Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid
Abstract
:1. Introduction
2. Problem Formulation
2.1. Physical Description
2.2. Governing Equations and Boundary Conditions
3. Numerical Procedure
3.1. Grid Generation and Independence Test
3.2. Code Validation
4. Results and Discussion
4.1. Effects of Brownian Motion
4.2. Effects of Nanoparticle Volume Fraction
4.3. Effects of Nanoparticle Diameter
4.4. Effects of Porosity
4.5. Effects of Radius Ratio
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
RR | radius ratio |
cp | thermal capacity, J/(kg × K) |
d | nanoparticle diameter, m |
Da | Darcy number |
g | acceleration due to gravity, m/s2 |
k | thermal conductivity, W/(m × K) |
K | medium permeability, m2 |
Nu | Nusselt number |
p | pressure, Pa |
P | dimensionless pressure |
Pr | Prandtl number |
r | radius, m |
Ra | Rayleigh number |
T | temperature, K |
(u, v) | velocity, m/s |
(U, V) | dimensionless velocity |
(x, y) | cartesian coodinates |
(X, Y) | dimensionless cartesian coodinates |
Greek symbols | |
α | thermal diffusivity, m2/s |
β | thermal expansion coefficient, K−1 |
γ | angle, deg |
ε | porosity |
θ | dimensionless temperature |
ρ | density, Kg/m3 |
μ | dynamic viscosity, kg/(m × s) |
ν | kinematic viscosity, m2/s |
ϕ | nanoparticle volume fraction |
Subscripts | |
avg | average |
bf | base fluid |
i, o | inner, outer |
loc | local |
mnf | porous medium filled with nanofluid |
nf | nanofluid |
s | porous medium |
sp | nanoparticle |
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Physical Properties | Base Fluid (Water) | Nanoparticle (Cu) | Porous (Glass Balls) |
---|---|---|---|
ρ [kg/m3] | 997.1 | 8933 | 2700 |
cp [J/(kg·K)] | 4179 | 385 | 840 |
k [W/(m·K)] | 0.613 | 76.5 | 1.05 |
μ [kg/(m·s)] | 0.001003 | - | - |
β × 105 [1/K] | 21 | 1.67 | 0.9 |
Physical Properties | Applied Model | |
---|---|---|
Without Brownian Motion | With Brownian Motion | |
k [W/(m·K)] | ||
μ [kg/(m·s)] | μnf = μbf/(1 − ϕ)2.5 | μnf = μbf/[1 − 34.87(dsp/dbf)−0.3ϕ1.03]; |
ρ [kg/m3] | (ρcp)nf = (1 − ϕ)(ρcp)bf + ϕ((ρ cp)sp | |
cp [J/(kg·K)] | ρnf(T) = (1 − ϕ)ρbf(T) + ϕρsp; |
Level | Number of Elements | Minimum Quality | Average Quality | Nuavg |
---|---|---|---|---|
normal | 894 | 0.4632 | 0.7779 | 2.2466 |
fine | 1344 | 0.4938 | 0.8284 | 2.2632 |
finer | 1882 | 0.5084 | 0.8305 | 2.2668 |
extra fine | 6394 | 0.5276 | 0.8424 | 2.2766 |
extremely fine | 17858 | 0.5053 | 0.8466 | 2.2769 |
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Zhang, L.; Hu, Y.; Li, M. Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid. Nanomaterials 2021, 11, 990. https://doi.org/10.3390/nano11040990
Zhang L, Hu Y, Li M. Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid. Nanomaterials. 2021; 11(4):990. https://doi.org/10.3390/nano11040990
Chicago/Turabian StyleZhang, Lingyun, Yupeng Hu, and Minghai Li. 2021. "Numerical Study of Natural Convection Heat Transfer in a Porous Annulus Filled with a Cu-Nanofluid" Nanomaterials 11, no. 4: 990. https://doi.org/10.3390/nano11040990