Comparative experimental analysis of the effect of convective heat losses on the performance of parabolic dish water heater

Abstract

This paper reveals comparative experimental analysis of the effect of variation of natural and forced convection heat losses on the performance of prototype parabolic dish water heater with coated and non-coated receivers. With the above-described system, hot water needs in domestic applications can be fulfilled instantly. A parabolic dish collector was used for instant water heating. Design of solar parabolic dish collector consists of truncated cone-shaped helical coiled receiver made up of copper at focal point. Instantaneous efficiency of 63% and 48% has been achieved with coated and non-coated receivers. This prototype has been evaluated for its performance with water flow rate of 0.0076 kg/s during the months of April and May 2010 at Shivaji University, Kolhapur, Maharashtra, India (latitude: 16.42° North, longitude: 74.13° West).

Keywords:

• solar thermal energy
• instant water heating
• truncated cone-shaped helical coiled receiver
• standard test conditions
• effect of variation of natural and forced convection heat losses

1. Introduction

The concentrated solar thermal energy system is designed and constructed with the conventional parabolic concentrator. The receiver is placed along the line between the centre of the concentrator and the sun. The receiver used is coiled helically with specific design so that all the solar rays concentrated at the centre have received without shadow. Manual tracking has been used during evaluation stage. This allows for effective collection and concentration of the incoming solar irradiation (Duffie and Beckman 2006). The concentrator receives approximately 1.064 kW/m² of total (global) solar insolation (dependent upon time of year), which is concentrated and reflected to the receiver. By concentrating the incoming radiation, the operating temperature of the system increases significantly and subsequently increases the efficiency of the conversion.

2. Literature survey

A simpler batch solar water heater has been investigated by Akuffo and Jackson (1988). This design achieved a maximum temperature of 45°C by 4:30 pm and provided 30°C water at 5:30 am the next day. Daily ambient peak temperatures exceeded 37°C. Hussain Al Madani (2006) studied a batch solar water heater in Bahrain consisting of an evacuated, cylindrical glass tube. Side-by-side testing of prototypes resulted in a maximum temperature difference between the inlet and outlet of the cylindrical batch system of 27.8°C with a maximum efficiency of 41.8%. Nahar (2002, 2003) studied a separated storage–collector system. Nahar found that this system can produce 60.6°C water at 4:00 pm and 51.6°C water the next morning. The overall efficiency of this system was determined to be 57%. Tripanagnostopoulos and Souliotis (2006) experimented on optimising an integrated storage–collector batch solar water heater that contained two cylindrical tanks and a compound parabolic concentrator made of aluminium mylar glazed with an iron oxide and black matte absorbing surface.

Zerrouki et al. (2002) studied a similar separated storage–collector system in Algeria. The maximum temperature was observed to be 57°C starting from an initial temperature of 17°C at 7:00 am.

3. Description of system used

System consists of parabolic dish of 1.4 m diameter. It has been made of anodised aluminium mirrors and supported with locally manufactured steel stand. At focus, truncated cone-shaped helical coil made up of copper is fitted and it has been coated with nickel chrome. Inner and outer diameters of hollow receiver coils are 5.0 and 5.1 mm, respectively. The spacing between two coils is 5 mm and angle of helix is 5°. Inlet and outlet pipes made of high temperature and pressure poly vinyl chloride (PVC) are attached to coil. Inlet water flow has been controlled by using inlet valve, and hot water at outlet is collected in insulated tank.

Flow of water has been kept as 0.0076 Kg/s. Thermocouples of K types have been used to measure the temperatures of inlet and outlet water, receiver surface temperature. Wind speed and solar radiation has been measured with anemometer and pyranometer respectively. This prototype has been evaluated for its performance during the months of April and May 2010 under standard test conditions (MNRE and BIS draft test procedure 2006, 2009). Tables 1 and 2 show the parameters used for experimentation.

Table 1 Parameters used for experimentation.

Name of component	Dimension
Absorptivity–transmitivity product of coating	0.94
Absorptivity–transmitivity product of copper	0.7
Aperture area of parabolic dish collector	1.54 m^2
Density of copper	8.9 gm/cm^3
Depth of dish	0.38 m
Diameter of parabolic dish	1.4 m
Diameter of receiver at bottom	0.135 m
Diameter of receiver at top	0.095 m
Effective length of receiver coil	3.96 m
Emissivity of coating	0.10–0.14
Emissivity of copper	0.725
Focal length of dish	0.3223 m
Mean diameter of receiver	0.115 m^2
Melting point of copper	1083 °C
Reflectivity of parabolic dish	0.86
Specific gravity of copper	8.9
Surface area of parabolic dish collector	1.9295 m^2
Surface area of receiver	0.2357 m^2
Thermal conductivity of copper	384 W/m k)
Thickness of mirror of parabolic dish	2 mm

Table 2 Nomenclature and subscripts.

Nomenclature and subscripts
I	Measured solar radiation on horizontal surface (W/m^2)
I bc	Beam radiation on collector (W/m^2)
T in	Temperature cold water at inlet from storage tank (°C)
T out	Temperature of water at outlet (°C)
T air	Temperature of air (°C)
T r	Average temperature of receiver (°C)
V	Wind speed (m/s)
Q useful	Useful heat energy gained by water (W)
Q optical	Optical energy trapped by receiver (W)
h conv.natural	Natural convective heat loss coefficient (W/m^2 °C)
h conv.forced	Forced convective heat loss coefficient (W/m^2 °C)
h Total	Total convective heat loss coefficient (W/m^2 °C)
U l	Overall heat loss coefficient (W/m^2 °C)
ηCollector	Instantaneous efficiency of collector (%)

4. Experimental procedure

Test set-up consists of a cavity receiver supported by support. The receiver has been kept vertically upright with respect to the horizontal. The cold water circulated in the receiver is supplied from a water tank of 100 litre capacity. The working fluid has been circulated through the receiver tubes by siphon, i.e. natural circulation. A rotameter at inlet measures the mass flow rate of cold water entering the receiver. The cold water has been circulated at constant inlet temperature through the receiver. The temperatures of the fluid in the tube at four locations (including the outlet) are measured using K-type thermocouples. The flow has been kept constant for the complete period of an experimental run on a given day. The system has been operated under open-loop condition as the water exiting from the receiver is not circulated back to the inlet cold water supply tank. The hot water has been stored in an insulated tank and kept near the outlet. The wind speed measurements have been taken at a fixed location near the parabolic dish collector plane. The wind blows in the direction normal to the receiver and also the direction of the wind is parallel to the receiver. The schematic of the experimental set-up witch has been used for instant water heating which is shown in Figure 1.

Figure 1 Schematic of the experimental set-up with non-coated receiver.

The working fluid used during experiment is cold water and inlet temperatures on the experimental day vary between 23°C and 27°C. For each test, the inlet fluid temperature has been measured by using thermocouple. The working fluid enters and exits the receiver as shown in Figure 1. The working fluid enters through inlet at the bottom portion of the receiver and flows through the helically coiled receiver and leaves receiver at the uppermost portion. The solar radiations, receiver surface temperatures and the fluid temperatures are measured at intervals of half-hour, and the experiment has been continued till the solar radiation is available at sufficient intensity. The thermal losses are estimated at steady state (Figure 2). Helical coil as shown in Figures 3 and 4 representing the receivers without coating and with coating of black nickel chrome paint. For the experiments with black-coated receiver, the region outside the cavity has been surrounded by a downward-facing cylindrical glass enclosure.

Figure 2 Schematic of the experimental set-up with coated receiver covered with glass.

Figure 3 Receiver (non-coated).

Figure 4 Receiver (black coated).

5. Calculations

5.1 Terrestrial solar radiation

Ground level radiation can be estimated using Hottel's clear sky model for urban visibility 5 km at Kolhapur

Constants a _o, a ₁ and K in Hottel's model can be calculated as follows:

Instantaneous direct radiation (IBN; I _bn) on horizontal surface at ground level is given by Duffie and Beckman (2006):

From IBN on horizontal surface, direct radiation on collector surface has been estimated.

5.2 Geometric concentration ratio for designed collector

Geometric concentration ratio for designed collector is given by (Duffie and Beckman 2006)

Useful heat gain by water is given by (Duffie and Beckman 2006)

where Q _opt = optical radiation trapped receiver (W) and Q _loss = rate of hest loss from receiver (W).

5.3 Calculation of heat losses from the receiver

Thermal losses from solar open cavity receivers include convective and radiative losses to air.

For focal plane, i.e. cavity receiver overall heat loss is given by (Duffie and Beckman 2006)

where T _r = average receiver temp (°C), T _a = temperature of air surrounding a receiver (°C), and U _l = overall heat loss coefficient.

To estimate natural convective heat loss, following correlation developed by Prakash et al. (2009) is used

where θ_r = receiver inclination angle = 90°, Gr = Grashof's number for natural convection, T _m = mean temperature of water in receiver coils at natural convection.

Forced convection loss coefficient is given by the following equation. This equation is developed by Ma (Gordon and Rabl 1982, Fraser 2008)

Overall heat loss coefficient (U _l) is given by (Duffie and Beckman 2006)

where radiative heat transfer coefficient (h _rad) is given by (Duffie and Beckman 2006)

Total convective heat loss coefficient (h _conv.total) is given by (Duffie and Beckman 2006, Fraser 2008)

5.4 Experimental data

See Tables 3 and 4.

Table 3 Experimental measurements and calculations for non-coated receiver at mass flow rate 0.0076 kg/s.

I (W/m^2)	I bc (W/m^2)	T in (°C)	T out (°C)	T amb (°C)	T r (°C)	V (m/s)	Q Optical (W)	h conv.natural (W/m^2°C)	h conv.forced (W/m^2°C)	h Total (W/m^2°C)	U l (W/m^2°C)	Q loss (W)	Q useful (W)	ηCollector (%)
610	508	28	40	30	63.50	2.80	449.75	3.98	2.48	6.46	6.48	51.16	398.58	50.92
720	608	28	43	30	64.25	4.28	538.75	3.72	4.48	8.20	8.22	66.34	472.41	50.38
830	706	29	46	31	67.75	4.73	624.85	3.63	5.16	8.79	8.81	76.33	548.52	50.44
930	790	29	48	31	75.75	4.05	699.46	3.73	4.15	7.89	7.92	83.51	615.95	50.60
940	790	30	48	32	83.75	5.43	699.32	4.06	6.26	10.32	10.36	126.35	572.98	47.08
990	824	30	50	33	85.75	3.80	729.53	4.10	3.80	7.90	7.94	100.58	628.95	49.54
1020	845	31	52	34	92.00	3.28	747.99	4.18	3.09	7.26	7.31	103.38	644.61	49.52
1010	847	31	50	34	101.25	4.03	749.99	4.64	4.12	8.76	8.82	144.02	605.97	46.43
1000	849	31	51	34	92.50	3.78	751.48	4.28	3.76	8.05	8.10	115.45	636.03	48.63
950	817	32	52	33	84.25	3.30	723.12	3.70	3.12	6.82	6.86	82.87	640.25	50.88
770	655	32	47	32	73.75	6.58	580.26	3.65	8.19	11.84	11.87	114.00	466.26	46.17
700	593	32	46	32	68.25	6.05	525.33	3.53	7.29	10.82	10.84	92.64	432.69	47.33
630	529	32	44	32	68.00	5.70	468.84	3.69	6.71	10.40	10.42	88.44	380.41	46.62
480	388	33	42	31	62.00	5.43	343.57	3.41	6.26	9.66	9.68	68.47	275.11	46.01
390	305	33	39	31	55.50	5.73	269.99	3.37	6.75	10.12	10.13	58.50	211.49	45.01

Table 4 Experimental measurements and calculations for coated receiver at mass flow rate 0.0076 kg/s.

I (W/m^2)	I bc (W/m^2)	T in (°C)	T out (°C)	T amb (°C)	T r (°C)	V (m/s)	Q Optical (W)	h conv.natural (W/m^2°C)	h conv.forced (W/m^2°C)	h Total (W/m^2°C)	U l (W/m^2°C)	Q loss (W)	Q useful (W)	ηCollector (%)
430	328	26	35	31	85.25	2.70	390.07	6.18	2.35	8.53	8.73	111.66	278.40	55.07
580	474	26	42	31	96.25	3.33	563.50	5.46	3.15	8.61	8.89	136.68	426.82	58.45
790	665	27	53	31	99.75	3.73	791.02	4.14	3.69	7.83	8.13	131.76	659.26	64.31
900	759	28	56	31	109.50	5.45	903.04	4.00	6.30	10.30	10.68	197.62	705.42	60.28
950	796	29	58	32	124.50	5.10	946.40	4.24	5.74	9.98	10.53	229.52	716.87	58.45
960	795	30	60	32	106.00	5.50	945.56	3.62	6.38	9.99	10.35	180.54	765.02	62.43
480	372	30	45	32	51.75	4.38	442.98	3.04	4.63	7.67	7.74	36.02	406.96	70.89
680	550	31	53	32	75.75	3.55	653.61	3.32	3.45	6.78	6.93	71.45	582.16	68.73
930	778	31	59	32	130.00	4.25	925.18	4.10	4.44	8.54	9.16	211.47	713.71	59.52
770	641	32	58	33	78.00	5.10	762.85	3.11	5.74	8.85	9.02	95.62	667.23	67.49
710	592	32	56	33	80.50	5.13	703.47	3.31	5.78	9.08	9.27	103.74	599.74	65.78
850	725	33	61	33	101.50	4.95	862.60	3.39	5.50	8.89	9.22	148.82	713.78	63.85
750	635	33	56	33	91.00	6.40	754.84	3.50	7.89	11.39	11.64	159.08	595.76	60.90
580	475	32	52	32	65.00	4.25	565.28	2.98	4.44	7.42	7.53	58.58	506.70	69.16
480	381	32	49	32	62.25	3.75	453.09	3.09	3.73	6.82	6.91	49.29	403.80	68.77

6. Results and discussion

Figure 5 indicates that receiver temperature increases rapidly as the solar radiation on collector increases. It, in turn, increases the outlet water temperature. Also it has been observed that as the atmospheric temperature rises there is rise in inlet water temperature. The rise of temperature of outlet water is also affected by wind velocity at that instant. It has been observed that there is average rise of 12% and 16% in outlet water temperature and average receiver temperature, respectively, with coated receiver and glass cover as compared with non-coated receiver. Maximum outlet water temperature of 61°C and average receiver temperature of 124°C have been achieved with the coated receiver and glass cover.

Figure 5 Variation of outlet water temperature and average receiver temperature throughout the day.

Figure 6(A–D) clarifies that as wind velocity at instant increases, there is a rapid rise in convective heat loss coefficients of both types, viz. natural and convective. It has been seen that forced convective heat loss coefficient has significant share in total convective heat loss coefficient. Comparatively for non-coated and coated receivers, for variation of 2% of wind velocity, total convective heat loss coefficient also varies by 2%. Also for same variation of wind velocity, forced convective heat loss coefficient varies by 3% and natural convective heat loss coefficient varies by 0.32% only. This proves that forced convective heat loss coefficient has significant share in total convective heat loss coefficient.

Figure 6 (A) Variation of total convective heat loss coefficient with wind velocity throughout the day. (B) Variation of natural, forced and total convective coefficient for non-coated receiver throughout the day. (C) Variation of natural, forced and total convective coefficient for coated receiver and glass cover throughout the day. (D) Comparison of variation of total convective coefficient for non-coated and coated receivers throughout the day.

Figure 7 explores variation of total heat loss. Heat lost by receiver adversely affects the performance of collector. The reason is that as overall heat loss coefficient increases, total heat loss increases and reduces collector efficiency significantly. Comparatively for non-coated and coated receivers, it has been observed that average variation in total convective heat loss is 28% and maximum variation is 37%.

Figure 7 Variation of total heat loss and collector efficiency with overall heat loss coefficient.

From variation plotted in Figure 8, it has been observed that though the beam radiation on collector is more and average receiver temperature increases, but due to higher wind speed, there are increased forced convective losses through the receiver and it affects adversely the performance of parabolic dish collector and total system. It has been observed that for coated and non-coated receivers, for average variation of total convective heat loss coefficient by 2%, there is variation of 13% in useful heat gain by water. Water gains 13% more heat with coated receiver and glass cover as compared to non-coated receiver. It has also been observed that forced convective heat loss have higher contribution in reducing the useful heat gain by receivers as compared to natural convective heat losses.

Figure 8 Variation of total convective heat loss coefficient with useful heat gain by water throughout the day.

Figure 9 presents variation of collector efficiency with convective heat losses. It has been observed that forced convective heat loss has higher contribution in reducing the efficiency of collector as compared to natural convective heat losses. Efficiency of collector drastically drops at higher wind speed because of higher convective heat losses. For average variation of 3% in forced convective heat loss coefficient as compared with average variation of 0.32% in natural convective heat loss coefficient, there is variation of 23% in collector efficiency for coated and non-coated receivers. Collector efficiency of 63% to 48% has been achieved with coated receiver and non-coated receiver, respectively.

Figure 9 Variation of natural and forced convective heat loss coefficient and collector efficiency throughout the day.

7. Conclusion

An experimental and numerical study of parabolic solar dish collector water heater with coated and non-coated receivers has been conducted under Kolhapur climatic conditions. General comparison between the parabolic solar dish collector water heater and common models such as flat plate and evacuated tube collectors demonstrated that parabolic solar dish collector water heater is a good alternative for flat plate and evacuated tube water heaters and could be applied effectively. Therefore, the developed model can be considered for designing commercial parabolic solar dish collector water heater. Proposed system is aimed at saving conventional energy sources and environment too. Such objectives are important parts towards the development of self-sufficient sustainable homes in rural as well as urban areas of India. Measure findings from experimentation have been listed. In future, this type of system can be used for heating boiler feedwater, laundry applications and other steam generation applications.

1.	With the above-described system, collector efficiency of 63–48% has been achieved with coated receiver and non-coated receiver, respectively.
2.	There is average rise of 12% and 16% in outlet water temperature and average receiver temperature, respectively, with coated receiver and glass cover as compared to non-coated receiver.
3.	This has been proved that forced convective heat loss coefficient has significant share in total convective heat loss coefficient.
4.	Forced convective heat loss coefficient varies by 3% and natural convective heat loss coefficient varies by 0.32% only.
5.	Comparatively for non-coated and coated receivers, it has been observed that average variation in total convective heat loss is 28%.
6.	Water gains 13% more heat with coated receiver and glass cover as compared with non-coated receiver.

Acknowledgement

The authors would like to thank the Department of Technology for providing lab support to this research work.