## Lesson 16. Performance evaluation of solar water heater

Solar water heater converts solar energy into thermal energy and is transferred to water to generated hot water.  The performance such as hot water generation, temperature of hot water, efficiency of hot water system etc. can be assessed by the following procedures.  The assessment can be carried out for a specific period say 8 hours in a day.  The seasonal variation can also be studied by parametric assessment in specified seasons.

Parameters to be measured

Solar insolation during the study period, S       :           W m-2

Capacity of hot water system, Q                    :           lpd

Length of the collector, l                                :           m

Width of the collector, w                                :           m

Number of collectors, n                                 :

Atmospheric temperature, Ta                         :           °C

Diameter of hot water pipe, Dm                      :           m

Length of hot water pipe, Dl                           :           m

Heat transfer coefficient, h                             :           W m-2°C

Temperature of hot water, Th                          :           °C

Transmissivity of glass cover, t                        :

Absoptivity of black coated surface, a              :

Instrumentation required are

Thermometers

Useful solar heat energy available

Total area of the collector area, Ac, m2                      =          n X length X width of each collector

=          n x l X w

1 J/s = 1 W    \ 1kWh = 3600 kJ

S X Ac X 8 X 3600

Daily available solar radiation, SD, kJ d-1                   =          -----------------------

1000

Heat energy required to heat the water

Specific heat of water, Cp                               =          4.18 kJ/kg °C

Rise in temperature of hot water, ∆T               =          Th - Ta, °C

Daily heat energy required to heat the water, Qu          =          Q × Cp × ∆T, kJ d-1

System performance

Energy transmission through the system

Solar energy transmitted through the glass, St   =          S X t

Energy absorbed by the absorber plate, Sta      =          St X a

Surface area of heat transfer, AS                     =          π Dm X Dl

Sta X Q X h X AS X3600 X ∆T X 8

Heat energy transferred to water, SH, kJ d-1      =          -----------------------------------------

1000

Output

Thermal efficiency of solar water heater, %    =          ---------- X 100

Input

QU

=          ----- X 100

SD

Economics of solar water heater

It is considered that the economics of solar water heater is compared with the electrical heaters.  The cost required for solar hot water system and electrical systems are calculated and the pay back period is calculated.

Cost of solar water heater                                =          Investment, Rs.

QU

Daily thermal energy requirement, QE, kWh    =          ------------------

0.95 X 3600

(Considering the efficiency of the electrical water heating system as 0.95)

Cost of electricity per day, PE, Rs.                   =          QE × Unit Price

Assuming 300 days of annual utilization of solar hot water system,

Annual saving, Rs.                                           =          PE X 300

Investment, Rs.

Simple payback period                                     =          --------------------------

Annual savings, Rs.

Problem

Daily hot water requirement of a hostel in a college is 5000 litres.  Solar radiation available on the location is 600 Wm-2.  Temperature of feed water is 30°C and the final hot water temperature should be 60°C.  The area of the solar collector is 50 m2.  Assess the performance of the collector and also calculate the pay back period of the water heater.  Assume the required data for hot water generation.

Solar insolation during the study period, S       :           600 W m-2

Capacity of hot water system, Q                    :           5000 lpd

Atmospheric temperature, Ta                         :           30°C

Temperature of hot water, Th                         :           60°C

Area of the collector area, Ac, m2                    =          50 m2

Useful solar heat energy available

S X Ac X 8 X 3600

Daily available solar radiation, SD, kJ d-1                     =          -----------------------

1000

Assuming 8 hours of daily operation.

600 X 75 X 8 X 3600

=          -----------------------

1000

=          1296000 kJ d-1

Heat energy required to heat the water

Specific heat of water, Cp                               =          4.18 kJ/kg °C

Rise in temperature of hot water, ∆T               =          Th - Ta, °C

=          60 -30

Daily heat energy required to heat the water, Qu   =  Q × Cp × ∆T, kJ d-1

= 5000 x 4.18 x 30

= 627000 kJ d-1

System performance

Output

Thermal efficiency of solar water heater, %    =          ---------- X 100

Input

QU

=          ----- X 100

SD

627000

=          ------ ---- X 100

1296000

=          48.38%

Economics of solar water heater

Cost of solar water heater                         =          Investment, Rs.

=          Rs. 6,00,000

Annual maintenance                                  =          Rs. 10,000

QU

Daily thermal energy requirement, QE, kWh    =          ------------------

0.95 X 3600

627000

Daily thermal energy requirement, QE, kWh    =             ---------------

0.95 X 3600

Cost of electricity per day, PE, Rs.                   =          QE × Unit Price

Cost of electricity per day, PE, Rs.                   =          193 × 5 = Rs. 915

Assuming 300 days of annual utilization of solar hot water system,

Annual saving, Rs.                                 =          PE X 300

=          915 x 300 = Rs. 2,74,500

Investment + Maintenance, Rs.

Simple payback period                           =          -------------------------------------

Annual savings, Rs.

610000

=          ---------

274500

=          2.22 years (2 years and 2½ months)