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

Figures & data

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 (%)

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

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

Figure 3 Receiver (non-coated).

Figure 4 Receiver (black coated).

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

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

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

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

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