:1) of solar energy collectors on the heat transfer were considered. The temperature distribution, streamline and entropy generation of nanofluids in the solar energy collectors were analyzed. Results demonstrated that the increase in Rayleigh number heightens the heat convection of nanofluids. The trapezoid cavity and parallelogram have a special structure, which will form a flow dead zone, weaken the heat transfer effect and determine the position of maximum entropy generation.

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Abbreviations

a :

Direction of vectors

A :

Aspect ratio

c :

Grid speed

c p :

Specific heat of nanofluids, J kg−1 K−1

d :

Length of the cavity

E :

Potential energy

Ec:

Eckert number

e :

Velocity vectors

F :

Force term, N

f :

Velocity distribution function

G :

Effective external force

g :

Gravity, m s−2

H :

Height of the cavity

Ha:

Hamaker constant

k :

Boltzmann constant

L :

Distance between particles

Ma:

Mach numbers

Nu:

Nusselt number

n:

Number of neighboring particles

Pe:

Peclet number

Pr:

Prandtl number

p :

Pressure, Pa

R :

Particle radius, m

Ra:

Rayleigh number

r :

Position of grid

S :

Entropy generation

T :

Temperature distribution function

T C :

Lattice temperature of the cool wall

T H :

Lattice temperature of the heat wall

T mid :

Outlet temperatures, K

t :

Time

u :

Velocity of nanofluids, m s−1

U :

Transversal velocity components

u :

Macro velocity

V :

Vertical velocity component

v :

Volume of a single grid

x :

Transversal grid length

y :

Vertical grid length

β :

Thermal expansion coefficient, 1 K−1

ρ :

Density, kg m−3

φ :

Volume fraction, %

δ t :

Time steps

λ :

Thermal conductivity, W m−1 K−1

μ :

Dynamic viscosity, Pa s

ν :

Kinematic air viscosity

ξ :

Gaussian distribution variable

σ :

Two components of nanofluids

τ f :

Dimensionless relaxation times of velocity

τ T :

Dimensionless relaxation times of temperature

χ :

Thermal diffusion coefficient

A:

Potential energy

a :

Vectors number

B:

Brown force

bf:

Base fluid

D:

Resistance between phases

eq:

Equilibrium states

FFI:

Irreversible fluid flow

f:

Nanofluids

H:

Gravity and buoyancy

HTI:

Irreversible heat transfer

nf:

Nanofluids

p:

Particle

w1:

External force of solid phase

w2:

External force of liquid phase

x:

The x-axis direction

y:

The y-axis direction

0:

Initial value

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Acknowledgements

This work was financially supported by “Natural Science Foundation of Jiangsu Province, China” (Grant No. BK20181359).

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  1. School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou, 221116, China

    Cong Qi, Chunyang Li, Keao Li & Dongtai Han

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  1. Cong Qi
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Qi, C., Li, C., Li, K. et al. Natural convection of nanofluids in solar energy collectors based on a two-phase lattice Boltzmann model. J Therm Anal Calorim 147, 2417–2438 (2022). https://doi.org/10.1007/s10973-021-10668-8

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