Keywords

1 Introduction

As a part of effort to increase the use of solar thermal energy, many researches about a solar assisted heat pump using solar collector have been conducted [1, 2]. Solar assisted heat pump system uses solar thermal energy as heat source for evaporator of heat pump. So, C.O.P. of heat pump can be increased with increment of evaporating temperature. And the collector efficiency also can be increased because of the lower operating temperature than the traditional collecting system. But these systems are hard to use the solar collector when the solar radiation is not enough such as a cloudy, rainy day and at night.

So, a hybrid solar collector being able to heat circulated water of the collector using ambient air has been developed [3, 4]. This collector is a flat plate solar collector that has fin-and-tube heat exchanger under the absorbing plate, so it can get a thermal energy from ambient air for heating circulated water like an outdoor unit of heat pump. This heated water can be used as heat source of the evaporator in heat pump when the solar radiation is not enough.

Thus, in this study, heat transfer between air and water was investigated according to length and installation angle of plate fin of fin-tube exchanger in the hybrid solar collector and the numerical analysis also performed for a foundation design. And this study aims to confirm heat transfer and pressure drop characteristic with respect to fin length and installation angle to find the best fin condition after considered heat transfer and pressure drop for real product.

2 Numerical Model and Methods

2.1 Hybrid Solar Collector

Figure 1 shows a schematics of hybrid solar collector for analysis. This collector was composed of glass cover, absorbing plate, fin-and-tube heat exchanger and case. A fin-and-tube heat exchanger was installed under the absorbing plate.

Fig. 1.
figure 1

Exploded view of hybrid solar collector

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This collector can use both solar thermal energy and ambient air selectively depending on the weather. The materials of glass cover, absorbing plate, copper pipe and plate fin were defined as glass, copper and aluminum respectively.

Figure 2 shows a schematic diagram of heat transfer method between air and water in the collector. Air came from the ambient air and it flows through the air channel of the collector and the cold water flows through the tube of fin-and-tube heat exchanger after coming from evaporator outlet of heat pump. Thus, the cold water can get thermal energy from ambient air when solar radiation is not enough and heat transfer between the air and the water occurred by cross counter flow as shown in Fig. 2.

Fig. 2.
figure 2

Schematic diagram of fin-and-tube heat exchanger in hybrid solar collector; (a) Side view (b) Plan view

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Simulation was conducted on various air flow rates with various fin length and installation angles. Simulation conditions including geometric conditions of the collector were tabled in Table 1.

Table 1. Simulation conditions
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2.2 Data Reduction

Heat transfer rate was obtained by calculated simulation results and Eqs. (1), (2) and (3).

$$ \dot{Q}_{w} = \dot{m}_{w} C_{p,w} \left( {T_{w,o} - T_{w,i} } \right) $$
(1)
$$ \dot{Q}_{air} = \dot{m}_{air} C_{p,air} \left( {T_{air,o} - T_{air,i} } \right) $$
(2)
$$ \dot{Q}_{avg} = \frac{{\dot{Q}_{w} + \dot{Q}_{air} }}{2} $$
(3)

Also, overall heat transfer coefficient, U, is obtained by simulation results and Eq. (4)

$$ \text{U} = \frac{{\dot{Q}_{avg} }}{{A_{o} F\Delta T_{lm,CF} }} $$
(4)

So, the overall heat transfer coefficient can be rewritten as

$$ \frac{1}{U} = \frac{1}{{h_{o} }} + R_{f} + R_{c} + \frac{{\Delta x}}{{A_{m} k_{t} /A_{o} }} + \frac{{A_{o} }}{{A_{i} h_{i} }} $$
(5)

Where

$$ h_{i} = \frac{{(f_{p} /8)(Re - 1000)Pr}}{{1 + 12.7(f_{p} /8)^{{\frac{1}{2}}} (Pr^{{\frac{2}{3}}} - 1)}}\left( {\frac{{k_{t} }}{{d_{t} }}} \right) $$
(6)
$$ f_{p} = (0.79\, \text{l} \text{n}\,Re - 1.64)^{ - 2} $$
(7)

Since the numerical analysis was conducted in this study, thermal contact resistance, \( R_{c} \), and fouling factor, \( R_{f} \), can be ignored. Then, air side heat transfer coefficient can be expressed by

$$ h_{o} = 1/\left( {\frac{1}{U} - \frac{{\Delta x}}{{A_{m} k_{t} /A_{o} }} - \frac{{A_{o} }}{{A_{i} h_{i} }}} \right) $$
(8)
$$ h_{o} = \eta h = \frac{{(A_{t} + \eta_{f} A_{f} )}}{{A_{o} }}h $$
(9)

But, fin efficiency is difficult to be obtained of this collector’s structure. So, air side heat transfer coefficient including the affect of fin efficiency referred to the research of Yun and Lee [5].

Colburn j factor and friction factor \( f \) are, respectively, expressed by

$$ j = \text{St}Pr^{2/3} = \frac{{h_{o} }}{{\rho C_{p,air} V_{avg} }}Pr^{2/3} $$
(10)
$$ f = \frac{{D_{h} }}{L}\frac{{{2\Delta }P}}{{\rho V_{avg}^{2} }} $$
(11)

Thus, area goodness factor considering heat transfer enhancement and pressure drop can be given by

$$ \text{Area}\;\text{goodness}\;\text{factor} = \frac{j}{f} $$
(12)

3 Results and Discussion

Heat transfer rate according to fin length and installation angle was shown in Fig. 3.

Fig. 3.
figure 3

Heat transfer rate between air and water according to fin length and installation angle

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Heat transfer rate was shown as range of 194 W to 500 W and it was increased with the increment of fin length and installation angle because of the increment of heat transfer area and improvement of mixture of air flow. But the lower heat transfer rate was shown on 45o of installation angle than 30o. The reason of decrement of heat transfer rate at 45 o was considered as too excessively velocity through the fin (Figs. 4 and 5).

Fig. 4.
figure 4

Heat transfer coefficient of air side according to fin length and installation angle

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Fig. 5.
figure 5

Colburn j-factor of air side according to fin length and installation angle

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The pressure drop is related to blowing power. It is also needed to be considered according to fin length and installation angle as well as heat transfer rate. Figures 6 and 7 are illustrating pressure drop and friction factor calculated by simulation results. These values have higher value on the higher length and installation angle of fin looking similar with heat transfer rate. So, it was confirmed that enhancement of heat transfer rate according to fin length and installation angle leads to higher pressure drop of air side.

Fig. 6.
figure 6

Pressure drop of air side according to fin length and installation angle

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Fig. 7.
figure 7

Friction factor of air side according to fin length and installation angle

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Thus, the area goodness factor comparing with both heat transfer increase and pressure drop simultaneously was shown in Fig. 8. As a result, the area goodness factor was decreased with increment of fin length and installation angle. Maximum value of this was shown at 50 mm of fin length and 0o of fin installation angle. Heat transfer rate, however, was increased with increment of fin length and installation angle. Thus, if there are some minimum or maximum heat transfer rate that we want to achieve, it is needed to be considered whether the installation condition shows maximum value of area goodness factor satisfying minimum or maximum heat transfer rate or not.

Fig. 8.
figure 8

Area goodness factor of air side according to fin length and installation angle

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4 Conclusion

In this study, heat transfer between air and water in the fin-and-tube heat exchanger of the hybrid solar collector was investigated according to fin length and installation angle. As a result, higher heat transfer coefficient was obtained on higher length with 30o of installation angle, but pressure drop also increased as the same as increment of heat transfer rate. So, the area goodness factor considering both heat transfer enhancement and pressure drop was confirmed and the maximum value was shown on 50 mm of fin length with 0o of installation angle.

Thus, it is confirmed that installation condition has the highest heat transfer improvement compare with increment of pressure drop among installation conditions of the plate fin investigated in this study. Higher heat transfer rate was mostly obtained when the area goodness factor was low. So, it is considered that the actual experiment should be conducted with the fin length and installation angle showing maximum area goodness factor after confirming whether this installation condition can satisfy minimum or maximum heat transfer rate or not.