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Reduction of electricity for domestic hot water with
tank-style heater
To cite this article: Tomislav Atanasov 2023 IOP Conf. Ser.: Earth Environ. Sci. 1128 012006
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PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
1
Reduction of electricity for domestic hot water with tank-style
heater
Tomislav ATANASOV
Technical University of Sofia, Department of Heating and Refrigeration Engineering,
1156 Sofia, Bulgaria,
E-mail: toatanasov@tu-sofia.bg
Abstract. The most widely used domestic water heaters in Bulgaria are the electric
ones, with a storage tank. The main construction factors for the efficiency of the hot
water boiler are considered in the present study: the temperature of water and the
volume of the tank; the dimensions of the tank; the time for heating and discharge
time; the insulation material and the thickness of insulation; the power of the electric
heater. The average volume temperatures have been calculated analytical, the
stratification effect is not taken into account. The different variants for design,
insulation and the power of heater have been proposed. The results indicate for a
possibility of reducing electricity for preparing hot water up to 13%. The further
evaluation of the economic capability of the options has to be made.
Keywords: water domestic heater, reduction of the electricity, factor for efficiency, analytic
determination of temperatures.
1. Introduction
Hot water is necessary for different needs in the home and industry. Every building must have an
installation for providing hot water, which - unlike heating and air conditioning - is used all year
round. The most common water heaters are [1]:
Tank-style water heaters (electric, gas, wood or oil)
Tankless on-demand or “instantaneous” water heaters
Indirect water heaters connected to a boiler (solar systems, thermodynamic systems)
For the reasons of the lowest initial costs and two tariffs for electricity, widely used domestic water
heaters in Bulgaria is the electric one, with a storage tank, insulated with polyurethane foam. The all
quantity of water is heated from 22:00 to 06:00, when the cost is significantly lower for domestic
PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
2
users, and is stored until it is used. The heat loss rise electricity consumption and they waste money
[2[. Measures to reduce heat losses are of two types - organizational and constructive.
The organizational decisions:
convergence of heating and consumption cycles;
delayed start of heating, depending on the water temperature in the boiler at 22:00 and power
of the electric heater;
reduction of the water heating temperature in case of decreasing the number of inhabitants or
in other instances of reduced consumption.
The constructive decisions:
the temperature of water and the volume of the tank - increasing the water content would
allow the water temperature in the boiler to decrease, but this means higher and unjustified
initial capital costs;
the dimensions of the tank - determining the diameter and the height of the water heater (at a
given volume) so that tank surface is as small as possible;
the time for heating - choosing an electric heater with a reasonably larger wattage than
required, which means a shorter heating cycle and less heat waste;
the thickness of insulation - as the thickness of the insulation increases, the heat loss
decreases, but this means higher initial capital costs, which should be justified;
For the aims of the present study, the following conditions were adopted:
temperature of the consumption water 37.5 °C;
distributed water temperature 40 °C;
necessary amount of hot water (at the above temperature) for one day – 250 l;
warm-up time - between 22:00 and 6:00;
time for intensive consumption – between 18:00 and 22:00.
type of the heater – tank-style, with electric heater
water heating temperature in the boiler - not lower than 60°C.
The heater is shown in figure 1.
Figure 1. Tank-style heater.
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IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
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doi:10.1088/1755-1315/1128/1/012006
3
2. Structural dimensioning
2.1. Volume of the tank and the water heat temperature
The mixing of the hot and cold water can be described by the next equations:
=,().
[kg] (1)
.,.+.,.=+.,. [kJ] (2)
where,
is the mass of water, [kg];
,() is the specific density of water at a given temperature, [kg/m³];
is the volume of the water, [m³];
is the mass of hot water in the tank [kg];
is the mass of cold water [kg];
, is the water specific heat capacity, [kJ/(kg.K)];
is the hot water temperature, [°C];
is the cold water temperature, [°C];
is the mixed water temperature, [°C].
Water with temperature 40°C can be obtained with mixing the hot water from the tank and cold
water from the water network (10°C) – figure 2. For 250 [l] per day we can choose between 2 options
- a tank with a volume of 200 [l] and temperature 80 [°C] or a tank with volume of 250 [l] and
temperature 73 [°C]. The better option is the 200 [l] tank with temperature 80 [°C], because of the
lower investments, the smaller dimensions and the smaller external surface.
Figure 2. Water tank volume selection.
0
50
100
150
200
250
300
350
400
tg=60°C
tg=65°C
tg=70°C
tg=75°C
tg=80°C
tg=85°C
tg=90°C
Mixed water quontity [l]
Water temperature in the tank [°C]
tm=40°C; tc=10°C
V=100 l
V=150 l
V=200 l
V=250 l
PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
4
2.2. Tank dimensions
Several variations for 200 [l] tank are shown in figure 3. The variant D=0.6 [m] and H=0.7 [m] have
minimum external surface 1.9 [m²]. The most mass-produced tanks have configurations close to
variant D=0.4 [m] and H=1.6 [m]. This article examines three options M1, M2, M3 – table 1.
2.3. Tank insulation
The most common used domestic heaters are insulated with 50 [mm] polyurethane foam (specific
thermal conductivity λ=0.032 [W/(m.K)]). Three options for thickness are considered: 50; 75; 100
mm. The heat transfer coefficient are calculated and shown in table 2.
Figure 3. External surface for tanks with different dimensions.
2.4. Electric power of the heater
To heat water with an initial temperature of 40 [°C] to 80 [°C] over a period of 8 hours, an electric
heater with a power of 1.16 kW is required. Three options of heaters are considered – 1.0; 1.5; 2.0
[kW].
Table 1.
BOILER
D X H
Ext. surface
Ф50
Ф75
Ф100
V=200 l
m x m
m²
[W/°C]
[W/°C]
[W/°C]
M1
0.40 x 1.60
2.3
1.662
1.233
1.012
M2
0.50 x 1.00
2.0
1.369
0.996
0.803
М3
0.60 x 0.70
1.9
1.265
0.905
0.720
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1.70
1.80
1.90
2.00
2.10
2.20
2.30
D=0.4 [m]
D=0.5 [m]
D=0.6 [m]
D=0.7 [m]
D=0.8 [m]
Tank height H [m]
Tank external surface [m²]
V = 200 [l]
Ehternal surface [m²]
H [m]
PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
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Table 2. Energy for heating the water
Insulation λ=0.032 [W/(m.K)]
50mm
75mm
100mm
Ext.
surface
α
[W/m².K]
U50
[W/m².K]
U75
[W/m².K]
U100
[W/m².K]
ver
10
0.602
0.409
0.310
hor↑
12
0.608
0.412
0.312
hor↓
8
0.593
0.405
0.308
3. Analytical models
The analytical model for tanks in heating and accumulating mode [3] is used. The procedures give
results for average water temperatures into the tank and take into account:
geometrical and the constructive parameters of the tank (D, H, insulation);
fluid characteristics;
temperatures – the initial fluid temperature and the ambient air temperature.
3.1. Analytical model for accumulation mode
The equations (3) - (7) described the processes [3] are:
,(=)=. ., +1 . . (3)
,=,(=).1.
. , (4)
(,,)=1
. ,
, , [s] (5)
=
., , [1/s] (6)
=(.), [W/] (7)
where,
,(=) is the water temperature in moment [s], [°C];
, is the initial temperature of the water, [°C];
, is the final temperature of the water, [°C];
is the ambient air temperature, [°C];
(,,) is the time for change the temperature from , , [s].
is the mass of the water in the tank, [kg];
, is the water specific heat capacity [kJ/kg.K].
3.2. Analytical model for the heating mode
The equations (8) - (11) described the processes [3] are:
,(=)=. ., +1 . .+1 . .
, [C]; (8)
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IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
6
,1,2=1
.,2
,1
,
[s]; (9)
=
.,
,
[1/s]; (10)
=.,,
3600
,
[kWh] (11)
where,
is the electricity for heating, [kWh];
is the electric power of heater, [kW];
4. Analytical calculations
4.1. Analytical calculations for accumulation mode
The average temperature in the tank have to be 80 [°C] at 18:00. The required water temperature in the
tank 12 hours (720 min) earlier (at 6:00) are calculated by (4) in the next conditions:
The volume of the tank is 200 [l];
Initial temperatures of water , (at 22:00) is 40 [°C];
The ambient temperature is 15 [°C];
Φ is calculated from (7) with the data in table 2.
The temperature curves for the different models M1, M2… M9 are shown in figure 4. The highest
temperature (85.6 [°C]) is for the basic model M1 with 50 [mm] insulation, the lowest temperature
(82.5 [°C]) is for the model M3 with 100 [mm] insulation.
Figure 4. Water temperatures at 6:00.
4.2. Analytical calculations for heating mode
The time to heat the water in the tank for different cases are calculated by (9). The consumption of
electricity for variants with 1000, 1500 and 2000 [W] heaters are calculated by (11). The results are
shown in table 3.
85.8
82.5
79.0
80.0
81.0
82.0
83.0
84.0
85.0
86.0
060 120 180 240 300 360 420 480 540 600 660 720
INITIAL TEMPERATURE [°C]
TIME (MIN)
M1; 50mm
M2; 50mm
M3; 50mm
M1; 100mm
M1; 150mm
M2; 75mm
M3; 75mm
M2; 100mm
M3; 100mm
PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
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doi:10.1088/1755-1315/1128/1/012006
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Table 3. Energy for heating the water
Model
tw,b
[°C]
Qh=1000 [W]
Qh=1500 [W]
Qh=2000 [W]
insulation
Energy consumption Eel [kWh]
M1; 50mm
85.8
11.6
11.3
11.1
M2; 50mm
84.7
11.1
10.9
10.8
M3; 50mm
84.4
11.0
10.8
10.7
M1; 100mm
84.3
11.0
10.7
10.6
M1; 100mm
83.5
10.6
10.5
10.4
M2; 75mm
83.4
10.6
10.4
10.3
M3; 75mm
83.1
10.5
10.3
10.2
M2; 100mm
82.7
10.3
10.2
10.1
M3; 100mm
82.5
10.2
10.1
10.1
5. Reduction of electricity
The net electricity savings for the variants of boiler construction, insulation and installed capacity, can
be calculated from the data in table 3. The savings, related to the consumption of the base model, are
shown in figure 5.
Figure 5. Relative savings of electricity.
6. Conclusions
By applying of the represented in [3] analytical method for calculating the average temperature in
water thermal accumulators and heaters are estimated different models of domestic tanks for hot
water. The different variants for design, insulation, power of heater are considered. The results shows
0.0%
4.0%
5.1%
5.5%
8.3%
8.6%
9.6%
10.9%
11.7%
2.8%
6.2%
7.1%
7.4%
9.8%
10.0%
10.9%
12.1%
12.7%
4.2%
7.2%
8.1%
8.4%
10.5%
10.8%
11.6%
12.6%
13.2%
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
M1;
50mm
M2;
50mm
M3;
50mm
M1;
75mm
M1;
100mm
M2;
75mm
M3;
75mm
M2;
100mm
M3;
100mm
Reduction of the Electricity
compared with the base case
Q=1000 W
Q=1500 W
Q=2000 W
base case
PEPM-2022
IOP Conf. Series: Earth and Environmental Science 1128 (2023) 012006
IOP Publishing
doi:10.1088/1755-1315/1128/1/012006
8
a possibility of reducing electricity for heating up to 13% end gives opportunity for future evaluation
of the economic compatibility of the options.
Acknowledgment
The author would like to thank the Research and Development Sector at the Technical University of
Sofia for the financial support.
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