Micro (Mini)-Channels and Their Applications in Solar Systems

Thierno Diallo; Min Yu; Jinzhi Zhou; Yi Fan; Xudong Zhao

doi:10.1007/978-3-030-17283-1_6

Advanced Energy Efficiency Technologies for Solar Heating, Cooling and Power Generation pp 165-209 | Cite as

Micro (Mini)-Channels and Their Applications in Solar Systems

Authors
Authors and affiliations

Thierno Diallo
Min Yu
Jinzhi Zhou
Yi Fan
Xudong Zhao

Chapter

First Online: 09 July 2019

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Part of the Green Energy and Technology book series (GREEN)

Abstract

This chapter presented micro (mini)-channels and their applications in solar systems. Two types of channels, micro (mini)-tubes and micro (mini)-heat pipes, have been presented, and the performance of their use in solar systems has been illustrated by studies in the literature. For solar thermal systems, the integration of micro (mini)-channels can increase significantly the thermal performance that achieves an increase of 28% compared to conventional channels. For PVT systems, the use of micro (mini)-channels enhances also the electrical output by decreasing the temperature of PV panels. Consequently, the use of these channels increases the overall efficiency of PVT systems that can achieve the overall efficiency of around 70%. Furthermore, in this paper, the use of micro-channel has been illustrated by the investigation of a novel solar PVT loop heat pipe employing a micro-channel heat pipe evaporator and a PCM triple heat exchanger. This illustration showed environmental parameters (i.e. solar radiation, air temperature, wind velocity), structural parameters (i.e. glazing covers, number of the absorbing heat pipes, PC cell packing factor) and the variable inputs (i.e. water inlet temperature, mass flow rate) that can influence the overall efficiency of the novel PVT system. This chapter showed that application of micro (mini)-channels in solar systems is promising, and their integration in solar technologies can enhance significantly their performance and their market share.

Keywords

Micro-channel Mini-channel Heat pipe Solar application Efficiency PVT systems

Nomenclature

A: Area (m²)
a: Mini-channel width (m)
b: Mini-channel height (m)
Bo: Bond number (m)
C: Heat capacity (W/K)
C, d: Discharge coefficient (−)
D, d: Diameter (m)
e: Thickness (m)
f: Liquid fraction, friction factor (−)
g: Gravitational acceleration 9.81 (m/s²)
G: Mass velocity (kg/m²/s)
H: Height (m)
h: Heat transfer coefficient (W/m²/K)
h_fg: Latent heat of vaporization (J/kg/K)
k: Thermal conductivity (W/m/K)
L: Length (m)
m: Variable (m⁻¹)
N: Number (−)
N_ch: Number channel ports (−)
Nu: Nusselt number (−)
P: Pressure (Pa)
ΔP: Pressure drop (Pa)
q: Heat density (W/m²)
Q: Heat transfer rate (W)
Ro: Specific gas constant (J/(kg K))
R: Radius (m)
R: Thermal resistance (W/K)
Re: Reynolds number (−)
t/T: Temperature (°C/°K)
U: Heat loss (W/K)
u: Velocity (m/s)
W: Collector width (m)
x: Vapour quality (−)

Subscripts

an: Annular
av: Average
c: Cold, charge, cover
ch: Channel
cond: Condensation
d: Discharge
f: Fin
F: Efficiency factor
e: Evaporator, electrical
eq: Equivalent
ei: Electrical insulation
EVA: Ethylene-vinyl acetate
fg: Fluid gas
g: Gravity
i: Inlet
min: Minimum
mt: Middle tube
h: Hole, header
he: Heat exchanger
hp: Heat pipe
hp-he: Heat pipe to heat exchanger
lf: The liquid film
lh: Liquid header
LO: Liquid only
ltl: Liquid transportation line
vtl: Vapour transportation line
l: Liquid
L: Loss
lf: Liquid film
o: Overall
out: Outlet
p: PV cell
PCM: Phase change material
Pr: Prandtl
p-fin: PV-fin
th: Thermal
tp: Two phase
u: Utile
v: Vapour
vtl: Vapour transportation line
w: Water

Greek Symbols

β: Packing factor
ε: Efficiency
Δ: Difference
λ: Thermal conductivity (W/(m K))
μ: Dynamic viscosity (Pa s)
ρ: Density (kg/m³)
δ: Thickness (m)
η: Efficiency (m)
σ: Surface tension (N/m)
ν: Specific volume (m³/kg)

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Supplementary material

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Annex 1: Characteristics of Different PVT Layers

Parameters	Nomenclature	Value	Unit
Emissivity of glazing cover	ε _c	0.84	(−)
Absorptance of glazing cover	A _c	0.05	(−)
Transmittance of glazing cover	τ _c	0.90	(−)
Emissivity of PV cell	ε _abs	0.96	(−)
Absorptance of PV cell	α _abs	0.90	(−)
Thickness of PV cell	δ _abs	0.0003	m
Thermal conductivity of PV cell	λ _abs	148	W/m/K
Reference efficiency of PV cell	η _rc	0.18	(−)
Temperature coefficient of PV cell	β _abs	0.0045	1/°C
Reference temperature of PV cell	t _rc	25	°C
Number of PV cell	N _pv	72	(−)
Area of single PV cell	A _pv	0.156 × 0.156	m²
Thickness of EVA grease	δ _eva	0.0005	m
Thermal conductivity of EVA grease	λ _eva	0.35	W/m/K
Thickness of electrical insulation	δ _ei	0.002	m
Thermal conductivity of electrical insulation	λ _ei	144	W/m K
Absorptance of blacken electrical insulation	A _ei	0.8	(−)
Thickness of fin sheet	δf	0.005	(−)
Thermal conductivity of fin sheet	λ _f	203	(−)

Annex 2: Heat Transfer from Outside to the PV Surface [18]

The solar energy received by the PV module is expressed as follows:

$$ Q_{\text{abs}} = \tau_{\text{c}}^{{{{N_{\text{C}} }} }} \tau_{{{\text{g}},{\text{pv}}}} \left[ {\alpha_{\text{p}} \beta_{\text{p}} + \alpha_{\text{b}} \left( {1 - \beta_{\text{p}} } \right)} \right]A_{\text{m}} I $$

(32)

where τ_c and τ_g,pv are the visual transmittances of cover plate and the glazing layer of PV lamination, respectively; N_c is the number of cover plates; α_abs and α_b are the absorption ratios of the PV layer and its baseboard; β_p is the packing factor of PV layer; A_m is the collector area of the module (m²). The loss heat from a double-glazed module will experience (1) heat transfer from the PV absorber surface to the inner glazing cover; (2) heat transfer from the inner cover to the outer cover; and (3) heat transfer from the outer glazing cover to the ambient air. As shown in the following Fig. 44, the three forms of heat transfer are laid in a series and achieve a balance.

Therefore, the total heat loss is written as:

$$ Q_{\text{L}} = U_{\text{L}} A_{\text{m}} \left( {T_{\text{p}} - T_{\text{a}} } \right) $$

(33)

where Q_L and U_L are, respectively, the total heat loss (W) and the heat loss coefficient (W/m² K); T_p and T_a are the average temperatures of PV layer and the ambient air (K), where the U_L is the overall heat transfer coefficient and could be written as:

$$ U_{\text{L}} = \left( {\frac{1}{{h_{{\text{c},\text{p-c}2}} + h_{{\text{R},\text{p-c2}}} }} + \frac{1}{{h_{{\text{c},\text{c2-c}1}} + h_{{\text{R},\text{c2-c}1}} }} + \frac{1}{{h_{{\text{c},\text{c1-a}}} + h_{{\text{R},\text{c1-a}}} }}} \right)^{ - 1} $$

(34)

where h_c,p-c2, h_c,c2-c1 and h_c,c1-a are, respectively, the convective heat transfer coefficients (W/m² K) of PV layer (p) to inner cover surface (c2), inner cover surface (c2) to external cover surface (c1) and external cover surface (c1) to ambient air (a); h_R,p-c2, h_R,c2-c1 and h_R,c1-a are the radiative heat transfer coefficients (W/m² K) of PV layer (p) to inner cover surface (c2), inner cover surface (c2) to external cover surface (c1) and external cover surface (c1) to ambient air (a), respectively.

$$ \begin{aligned}h_{{\text{c},\text{p-c}2}} &= \frac{{k_{{\text{a},\text{p}}} }}{{\delta_{{\text{a},\text{p}}} }}\left\{ 1 + 1.446\left( {1 - \frac{1708}{{\text{Ra}_{{\text{a},\text{p}}} \cos \theta }}} \right)^{ + } \left[ {1 - \frac{{1708\sin \left( {1.8\theta } \right)^{1.6} }}{{\text{Ra}_{{\text{a},\text{p}}} \cos \theta }}} \right] \right. \\ & \quad \left.+ \left[ {\left( {\frac{{\text{Ra}_{{\text{a},\text{p}}} \cos \theta }}{5830}} \right)^{0.333} - 1} \right]^{ + } \right\} \end{aligned} $$

(35)

where k_a,p is thermal conductivity of air gap at the average temperature of PV layer and inner cover surface (W/m k); δ_a,p is the PV layer to glazing cover distance (m); θ is the collector slop (degree); the bracket with plus means zero and positive values only; Ra_a,p is the Rayleigh number of the air gap at PV layer and inner cover surface, given by:

$$ \text{Ra}_{{\text{a},\text{p}}} = \frac{{g\left( {T_{\text{P}} - T_{{\text{C}2}} } \right) \delta_{{\text{a},\text{p}}}^{3} }}{{v_{{\text{a},\text{p}}}^{2} T_{{\text{a},\text{m}}} }} \Pr _{{\text{a},\text{p}}} $$

(36)

where g is the gravitational acceleration (m/s²) and ν_a is kinematic viscosity of air at the PV and inner cover surface (m²/s); Pr_a,p is the Prandtl number of the air gap at PV layer and inner cover surface, which is assumed to be independent of temperature and is taken equal to 0.7; T_a,m is the average air temperature of PV layer and inner cover surface which is

$$ T_{{\text{a},\text{m}}} = \frac{{\left( {T_{\text{P}} + T_{{\text{c}2}} } \right)}}{2} $$

(37)

where T_p and T_c2 are, respectively, the average temperatures (K) of PV layer and inner cover surface. Converting the radiation transfer into the equivalent convective one, a radiation-relevant factor, h_{R, p-c2}, is expressed by:

$$ h_{{\text{R},\text{p-c}2}} = \frac{{\sigma \left( {T_{\text{p}} + T_{{\text{c}2}} } \right) \left( {T_{\text{p}}^{2} + T_{{\text{c}2}}^{2} } \right)}}{{\left( {\frac{1}{{\varepsilon_{\text{p}} }}} \right) + \left( {\frac{1}{{\varepsilon_{{\text{c}2}} }}} \right) - 1}} $$

(38)

where T_c1 is the average temperature of external cover surface (K); ε_p and ε_c2 are emissivity of the PV layer and inner cover surface; σ is the Stefan–Boltzmann constant (5.6679 × 10⁻⁸ W/m² K⁴).

Heat Transfer from the Inner Glazing Cover to the Outer Cover: Similarly, heat transfer from the inner glass to the outer glass can be calculated using equations (A.5) to (A.7) to substitute corresponding parameters, including temperature, air properties and emissivity.

Heat Transfer from the Cover’s Outer Surface to the Surrounding Air: For a surface exposed to the outside wind, the convective coefficient could be calculated using the Klein equation expressed as follows:

$$ h_{{\text{c},\text{c1-a}}} = \frac{{8.6\, V^{0.6} }}{{L^{0.6} }} $$

(39)

where V is the wind speed (m/s); L is the characteristic length of the collector (m). The minimum convective coefficient for a wind-exposed surface is considered to be 5 W/m² K [7]; if the above calculation gives a lower value, this should be replaced by the minimum value since the temperature of the sky has little influence on the calculation result, it is usually represented by the air temperature, and thus

$$ h_{{\text{r},\text{c1-a}}} = \varepsilon_{{\text{c}1}} \sigma \left( {T_{{\text{c}1}} + T_{\text{a}} } \right) \left( {T_{{\text{c}1}}^{2} + T_{\text{a}}^{2} } \right) $$

(40)

The PV cells’ electrical efficiency is adversely proportional to their surface temperature, and this dependency can be written as:

$$ \eta_{\text{e}} = \eta_{\text{rc}} \left( {1 - \beta_{\text{PV}} \left( {T_{\text{p}} - T_{\text{rc}} } \right)} \right) $$

(41)

The overall electricity output is, therefore, given as:

$$ Q_{\text{e}} = \eta_{\text{e}} \beta_{\text{p}} \alpha_{\text{p}} \tau_{\text{c}}^{{N_{\text{c}} }} \tau_{{\text{g},\text{pv}}} IA_{\text{m}} $$

(42)

The module’s solar electrical efficiency could be calculated through

$$ \eta_{\text{e}} = \frac{{Q_{\text{e}} }}{{IA_{\text{m}} }} $$

(43)

Under the steady-state condition, the rate of useful heat delivered by the module equals the rate of the absorbed energy minus the overall heat loss and converted electricity, expressed as

$$ Q_{\text{th}} = Q_{\text{abs}} - Q_{\text{L}} - Q_{\text{e}} $$

(44)

This part of the heat will eventually be converted into the heat received by the water and stored, which is denoted by Q_u. In this case, the module’s thermal efficiency can be defined by:

$$ \eta_{\text{th}} = \frac{{Q_{\text{th}} }}{{A_{\text{m}} I}} $$

(45)

Annex 3

A.

The two-phase heat transfer coefficient

The two-phase heat transfer Kandlikar correlation [34] has been used and is expressed as follows:

$$ {\text{For}}\,\text{Re}_{\text{LO}} >100\,h_{\text{TP}} = \text{larger of}\,\left\{ {\begin{array}{*{20}l} {h_{{\text{TP},\text{NBD}}} } \\ {h_{{\text{TP}, \text{CBD}}} } \\ \end{array} } \right. $$

(46)

$$ h_{{\text{TP},\text{NBD}}} = 0.6683\,\text{Co}^{ - 0.2} \left( {1 - x} \right)^{0.8} h_{\text{LO}} + 1058.0\,\text{Bo}^{0.7} \left( {1 - x} \right)^{0.8} F_{\text{F1}} h_{\text{LO}} $$

(47)

$$ \left\{ {\begin{array}{*{20}c} {{\text{h}}_{{{\text{TP}},{\text{NBD}}}} = 1.136\,{\text{Co}}^{ - 0.9} \left( {1 - x} \right)^{0.8} {\text{h}}_{\text{LO}} + 667.2\,{\text{Bo}}^{0.7} \left( {1 - x} \right)^{0.8} {\text{F}}_{{{\text{F}}1}} {\text{h}}_{\text{LO}} } \\ {\text{Co} = \left[ {\left( {1 - x} \right)/x} \right]^{0.8} \left( {\frac{{\rho_{\text{v}} }}{{\rho_{\text{L}} }}} \right)^{0.5} } \\ {\text{Bo} = \frac{\text{q}}{{{\text{G}\,\text{h}}_{\text{fg}} }}} \\ \end{array} } \right\} $$

(48)

$$ \text{For}\,10^{4} \le \text{Re}_{\text{LO}} \le 5\times 10^{6} \quad h_{\text{LO}} = \frac{{\text{Re}_{\text{LO}} \Pr _{\text{L}} \left( {\frac{f}{2}} \right)\left( {\frac{{k_{\text{L}} }}{D}} \right)}}{{1 + 12.7\left( { \Pr _{\text{L}}^{2/3} - 1} \right)\left( {f/2} \right)^{0.5} }} $$

(49)

$$ \text{For}\,3000 \le \text{Re}_{\text{LO}} \le 10^{4} \quad h_{\text{LO}} = \frac{{\left(\text{Re}_{\text{LO}}-1000\right) \Pr _{\text{L}} \left( {\frac{f}{2}} \right)\left( {\frac{{k_{\text{L}} }}{D}} \right)}}{{1 + 12.7\left( { \Pr _{\text{L}}^{2/3} - 1} \right)\left( {f/2} \right)^{0.5} }} $$

(50)

$$ \text{For}\,100 \le \text{Re}_{\text{LO}} \le 1600\quad h_{\text{LO}} = \frac{{Nu_{\text{LO}}\, k}}{{D_{\text{h}} }} $$

(51)

In the transition region between Reynolds numbers of 1600 and 3000, a linear interpolation is suggested for $ h_{\text{LO}} $.

For Reynolds numbers below and equal to 100 (Re ≤ 100), the nucleate boiling mechanism governs, and the following Kandlikar correlation is proposed:

$$ \text{For}\,\text{Re}_{\text{LO}} \le 100 $$

(52)

$$ h_{\text{TP}} = h_{\text{TP},\text{NBD}} = 0.6683\,\text{Co}^{ - 0.2} \left( {1 - x} \right)^{0.8} h_{\text{LO}} + 1058.0\,\text{Bo}^{0.7} \left( {1 - x} \right)^{0.8} F_{\text{Fl}} h_{\text{LO}} $$

(53)

For R-134a, the recommended value of $ F_{\text{Fl}} $ is 1.63.

The vapour quality in the channel port is estimated as:

$$ x = \frac{{\pi D_{\text{h}} Q_{\text{th}} }}{{\dot{m}h_{\text{fg}}\,(N_{\text{ch}} N_{\text{hp)}} }}z $$

(54)

B.

The condensation heat transfer coefficient [36]

For R_ev < 35,000:

$$ h_{\text{cond}} = 0.555\left[ {\frac{{\rho_{\text{l}} g\left( {\rho_{\text{l}} - \rho_{\text{v}} } \right)k_{\text{l}}^{3} h_{\text{fg}} }}{{\mu_{\text{l}} \left( {T_{\text{sat}} - T_{\text{w}} } \right)D}}} \right]^{1/4} $$

(55)

For R_ev > 35,000:

$$ \left\{ {\begin{array}{*{20}c} {h_{\text{cond}} = \frac{{k_{\text{l}} }}{D}0.23\,\text{Re}_{D}^{0.8} \Pr _{\text{l}}^{0.4} \left[ {1 + \frac{2.22}{{X_{\text{tt}}^{0.89} }}} \right]} \\ {\text{Re}_{\text{D}} = 4\,\dot{m}(1 - \dot{x})/(\pi D\mu_{\text{l}} )} \\ {X_{\text{tt}} = \left( {\frac{1 - x}{x}} \right)^{0.9} \left( {\frac{{\rho_{\text{v}} }}{{\rho_{\text{l}} }}} \right)^{0.5} \left( {\frac{{\mu_{\text{l}} }}{{\mu_{\text{v}} }}} \right)^{0.1} } \\ \end{array} } \right\} $$

(56)

C.

The fins efficiency in the micro-channel [37]

$$ \varepsilon_{\text{of}} = 1 - N_{\text{f}} A_{\text{f}} \left( {1 - \varepsilon_{\text{f}} } \right)/A_{\text{tf}} ;\quad \varepsilon_{\text{f}} = \tanh \left( {m_{\text{f}} L_{\text{cf}} } \right)/m_{\text{f}} L_{\text{cf}} $$

(57)

$$ m_{\text{f}} = \left( {2 \times h_{\text{tp}} \times \left( {L_{\text{e}} + t_{\text{f}} } \right)/\left( {K_{\text{hp}} L_{\text{e}} t_{\text{f}} } \right)} \right)^{0.5} $$

(58)

$$ L_{\text{cf}} = b + \frac{{\delta_{\text{f}} }}{2};\quad A_{\text{tf}} = N_{\text{f}} A_{\text{f}} + A_{\text{b}} \quad A_{\text{b}} = L_{\text{hp}} L_{\text{e}} \quad A_{\text{f}} = L_{\text{e}} \delta_{\text{f}} $$

D.

Heat transfer in the annulus [38]

The flow in the annular is characterized by the following Nusselt number and friction factors:

For laminar flow:

$$ \text{Re} < 2200\quad f = 24\,\text{Re}^{ - 1} \quad \text{Nu} = 9.33 $$

(59)

$$ \text{Re} > 4000\quad f = 0.0885\,\text{Re}^{ - 0.263}\quad \text{Nu} = 0.02\,\text{Re}^{0.733}\, \Pr ^{1/3} $$

(60)

For $ 2200 \le {\text{Re}} \le 4000 $ an interpolation has been performed.

$$ h_{\text{w}} = \frac{{{\text{Nu k}}_{\text{w}} }}{{{\text{D}}_{45} }} $$

(61)

where $ D_{45} $ is the hydraulic diameter based on wetted perimeter, m

$$ D_{45} = \frac{{\pi (D_{5}^{2} - D_{4}^{2} )}}{{\pi D_{5} + \pi D_{4} }} $$

(62)

Reynolds number $ {\text{Re}}_{\text{w}} $ can be calculated by:

$$ \text{Re}_{\text{w}} = \frac{{\rho_{\text{cf}} u_{1} D_{45} }}{{\mu_{\text{cf}} }} $$

(63)

The Prandtl number $ \Pr _{\text{w}} $ is calculated using:

$$ \Pr _{\text{w}} = \frac{{\mu_{\text{cf}} c_{\text{pcf}} }}{{k_{\text{w}} }} $$

(64)

where $ \mu_{\text{cf}} , c_{\text{pcf}} $, $ \rho_{\text{cf}} ,\,k_{\text{w}} $ are the relevant mean dynamic viscosity (kg/m s), specific heat, density, thermal conductivity of the water.

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Thierno Diallo
- 1
Email author
Min Yu
- 1
Jinzhi Zhou
- 1
Yi Fan
- 1
Xudong Zhao
- 1

1.School of Engineering and Computer ScienceUniversity of HullHullUK

Micro (Mini)-Channels and Their Applications in Solar Systems

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