A Book Review for Design Analysis of Solar-Hot-Water-Heating Technologies in Azacilo, Bolivia

By: Joseph Rendall

For: ARCE 700 Directed Readings

Abstract

Designing engineering solutions for developing nations has an unique set of design variables. These

variables should be quantified when possible. Developed world technologies often supersede the

manufacturing capacities of a developing nation. A sustainable model for growth, suggests using local

materials in developing nation engineering technology solutions. The report aims to expand on these

topics while developing a solar-hot-water heating system (SH) for the people of Azacilo, Bolivia. The

first major concern for SH is the climate of Azacilo, Boliva that drives the technology fail modes of

freezing and over pressurization. Many components and materials can be made to combat these fail

modes in fully industrialized countries.

A book review of, “Solar-Thermal Energy Systems, Analysis and Design” by: John Howell, Richard B.

Bannerot and Gary C Vliet was done to help design a SH for Azacilo, Bolivia. Unfortunately, the rules-

of-thumb for sizing may not be appropriate. The complex math in the book was avoided besides in the

cases of the fail modes because the report was more of a feasibility study. The results of the study suggest

that a SH could be done in Azacilo, Bolivia (they receive 20% more radiation per year than Topeka,

Kansas) but the type of system based on costs, amount of insulation and community needs (load) requires

further study.

Introduction

Solar heaters have been used for about 2,500 years (Butti & Perlin, 1980). Improvements

to water heating technologies for developed nations has increased significantly from batch

heaters to selective-surface-vacuum tubes. In developing nations one sustainable-design

methodology for technologies is to use a local product that the local community can afford to

maintain (Mihelcic et. al, 2009). This design constraint directs solar-water-heating apparatus

away from selective-surfaces, glass and extruded aluminum. These materials are often used in

developed nation solar water heater technologies currently used (e.g. flat plate collectors and

evacuated tube). The good news is some low-tech. materials do have good thermal properties for

solar-water heaters (e.g. water, black paint, steel and Styrofoam).

The aim of this report is to analysis current solar water heating systems and suggest a

design(s) for a community of 100 people in Azacilo, Bolivia. The designs suggested are

theoretical. Materials and water usage data is based on what the people of Azacilo could get

(steel, fiberglass panels, ect.) and surveyed on KU EWB‟s summer 2012 trip (2 showers per

week per person). The prices of the materials in Bolivia will be determined on the KU EWB

winter trip (January 1st to 7

th) but a modified flat-plate design was priced at local home

improvement stores to compare with prices from the January trip.

This report designs will be compared common solar heating technology (SH) by (1) cost

(2) maintenance (3) performance and (4) long term durability. The common SH designs

compared are: a) black-plastic-pipe (BPP) rolls on roof, b) batch heating with insulation (BHI)

and c) batch heating without insulation (BH), d) flat-plate thermosiphon (FPT), e) flat-plate PV-

pump assisted (FPPP), f) flat-plate fully active (FPA) and g) evacuated tube (ET). The thermal

storage designs compared are based on material and location (e.g. (i.) metal (ii.) plastic (iii.)

stored inside or (iv.) outside or (v. none)). Thus, there were 35 different designs that could be

chosen. To further help select the designs for deeper analysis (e.g. fail-modes, components, sizes

and costs) a decision matrix was used.

To compare the technologies typical-meteorological-year (TMY3) data was analyzed for

La Paz, Bolivia. The Bolivia weather was compared and contrasted to Kansas weather. Fail

modes calculations (freezing and over-pressurization) were performed for selected designs and

compared by fluid medium and cover material.

The main book read for the analysis was, “Solar-Thermal Energy Systems, Analysis and

Design” by: John Howell, Richard B. Bannerot and Gary C Vliet. A secondary source for ideas

was, “A Golden Thread” by Ken Butti and John Perlin. Another source of ideas was a course

was taken on developing nations work at KU taught by Dr. Adams (Spring 2012). The book from

this class, “Field Guide to Environmental engineering for Development Workers” by: Mihelcic

et al. was also helpful. Dr. Rock‟s and Dr. Adams‟ ideas also enter this report coming from many

brainstorming sessions on the technologies and community.

Methods

Comparison of common solar heating technologies by a developing nation decision matrix

To determine what heating system were appropriate for analysis a decision matrix was

made for the designs based on the four developing nation metrics (Table 1). The decision matrix

was developed to take out “technology bias” and mainly because the writer of this topic is not an

expert. No technology could be selected based on experience selecting and sizing solar-thermal

systems. To determine the actual system EWB KU selects for Azacilo, Boliva experts in the

field of solar thermal-systems and developing-nation work should be consulted. Table 1 First-cut review of design types by first costs, user maintenance requirements, thermal performance and

durability over five years.

BPP BHI BH FPT FPPP FPA ET

Cost (1) 1 0 0 -1 -1 -1 -1

Maintenance (2) -1 1 1 1 0 -1 -1

Performance (3) -1 -1 -1 0 1 1 1

Durability (4) -1 1 1 1 0 0 -1

Total Ranking -0.08 0.42 0.42 -0.25 -0.67 -1.17 -1.42

Rankings of 1 (positive), 0 (neutral), -1 (negative) were given based on general

knowledge of solar thermal systems. To determine the final ranking the comparison ranking (1 to

4) was divided summed for each technology (e.g. BPP ranking = [1/1 + -1/2 + -1/3 + -1/4] = -

0.08). The highest positive number was the best selection. The weighting of 1/n was selected

because cost and maintenance are very important factors (1 and ½) for developing nations.

The roughness of the analysis can quickly be determined because insulated batch heating

and un-insulated batch heating had the same score. The first widely accepted water heating

technology while the USA was developing was batch-water-heating systems suggests that the

ranking system valid (Butti & Perlin, 1980).

What can also be determined from the analysis is that evacuated tubes and flat-plate fully

active solar technologies are not good options for the people of Azacilo, Bolivia. Efforts were

then placed on deciding what (if any) thermal storage option should be selected.

The decision matrix was altered; because adding thermal storage to a system uniformly improves

the thermal performance of a system, +1 was added to performance for all the systems (Table 2).

Table 2 Decision matrix with thermal-storage addition (+1 performance).

BPP BHI BH FPT FPPP FPA ET

Cost (1) 1 0 0 -1 -1 -1 -1

Maintenance (2) -1 1 1 1 0 -1 -1

Performance (3) 0 0 0 1 2 2 2

Durability (4) -1 1 1 1 0 0 -1

Total Ranking 0.25 0.75 0.75 0.08 -0.33 -0.83 -1.08

BPP and FPT change position in the rankings because of thermal storage addition. Using a

plastic or metal tank changes the matrix also. Maintaining a metal tank is easier (bolt -plate over

hole) than a plastic tank (epoxy holes) but will cost more. Both tanks will deform or break under

freezing conditions, although the metal tank is less likely to break (malleable) Tables 3 & 4

compare, using a plastic tank (+1 cost, -1 maintenance, -1 durability) or a metal tank (-1 cost, +1

maintenance, +1 durability).

Table 3 Decision matrix of systems with plastic thermal storage tank (+1 cost, -1 maintenance, -1 durability).

Plastic Tank BPP BHI BH FPT FPPP FPA ET

Cost (1) 2 1 1 0 0 0 0

Maintenance (2) -2 0 0 0 -1 -2 -2

Performance (3) 0 0 0 1 2 2 2

Durability (4) -2 0 0 0 -1 -1 -2

Total Ranking 0.50 1.00 1.00 0.33 -0.08 -0.58 -0.83

Table 4 Decision matrix of systems with metal thermal storage tank (-1 cost, +1 maintenance, +1 durability).

Metal Tank BPP BHI BH FPT FPPP FPA ET

Cost (1) 0 -1 -1 -2 -2 -2 -2

Maintenance (2) 0 2 2 2 1 0 0

Performance (3) 0 0 0 1 2 2 2

Durability (4) 0 2 2 2 1 1 0

Total Ranking 0.00 0.50 0.50 -0.17 -0.58 -1.08 -1.33

Overall using a plastic tank increases the rankings of the systems. For batch heating a metal tank

must be used for the heating element as most thick-plastics degrade in UV light and elevated

temperatures. The thermal performance differences of selected systems will be addressed with

two steady-state equations at near-worst case scenarios (e.g. stagnation (over pressurization) and

freezing conditions) based off La Paz climate data. The performance of tubes will also be

discussed comparing surface temperature and tube maximum rated temperatures.

Thermal performance fail modes and general performance due to climate

Freezing

The thermal performance of a SH is based on the climate in which it is installed (e.g.

freezing the system). The climate data for La Paz, Bolivia was used in lieu of Azacilo because

there is no weather station in Azacilo. La Paz and Azacilo have similar elevations and on average

La Paz should be a few degrees (2-5 °F) warmer because large cities have a heat island affect

(Azacilo is a very small community). Unfortunately, the record low for all months is at or below

freezing (Table 6) which suggests a system should have freeze protection or be drained at night

for most days.

Table 5 La Paz, Bolivia climatic data (Wikipedia, 2012)

Something the record data does not address is amount of extreme weather. Energy Plus Weather

data (TMY3) for La Paz, Bolivia was used to derive how often (and what type of) extreme

weather occurs in Azacilo, Bolivia (Table 7).

Table 6 Monthly Statistics for Extreme Dry Bulb temperatures °C – La Paz, Bolivia (EPW, 2012)

#Days Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Max >= 32

Max <= 0

Min <= 0 1 16 28 31 29 16 6 2

Min <=-18

Any day that the ambient dry bulb temperature ( reaches below 0 freezing of a solar

heating system could occur. The heat loss the collector experiences will be a combination of

conduction and convection ( ) and radiation to the environment

, where is the area of the absorber. is the combined average conduction and convection

loss coefficient (Figure 1 shows the calculation for the cover – the major heat loss surface).

and are temperatures of the absorber fluid and local environment – respectively. is the

emissivity of the collector body exchanging heat with the environment. is Stephen

Boltzmann‟s constant.

Figure 1 Equation for heat loss from the cover of a SH (Equation 5-32 Howell, Bannerot, Vliet, 1982).

Steady-state equations for heat loss are impractical for calculating actual occurrences of

freezing fluid because freezing happens over a period of time and is dependent on the volume of

water. A hard freeze is a very loose definition but “most forecasters will call it a hard freeze

when they expect temperatures at or below 28 degrees F for a minimum of 4 hours” (Yans,

2012). Looking at the TMY3 dry-bulb temperatures for La Paz, Bolivia hard freezes occur in

July, August and September. Many months get close to hard freezes (e.g. May through

September have 4 hrs of sub-zero temperatures). Using „typical‟ data for fail analysis is not

conservative because typical-data is a statistical analysis of 30 years of data. A sustained-cold

weather front in just about any month could cause a hard freeze (all months experience a 5 °C

low).

To estimate freezing failure the heat loss equation was used in combination with the heat

loss required to freeze the solution (heat of fusion). For the analysis the ambient temperature was

set at -1 °C and water fluid temperature of 0 °C. The wattage of energy loss was put into an heat

balance (with time variable t ) for a fluid changing phase , where

is the heat of fusion of water, V is the volume of the water. For the same environmental

conditions, the time to freeze a 50% water/(propylene-glycol-water mix) was determine by the

equation

, where is the specific heat

of the mixture and = -34 °C for a 50/50 (volume) propylene-glycol-water mix.

An un-insulated batch heater and un-insulated plastic pipe energy loss was calculated by

an energy balance at the exposed surface by the equation:

: This equation ignores

air-film resistance but is used as an first approximation of performance (the actual heat loss will

be slightly lower than what is approximated).

Freezing of exposed steel ¾” water pipes has not been observed in Azacilo, Bolivia. The

temperature of the exposed pipes will be recorded by infrared camera this January (2013).

Freezing has happened in batch collectors installed in California in the 1950‟s during an

extremely cold period: this freezing slowed the momentum the batch collector had in California

and a freezing event in a developing nation could have the same negative-social impact for the

technology (Butti & Perlin, 1980).

Stagnation (high pressures because pressure relief value fails)

Stagnation issues are important (pipes could burst) to design the system below the

pressure and temperatures that could arise on high-isolation & hot-temperature days when the

pressure relief valve (PRV) fails. The record high for La Paz, Bolivia (2011) is 86 °F. For a daily

performance, this temperature is unfortunate because the heat loss to the environment is high

compared to warmer climates (large ΔT between the environment and the collector). The

following modified (equation 2-9, Howell, Bannerot, Vliet, 1982) equation was used to estimate

the stagnation pressure, at the maximum solar radiation and temperature, for flat-plate or

insulated-batch collector.

( )

(1)

is the effective transmittance and absorbance of the collector glass, is incident radiation,

is the area of the collector and is the area of the absorber. is the combined conduction and

convection loss coefficient. and are temperatures of the absorber fluid and local

environment – respectively. is the emissivity of the collector body exchanging heat with the

environment. is Stephen Boltzmann‟s constant.

Many assumptions are needed to use (equation 1) for an insulate-batch or flat plate collector in

Azacilo, Bolivia. Firstly, hourly-maximum solar radiation is unknown and must be estimated

from average-hourly data. Solar radiation typically takes on a parabolic shape and thus, the

maximum radiation level is about 3/2‟s the average. The highest air temperatures occur in

Azacilo during the month of April or May but the highest radiation (by > 100 W/m²) happens in

August. August high temperature and solar radiation data were used in stagnation calculations

(equation 1). The tilt of the collector cover is also important to the actual direct radiation

received.

Insolation correction for absorber tilt

Optimizing the angle for La Paz (16.4942° S, 68.1475° W) for August 15th

(noon) the direct

radiation gain due to tilt angle is 3.3% (1-cos(elevation angle – collector angle))*100. The

NOAA ESRL solar position calculator was used to determine the solar angle (NOAA, 2012).

The ROT of adding 10° to latitude for collector angle was used (Howell, Bannerot & Vliet,

1982).

Table 7 Typical Average-Hourly Statistics for Incident Solar Radiation (W/m²) on a 26.5° tilted SH

Table 8 Typical Average-Hourly Statistics for Total Sky Cover – La Paz, Bolivia

Hour/Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1 0 0 0 0 0 0 0 0 0 0 0 0

2 0 0 0 0 0 0 0 0 0 0 0 0

3 0 0 0 0 0 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0 0 0 0

7 12 5 3 2 0 0 0 1 8 36 54 32

8 138 122 98 98 77 57 49 84 168 243 224 186

9 299 317 284 307 295 263 264 328 418 473 398 366

10 435 497 464 502 503 466 482 562 614 667 531 522

11 543 638 604 653 657 615 656 752 756 809 628 635

12 614 692 671 729 746 711 769 857 838 858 679 680

13 629 706 690 737 769 730 802 875 851 835 685 667

14 595 665 659 675 730 672 758 803 775 743 664 603

15 550 597 581 592 638 599 664 695 661 644 602 537

16 462 484 459 457 489 464 503 526 508 498 475 431

17 341 336 309 284 290 279 298 316 321 316 323 294

18 187 194 150 115 73 75 97 115 121 134 150 151

19 43 41 14 4 0 0 2 3 4 6 11 24

20 0 0 0 0 0 0 0 0 0 0 0 0

21 0 0 0 0 0 0 0 0 0 0 0 0

22 0 0 0 0 0 0 0 0 0 0 0 0

23 0 0 0 0 0 0 0 0 0 0 0 0

24 0 0 0 0 0 0 0 0 0 0 0 0

Hour/Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1 84 71 74 42 40 22 13 19 53 55 64 74

2 84 70 75 43 40 21 13 19 53 52 63 73

3 84 70 75 46 40 21 14 19 52 53 64 73

4 83 71 76 49 38 21 16 20 51 54 66 75

5 83 70 77 53 36 20 17 19 50 54 65 74

6 84 72 78 57 38 24 22 21 51 57 70 75

7 83 74 77 59 39 30 26 21 51 56 70 77

8 84 75 75 60 39 32 33 21 47 55 77 78

9 85 75 76 61 39 34 33 22 46 56 77 78

10 86 74 75 60 39 34 32 24 48 56 79 77

11 87 74 73 59 39 34 31 23 49 55 80 78

12 87 79 76 63 42 36 32 30 53 59 82 80

13 88 81 77 68 43 42 35 39 56 65 83 84

14 89 83 79 70 44 45 35 47 62 67 81 85

15 89 84 81 72 44 43 38 49 65 70 81 86

16 88 86 82 73 42 41 39 52 68 70 80 86

17 87 88 84 73 39 37 43 55 69 71 79 87

18 88 86 82 67 38 35 39 50 70 68 77 85

19 88 83 81 60 35 30 33 46 70 67 77 85

20 88 81 79 53 32 27 25 36 69 67 74 82

21 86 79 78 49 32 25 21 31 63 65 70 80

22 84 78 74 44 32 23 16 24 57 61 66 79

23 82 76 72 38 32 21 11 18 57 59 62 76

24 82 75 72 41 34 22 12 20 54 56 62 75

Comparing the data to Topeka, Kansas, the actual watts per hour - meter² hitting the surface of a

SH is higher than would be found in Topeka, Kansas (for the year, 18% more) even though the

cloud cover is 10% (yearly average) higher in La Paz, Bolivia than Topeka, Kansas.

The mountainous region of Bolivia has a higher swing in cloudiness than Topeka. The

standard deviation for La Paz, Bolivia is 22% whereas the standard deviation for Topeka is 10%.

This difference in cloud cover suggests the thermal performance of a SH in Bolivia will vary day

to day much more than in Kansas.

Typical SH setup for hot-water (i.e. shower) heating.

Typical SH designs include hot-water storage. The schematics of most systems can seem

simple (Figure 2) but many components go into a successful installation (Figure 3).

Figure 2 Typical schematic for a flat-plate active solar

heating technology (Howell, Bannerot & Vliet, 1982).

Figure 3 Typical components for flat-plate active solar

heating technology (Howell, Bannerot & Vliet, 1982).

Running an active system in a developing nation would be difficult because the parts may not be

mass produced and cannot be replaced when the part fails. A possible solution is a thermosiphon

(passive) design. Although, to successfully (by developed nation standards) many components

are required.

Figure 4 Typical components of a flat-plate thermosiphon setup (Howell, Bannerot & Vliet, 1982).

The schematic (+system components) of a typical flat-plate thermo-siphon shows

controls, drain down valves, storage tank and a secondary heating element. For developing

nations a secondary heating element, control system and the pressure and temperature relief

value may be hard to find: most of the other parts may not be that difficult to make or find. Only

25 cm is required to make the thermosiphon system work between the bottom of the tank and top

of the collector (Figure 4). The operation of the thermosiphon system could be improved by

controls or a very watchful eye.

Solar Water Heating Controls

To increase performance and guard against failure modes, controls are required for most

solar heating designs.

Figure 5 Typical control system for SH (Howell, Bannerot & Vliet, 1982).

The controls drain the system when freezing condition are present (Figure 5). At stagnation

temperatures the controller opens solenoids to drain he hot water. The controller increases

efficiency by allowing a base-temperature to be reached in the collector before turning the pump

on (e.g. cold water will not be circulated through the thermal-storage tank).

Sizing Thermal Storage

The effect of over or under sizing the thermal storage for a SH will effect the

performance of the system as a whole and the temperatures reached in the storage tank. The

overall performance is imporant to harness the most energy possible and the temperature reached

in the tank is imporant for pathogen reproduction. If you double the storage size the temperature

of the tank is reduced: if the collector area is double the temperature of the tank will increase and

the efficiency will go down (Figure 6).

Figure 6 Storage size compared to storage temperature (Howell, Bannerot & Vliet, 1982).

Adding any size thermal storage to a design for Azacilo, Boliva will increase the complexity of

the system but will allow for better performance and freeze protection.

Storage Medium Selection

If thermal storage is required selecting the medium to have anti-freeze and high thermal storage

per volume will decrease the likelihood of failure and size of the storage tank. Figure 7 lists the

melting point and heat of fusion for common materials used for thermal storage.

Figure 7 Latent heat of storage for common materials used in SHs (Howell, Bannerot & Vliet, 1982).

In general, water has great thermal properties (high heat of fusion, high thermal conductivity and

high specific heat). It is hard to reach boiling temperatures in most solar thermal devices and the

thermal storage property of changing phases (vertical lines on Figure 8) are not available to the

solar thermal system.

Figure 8 Thermal storage of material per weight and by temperature. Vertical lines are controlled by the equation Q = H

(ΔT) and the slanted lines by Q = Cp (ΔT) where H is heat of fusion (solidification) and Cp is specific heat. (bee’s wax

approximation hand drawn – not fit exactly) (Howell, Bannerot & Vliet, 1982).

Although the properties of phase change materials is better for shower designs (specifically bee‟s

wax melts around 140 °F a great set-point for hot water) water is likely the best medium because

it is readily available - amorphous wax (melting point 166 °F) may be an interesting alternative

to water for developed nations.

Sizing designs by rule of thumb and other approximations

The rules of thumb indicated in the figure x is assuming a insulated thermal storage tank inside a

building – this may not be the case in Azacilo, Boliva. Also, domestic water heating systems

include many hot-water uses besides showers. In Azacilo there are 30 families that include about

four people per family.

Figure 9 Rule of thumbs for sizing SHs (Howell, Bannerot & Vliet, 1982).

Using this chart directly, the storage size would be about 1600 gallons and a collector

size of 1400 ft². The shower facility will likely be 300 ft². This would indicate a 4-5 factor under

sizing if all of the roof was used. The rules of thumb for developed nations domestic-water

heating is likely to high for developing nations: in general, people the USA use twenty times

water in the home than those in Bolivia (Clarke and King, 2004). Thus, the metric for amount

and quality (in this case temperature) required for the people of Azacilo may be covered by 300

ft² of collector and 500 gallons of thermal storage. Also, they may take cold showers without

issue.

Results

Decision Matrix Results

The last information entered into the decision matrix is to store the plastic tank inside a

structure out outside. Storing the tank inside added +1 to the thermal performance.

Table 9 Decision matrix of systems with plastic thermal storage tank (+1 performance, +1 cost, -1 maintenance, -1

durability).

Plastic Tank

(Inside)

BPP BHI BH FPT FPPP FPA ET

Cost (1) 2 1 1 0 0 0 0

Maintenance (2) -2 0 0 0 -1 -2 -2

Performance (3) 1 1 1 2 3 3 3

Durability (4) -2 0 0 0 -1 -1 -2

Total Ranking 0.83 1.33 1.33 0.67 0.25 -0.25 -0.50

The first-cut decision matrixes suggests insulated or un-insulated batch heating system should be

used in tandem with a plastic storage tank, with the tank is placed inside a building. What the

first-cut matrixes did not determine is the total, cost difference, thermal performance and

feasibility of a newly designed system for the people of Azacilo, Boliva based on operational

variables (e.g. draining the system daily). The report cannot (at this time) analyze the cost of

systems because the materials will be priced this January.

The time to freeze is reported in the following Table 6. Time to freeze in pipe is a gross

approximation (1/10th

a gallon) because actual pipe length, diameter and wind speed is needed to

estimate energy loss from an expose plastic pipe. In practice, pipes should be insulated with UV-

resistant insulation when possible. All energy losses for freeze issues were calculated for a -1 °C

ambient condition.

Freezing times for selected solar heaters Table 10 Time for fluids used in SH to freeze under -1 °C ambient conditions.

Collector Eloss Volume

Time water to freeze

Time 50%-50% mix to freeze

Type kJ/s gallons hours hours

In pipe 0.006 0.1 6 113

Flat Plate 0.015 1 23 484

Ins. Batch 0.018 50 1039 20717

Batch 0.042 50 374 7317

Sensitivity analysis was also run for an un-insulated batch collector and un-insulated pipe at

ambient temperatures below -1 °C for water because temperate below -1 °C are likely

experienced in Azacilo, Bolivia (Table 9).

Table 11 Time for fluids to freeze under -1,-5 and -10 °C ambient conditions by fluid type.

Eloss Ambient

Temperature Time water

to freeze Time 50%-50% mix

to freeze

Watts °C hours hours

Un-insulated Batch 42.3 -1 374 7317

Un-insulated Batch 211.4 -5 75 1463

Un-insulated Batch 422.8 -10 37 732

Un-insulated Pipe 5.6 -1 5.7 113

Un-insulated Pipe 28.0 -5 1.1 23

Un-insulated Pipe 55.9 -10 0.6 11

It is unlikely for an un-insulated batch collector to completely-freeze in Azacilo, Bolivia by these

calculations but portions may ice over.

Stagnation pressures for various designs and covers

Buying tempered glass (hail protection) may not be feasible in developing nations so

translucent fiberglass may be substituted for glass. The properties used to calculate stagnation

pressures are listed in the following table.

Table 12 Batch and flat-plate collector stagnation pressures for glass and fiberglass covers.

Detailed sizing example for selected solar-water-heating technology

Black-plastic-pipe (BPP) rolls on roof

The equation C-6 in Figure 10 was used to calculate heat loss and gain (-negative values

in table) for design, conditions and surface temperatures were assumed. To get a real feel of

surface temperatures pipes experience an infrared camera should be used.

Cover Collector Pstag Tstag Ū α τ Fr ατ EFF Ac Ae ɛ (long wave) σ Ta

Material Type atm Range* °C W/m²-K m² m² W m−2 K−4 K

Flat Plate 3 to 4 162 1.58 96% 90% 91% 95% 2.8 2.6 93% 5.67E-08 345

Ins. Batch 5 to 6 171 2.0 96% 90% 91% 95% 3.5 2.8 93% 5.67E-08 345

Flat Plate 5 to 6 173 1.58 96% 75% 91% 79% 2.8 2.6 75% 5.67E-08 345

Ins. Batch 9 to 10 182 2.0 96% 75% 91% 79% 3.5 2.8 75% 5.67E-08 345

*Pressures vary between a full water mixture (higher pressure) to a 50% proplyene gycol mix (lower pressure)

Fiberglass

Glass

Figure 10 Conduction and convection equations for tubes used in SHs (Howell, Bannerot & Vliet, 1982).

Condition 1 is heating condition where the maximum temperature of vinyl is reached

(175 °F) and the internal temperature is high enough to stop Legionella reproduction (120 °F)

(Table 13). At this condition very little heat is being transfer for a pipe length of 50 feet (about 7

watts into the system). This suggests a more heat resistant plastic should be used (e.g. PEX, 200

°F melting point at about 5 atm) (Viega, 2012).

Table 13 Heat loss from plastic pipe (3/4”) based on equation C-6 (Howell, Bannerot & Vliet, 1982).

neg. = heat in inside outside inside outside conductivity Length

Q r1 r2 T1 T2 K L

Conditions Watts m m K K W/m K m

max vinyl pipe temp. to Legionella pasteurization

-7.2 0.01 0.01 322 353 0.35 50

freezing to ambient hard freeze temp.

0.5 0.01 0.01 273 271 0.35 50

Condition 2 is when a hard freeze (28 °F ambient) is the outer surface temperature and the inner

temperature is the water freezing point (32 °F). The result of this calculation calls into question

the assumption made in the freezing failure mode calculated earlier in this report. A heat loss of

5.6 watts was assumed for pipes earlier in the report where these calculations are showing 0.5

watts (this is an order of magnitude difference). A solution to checking this discrepancy will to

take black plastic pipe to Azacilo and fill it with water to see if it will freeze. A second method

would be to take surface temperatures of black pipes filled with water at KU to determine the

weather parameters that cause freezing. Wind could drive the surface temperature of the pipe

below ambient conditions this affect is called wind-chill.

Estimating the cost of a solar hot-water system for developing nations

Materials costs for a flat-plate collector

The costs for the materials are estimated by using prices for Lowes and Home Depot.

Actual prices for materials will be recorded in the EWB winter trip to Azacilo. Hopefully a

general rule of thumb for cost differences between USA home improvement stores (easily found

by students) and El Alto, Bolivia (where construction materials are readily sold for the region)

can be calculated by these two sets of data (Table 13).

Table 14 Costs for materials from Home Depot or Lowes (Kansas) for one (home-constructed) solar panel.

Item Cost/unit units Total Cost

Type of Item Desciption $/# # $

Pipe steel pipe 1/2"d by 10' 10.62 10 106.20$

nipple 1"d x 3" 1.63 18 29.34$

Tee 1 " 3.54 20 70.80$

Elbow 90° 1" 3.32 2 6.64$

Reducer 1" to 3/4" 2.24 20 44.80$

Reducer 3/4" to 1/2" 5.24 20 104.80$

Corrugated Cover Materials

Translucent White Fiberglass Panel 25.39 3 76.17$

Side Wall Materials

2 in. Steel C-Channel 1/8" thick by 36" long 14.96 5 74.80$

Back Wall Materials

3/4" Painted Pine Plywood 36.97 1 36.97$

Corrucated Steel Roof Panel 12.98 3 38.94$

Insulation Materials

1" extruded polystyrene 4' x 8' 13.35 2 26.70$

Heat absorber

Roll flashing 20" x 12' 36.1 2 72.20$

Black Paint Rust-Oleum 10.03 2 20.06$

Misc Fasterners

Galvanized Screws, Solder, Spray Foam, ect. 200 1 200.00$

Total 908$

20% incidentals 1,090$

* May not be able to get in Bolivia

Conclusions

Qualitative The results of the equations presented in this document are first order approximations and

the final answers are used as comparisons – not absolute.

Insulated batch water heating is likely the best design for Azacilo, Bolivia.

Stagnation pressures reached in solar heating devices are multiples of standard

atmospheric conditions and bursting may be an issue for designs in Azacilo, Bolivia.

The climate of Azacilo, Bolivia is much different than what is experienced in Lawrence,

KS. Further research is needed or experts contacted about the performance of solar

heating technologies in cloudy-mountainous regions

Specific Water is the best thermal storage medium for showers in developing nations.

Vinyl shouldn‟t be used in solar water heaters because of low pressure and temperature

tolerances.

Freezing is an issue - drain down or anti-freeze (e.g. propylene-glycol-water mix)

methods should be used.

Temperatures of black pipe should be taken while in Azacilo to determine potential heat

gain (expected performance) and loss (freezing).

The cost of a making a “home made” flat plate collector in the mid-west is about $1,100

per collector and should be compared with costs in Bolivia.

Discussion

The social concerns of implementing a project in Azacilo, Bolivia include security, community

buy-in and shower facility management and many more. The advantages and disadvantages of

the systems should be discussed with the community and community leaders.

References

Answers, Y. (2012, December). What is a hard freeze?. Retrieved from

http://answers.yahoo.com/question/index?qid=20110107194750AAay4OL

DOW Corners. (2012, December). Properties of propoleyene glycol mixes. Retrieved from

http://msdssearch.dow.com/PublishedLiteratureDOWCOM/dh_0040/0901b80380040bcb

.pdf?filepath=heattrans/pdfs/noreg/180-01314.pdf&fromPage=GetDoc

Energy Plus Weather. (2012, December). La paz, bolivia weather (modified TMY3). Retrieved

from

http://apps1.eere.energy.gov/buildings/energyplus/cfm/weather_data3.cfm/region=3_sout

h_america_wmo_region_3/country=BOL/cname=Bolivia?print

Engineering Toolbox. (2012, December). Latent heat of melting and solidification. Retrieved

from http://www.engineeringtoolbox.com/latent-heat-melting-solids-d_96.html

Engineering Toolbox. (2012, December). Thermal conductivity of selected materials. Retrieved

from http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html

ESRL NOAA (2012, December). Solar angle calculator. Retrieved from

http://www.esrl.noaa.gov/gmd/grad/solcalc/azel.html

Viega. (2012, December). PEX plus specifications. Retrieved from

http://www.viega.net/xchg/en-us/hs.xsl/5876.htm

Wikipedia. (2012, December). La Paz, Bolivia. Retrieved from

http://en.wikipedia.org/wiki/La_Paz

Appendix: Sketches of a possible SH devices for Azacilo, Bolivia

Figure 15 Sketch of a thermosiphon flat plate collector SHT with thermal storage - can become active with pump and controls.

Figure 16 Sketch of gravity fed black-plastic-tube and required components for drain down (non-freezing) system.

Figure 17 Sketch of an insulated (gravity fed) batch heating system.

Figure 118 Sketch of construction details for "home made" flat-plate collector.

Figure 19 Thermosiphon system with insulated tank inside residence.

Figure 20 Sketch of gravity fed black pipe and insulated batch heater (bottom)