Nanofluid Heat Transfer in Porous Media Review

Accepted Manuscript
Review
Review on Heat Conduction, Heat Convection, Thermal Radiation and Phase
Change Heat Transfer of Nanofluids in Porous Media: Fundamentals and Ap-
plications
H.J. Xu, Z.B. Xing, F.Q. Wang, Z.M. Cheng
PII: S0009-2509(18)30692-4
DOI: https://doi.org/10.1016/j.ces.2018.09.045
Reference: CES 14521
To appear in: Chemical Engineering Science
Received Date: 7 July 2018
Revised Date: 4 September 2018
Accepted Date: 26 September 2018
Please cite this article as: H.J. Xu, Z.B. Xing, F.Q. Wang, Z.M. Cheng, Review on Heat Conduction, Heat
Convection, Thermal Radiation and Phase Change Heat Transfer of Nanofluids in Porous Media: Fundamentals
and Applications, Chemical Engineering Science (2018), doi: https://doi.org/10.1016/j.ces.2018.09.045
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers
we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and
review of the resulting proof before it is published in its final form. Please note that during the production process
errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

1
Review on Heat Conduction, Heat Convection, Thermal Radiation
and Phase Change Heat Transfer of Nanofluids in Porous Media:
Fundamentals and Applications
H. J. Xu1, Z.B. Xing3, F. Q. Wang2,*, Z. M. Cheng2
(1 China-UK Low Carbon College, Shanghai Jiao Tong University, Shanghai 200240, China; 2
School of Automobile Engineering, Harbin Institute of Technology at Weihai, Weihai 264209,
China; 3 Zhongtong Bus Holding Co., Ltd., Liaocheng 252000, China)
*Corresponding Author, Email Address: [e-mail] Tel: [phone]
Contents
1. Introduction.............................................................................................................. 5
2. Flow and thermal transport of fluids in metal foams .............................................. 6
2.1 Flow characteristics ..................................................................................................... 6
2.2 Heat conduction ........................................................................................................... 8
2.3 Convective heat transfer ............................................................................................ 11
2.4 Radiative transfer in porous media ............................................................................. 15
3. Transport of nanofluids and nanoparticles ........................................................... 19
3.1 Heat conduction and thermal conductivity ................................................................. 19
3.2 Viscosity and friction factor ....................................................................................... 24
3.3 Thermophoresis ......................................................................................................... 24
3.4 Convective heat transfer ............................................................................................ 25
3.4.1 Correlations ............................................................................................................ 25
3.4.2 Mathematical models .............................................................................................. 28
3.5 Radiative transfer of nanofluids ................................................................................. 29
3.5.1 Optical properties of a single nanoparticle ............................................................... 30
3.5.2 Optical properties of nanofluids .............................................................................. 32
3.5.3 Radiative transfer of nanofluids .............................................................................. 33
3.6 Fouling of nanofluids and aggregation of nanoparticles .............................................. 35
4. The nanofluid transport studies in porous media ................................................. 37

2
4.1 Experimental investigations ....................................................................................... 37
4.2 Modeling the convective heat transfer ........................................................................ 38
4.3 The non-Newtonian effect of nanofluids in porous media ........................................... 42
4.4 Second law analysis ................................................................................................... 44
5. Research on phase change heat transfer................................................................ 46
5.1 Heat transfer with liquid-gas phase change................................................................. 46
5.2 Heat transfer with liquid-solid phase change .............................................................. 49
6. Conclusions ............................................................................................................. 51
Acknowledgement ......................................................................................................... 51
References ...................................................................................................................... 51
Abstract: Increasing the heat transfer rate of heat transfer equipment is an ever-lasting topic in
thermal engineering. Due to the advantages of light weight, high specific surface, high thermal
conductivity, metal foam is a good extending surface for heat transfer enhancement. Nanofluid has
a higher thermal conductivity than the traditional base fluid, so it can be used as an efficient heat
transfer medium. This paper focuses on various flow and heat transfer modes of nanofluid, metal
foam and the combination of the two, with the physical properties of nanofluid and metal foam
summarized. The characteristics of flow and heat transfer are introduced. The motivation of this
review paper is to arouse the researchers to pay attention to the basic transport understandings for
the heat transfer enhancement of nanofluids in porous media. The knowledge reviewed in this
paper is useful for improving the performance of compact heat exchangers, and heat sinks for
cooling electronics with porous media and nanofluids.
Keywords: Nanofluid; Porous Media; Heat Transfer; Convection; Thermal Radiation; Phase
Change
NOMENCLATURE
sf
a
specific surface area,
-1
m
b
Half-thickness of bump,
m
p
c
specific heat,
-1 -1
J kg K

3
B
D
Brownian diffusivity,
21
ms
T
D
Thermophoretic diffusivity,
21
ms
Da
Darcy number
d
Diameter,
m
f
d
Diameter of the fiber of metal foam,
m
l
d
Microscopic characteristic length,
m
p
d
Particle diameter,
m
; Pore diameter,
m
f
Friction factor
D
C
Friction coefficient
Fourie
f
Viscous shear factor
F
Inertia coefficient
h
heat transfer coefficient,
-2 1
W m K
sf
h
local convective heat transfer coefficient,
-2 1
W m K
v
h
volumetric heat transfer coefficient,
-3 1
W m K
K
Permeability,
2
m
k
Thermal conductivity,
-2 1
W m K
d
k
Dispersion thermal conductivity,
-2 1
W m K
r
k
thermal conductivity ratio (
r f s
/k k k
)
L
Length of metal foam,
m
Nu
Nusselt number
p
Pressure,
-2
Nm
p
Pressure drop,
-2
Nm
Pr
Prandtl number

4
q
Internal volumetric heat source,
-3
Wm
r
radius,
m
Re
Reynolds number
Ra
Rayleigh number
t
Time,
s
T
Temperature,
K
u
Velocity,
-1
ms
x
x axis,
m
GREEK SYMBOLS
Porosity
Dimensionless temperature
Dimensionless temperature difference between solid and fluid
Dynamic viscosity,
-1 1
kg m s
Steradian of nanoparticles
Nanoparticle volume fraction
Density,
-3
kg m
Pore structure tortuosity
SUBSCRIPTS
bf
Base fluid of nanofluid
e
Effective
f
Fluid
fe
The effective value of the fluid
in
Inlet
m
Mean
max
Maximum value
nf
Nanofluid