Scambiatore Interno_calcolo

8/2/2019 Scambiatore Interno_calcolo

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Dr. Chris Bull: Advisor and MentorAlex Surasky-Ysasi: GISP Leader

Melissa LoureiroAmalia Telbis

Suza GilbertZachary Auger

Stephanie AngioneAdrienne Buelle

Emily Kunen

May 3, 2006


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1. Introduction and Problem Description

Many Central Asian countries would benefit from solar thermal collectors for water and space heating.High quality manufactured collectors are not available there. However, basic materials such as wood,

horsehair, sheet metal, glass, and black paint are.

A solar collector is a passive or active device which takes in solar radiation to heat a transfer medium,

such as copper, that in turn gives heat energy to an open space or water basin. With the division of

passive and active systems, there are also different solar systems that can incorporate these solar

collecting devices. Having such a variety of systems to choose from, this paper reviews all of the systems

and chooses the best setup for heating water in a cheap fashion.

The essence of these designs is to lower the cost of a typical solar water system, by using materials and

techniques that are regional to the people of Central Asia. The solar collector system must also beeffective and durable. Because of the numerous variables in these designs, there are several

assumptions that had to be made within the constraints given. One of the first assumptions that had to be

made for this project was the location for the solar collector system. Tajikistan was chosen to be the area

of interest, with a location of 37N longitude and 70E latitude. Modeling for the Tajikistan region will

allow for this system to be used in several other countries with the same climate and terrain. Many

civilizations of Central Asia do not have access to electricity, and if they do have any access, electricity is

very expensive. This being the case, it is thought that having hot water for cooking and bathing is an

extremely important issue to conquer before any type of civilization can be improved.

1.1 AssumptionsThe amount of water that is consumed per person per day is approximately 25L. In a typical Tajikistan

family, we have assumed that there are 7 people.1

The optimal temperature for water use for cooking

and hygiene has been taken as approximately 60C. Both designs, which are described below, use these

numbers for the calculations of each solar collecting system. In Tajikistan, approximately 95% of rural

communities have electricity. This electricity can alleviate some of the problems transporting the water to

the homes in the villages. This paper focuses on the solar collecting system and we have assumed that

the people somehow have the water connected to this system.

These systems have been modified for the worse case of all of the researched data. For example, all

calculations have been done using the values for the hours and power of sunlight for the month of

December, which is the coldest month of the year. We have assumed that if the collector works during

this time, then it will only work that much better in the warmer months.

1 Tajik embassy


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2. Background

2.1 Location, Geography and Climate

Figure 1: Map of Central Asia Featuring Major Cities in Afghanistan and Tajikistan

2.1.1 Afghanistan

Afghanistan is located in Central Asia, on the Iranian plateau at a longitude of 3300N and a latitude of

6500E. It is a mountainous country, including the Hindu Kush mountain range in the south-western area

of the country. The country is bordered by Waziristan, Pakistan, Tajikistan, Turkmenistan, Uzbekistan and

China.

The Hindu Kush are the most rugged mountains of the region and the north and southwest areas are

mostly agricultural plains with sandy deserts in the south. The area can be divided into three distinct

regions; the Central Highlands, the Southern Plateau and the Northern Plains.

The Central Highlands consist of an area of 16,000 square miles and have deep narrow valleys and high

mountains, including the Khyber Pass. This area has a relatively dry climate with cold winters and warm

summers. The Southern Plateau is a region that consists of high plateaus and sandy deserts with severalrivers passing through. The elevation is about 3,000 ft. and the area is prone to sand storms and a dry

climate. The Northern Plains are fertile foothills which are supplied by the Amu River. This area is an

agricultural center and is rich in minerals and natural gas.

The climate of Afghanistan varies greatly depending on which area of the country is being considered.

The highlands of Afghanistan are similar to the climate of the lower Himalaya and the range of average

temperature from 50-60 F. The average temperatures vary greatly between the minimum temperatures

in the north during cold weather to the hottest temperatures in the southwest. Waves of intense cold


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occur and sometimes temperatures drop below zero. In areas like Kabul, snow remains in the area for 2

to 3 months and people remain inside to keep warm and endure the rigorous winter.

In warmer areas of the country the climate is more like that of India, with an intense summer heat. The hot

season is frequented by dust storms and strong winds. Low land areas like Heart have a more temperate

climate, but are still affected by the monsoon season typical of India, during the winter months. In general

the climate is relatively dry with months of sunshine in the summer. The great variation because of

elevation and summer and winter cause great shifts in temperature and weather.

The lifestyles and housing in Afghanistan needed to be studied in order to understand how a solar

collector would be most helpful in their everyday lives. Each village consists of around three hundred

families and each family has approximately seven children. The life expectancy of both men and women

is around 43 years. Around 85% of the water is used for agriculture. Less than 20% of the population has

access to piped water, and only 4% of the population has electricity.

The houses in Afghanistan are built using local materials such as stone, wood, plaster, straw and brick.

The houses are built using a terraced architecture so that the roof of one house is used as a yard for

another which is built on top. Coniferous wood is used to make posts and beams for constructing the

houses. The houses are commonly two stories. The upper level is used for cooking, eating and living,

while the lower level is used for storage and livestock.

2.1.2 Tajikistan

Tajikistan is another Central Asian country, located between Kyrgyzstan, Uzbekistan, China and north of

Afghanistan. 93 % of the country is covered in mountains, including the Pamir and Alay ranges which

have glacier fed streams and rivers which are used for irrigation. The Tian Shan Mountains in northern

Tajikistan separate the populous areas in the lowlands of the south and north.

More than half of Tajikistan is above an elevation of 3,000 meters and the lowlands of the Fergana Valley

are significantly above sea-level. The highest elevations of the range are on the Kyrgyzstan border and

the Fergana Valley is the most densely populated region in Central Asia which spreads across Tajikistan

from Uzbekistan to Kyrgyzstan. Tajikistan has dense river network including the Syrdariva and the

Zarafshon, which stretches across the Valley. Other lakes and rivers are glacier fed and reach high levels

during the spring due to the rainy season and in the summer.

The climate of the region ranges from continental, subtropical and semi-arid, with some desert areas. LikeAfghanistan, the climate changes greatly with increasing elevation. The lowlands are not subject to the

Artic air that influences the mountainous regions, but the temperatures still drop below freezing for more

than 100 days a year. In the lowlands, the climate is arid with average temperatures ranging from 23 to

30 in July and -1 to 3 in January. The Eastern mountainous regions have colder temperatures, with 5

to 10 C in July and -15 to -20 C in January. Precipitation averages are from 700 to 1600 mm and theheaviest precipitation in near the Fedchenko Glacier, and lightest in the Pamirs. The winter and spring are

generally the rainy and snowy seasons.


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Similarly to in Afghanistan, the Tajikistan lifestyle needed to be researched. In Tajikistan two thirds of the

population lives in rural areas and most families have around six children. The life expectancy in

Tajikistan is longer than that of Afghanistan and most men live close to 67 years. The majority of natural

water systems within the country are infected with either chemicals, bacteria or both. In the rural areas

only 20% of the water is clean while in urban areas 90% of the water is clean. In contrast to Afghanistan,

95% of the rural areas in Tajikistan have electricity.

The housing styles in Tajikistan vary depending on the location. In urban areas housing consists of

apartments, while in flat areas houses are one story with flat roofs and covered courtyards. In the

mountainous regions, the houses are built directly into the mountains. These houses have low ceilings,

small rooms and openings as well as a fireplace in a central room which is used for heat and cooking.

More than one family often lives in this type of mountainous houses.

Just as in Afghanistan, Tajikistani houses are built from local materials consisting of raw bricks, plasterand cut straw which is layered horizontally. Wood is used as beams for roofs when available but the

material is becoming increasingly harder to find in the region. When wood beams are not available,

cement is often used for roofing. The average ground area of a mountainous house is 52.1 m2.

2.2 MaterialsMaterials that were used in this paper are generally chosen to be low cost and readily available materials.

Horsehair and sheep wool are considered to be regional materials that can be attained for a free or a very

low cost. There are approximately 0.3 million horses and 12.5 million sheep in the region of Tajikistan.

Another type of insulation is called bousillages, which is a mixture of moss and clay. The outer layer of

the bousillages is formed by a mixture of horsehair, water and clay, which gives the bousillages a finerand smoother finish. Thermal properties for these materials are not available, but the materials have

proven to be effective in the past. Houses have been using insulation using horsehair and sheep wool for

over 200 years, thus we can assume the durability of our solar collector.

2.2.1 Black Paint

The absorber needs to have a darkened surface to help it collect the incoming energy. Black paint is

utilized in these designs since it can withstand high temperatures. The spectral properties of the semi-

selective black painted surface are: absorptivity = a = 94% and emissivity = e = 28 %. Any coating that is

on a surface can be either selective or non-selective. These terms generally describe the coating applied

on a metal absorbing surface. Black paint is a type of non-selective coating; generally matt black paint is

used for solar collectors. These surfaces are good absorbers of radiation, absorbing 90-95 % of all solar

radiation. These surfaces are also strong emitters of thermal radiation, radiating back about 90% of the

theoretical maximum heat energy for a given temperature, thus a glazing surface must cover the copper

tubing. Since glass is readily available in both Tajikistan and Afghanistan it has been chosen to reduce

the amount of radiation from the copper tubing.

2.2.2 Wood

Another regional material that can be used for construction in our solar collector system is wood. Simple

construction techniques for wood can be performed using hand tools and are easy to learn. Wood kept


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constantly dry does not decay over long periods of time. In addition, if wood is kept continuously

submerged in water, it does not decay significantly by the common decay fungi regardless of the wood

species or the presence of sapwood. Bacteria and certain soft-rot fungi can attack submerged wood, but

the resulting deterioration is very slow. A large proportion of wood in use is kept so dry at all times that it

lasts indefinitely. Moisture and temperature, which vary greatly with local conditions, are the principal

factors that affect rate of decay. Wood deteriorates more rapidly in warm, humid areas than in cool or dry

areas. High altitudes, as a rule, are less favorable to decay than are low altitudes because the average

temperatures at higher altitudes are lower and the growing season for fungi, which cause decay, is

shorter. To alleviate mild decay, wood can be preserved by soaking in specialized solutions after cutting

and boring operations are complete.

2.2.3 Metals

Copper and aluminum are the most commonly used metals since they exhibit higher thermal

conductivities than other metals (See Appendix 6). Aluminum is sometimes preferred over copperbecause it's lighter (about 1/3 lighter than copper) and its heat capacity is 870 [J/kg*K] versus copper's

385 [J/kg*K], which means that once it heats up it stays hotter for a longer period of time. However,

copper exhibits a larger thermal conductivity (401 [W/m*K] compared to 250 [W/m*K] that aluminum

exhibits) and it is also easier to solder copper. Aluminum soldering differs from other common metals in

several ways: it needs special techniques to achieve flow into the joints, the use of reaction fluxes is

mandatory and the solder composition is more important with aluminum than with many other metals

because galvanic corrosion can cause catastrophic failure. On the other hand, nearly all solders and

fluxes can be used with copper and hence even unskilled workers can easily learn how to work with it.

Steel has been chosen for certain foundation components of the solar collecting system. The tensile

strength has proven to be quite high, making it a very strong material. This metal has been chosen over

other metals since the cost is much lower.

2.3 Types of Solar Collectors and Selection for this ProjectThere are many types of solar water heating systems that were considered for design in this project.

These systems can be divided into the categories of active and passive systems. An active system

requires a pump to circulate fluid and therefore an energy input as well. A passive system circulates the

fluid via natural forces such as gravity or thermosyphoning. Another categorical division is open versus

closed loop systems. An open loop system has only one circulating fluid, which is directly heated by the

collector and then output for use. A closed loop system has two liquids; one is circulates through the

collector, where it is heated, and the heat exchanger where it transfers that heat to the working liquid.

There are four basic designs that were considered which are representative of each category. Given that

there were to be two models created, two different types of solar water heater systems were selected for

modeling, in order to derive a comparison.

2.3.1 Selecting Which Solar Collector to Model

The first system that was not selected was an open-loop active system. In this system a pump circulates

fluid through a collector plateit is directly heated and then used. This system was not seriously

considered because the only freeze-protection option is a drain down system, which is not effective in

cold climates. This type of freeze-protection depends on valves being activated at freezing temperatures,


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so as to drain the system.2 The second system ruled out is a batch heater system, which is a passive

open loop system. In this system water sits in a large tank and heats over the course of the day. This

system is the least efficient and not reliable in areas that experience long term cold temperatures.

The remaining two systems were selected for modeling and the manner in which they function will be

discussed later in more detail. The first system is the drainback system. It is an active, closed-loop

system, which drains the water from the pipes into a reservoir tank to protect against freezing. When the

system is on, the pump circulates a heat transfer fluid through the collector and to a heat exchanger,

where the working water is heated by the heat transfer fluid. The second system is a closed-loop

thermosyphon system in which the heating liquid circulates through the decrease in density as its

temperature increases. This working fluid transfers its heat to water in a heat exchanger sitting above the

collector plate.

2.4 Testing and ModelingSo what does testing and modeling really entail? Unlike the other background research groups, ours was

not completely implemented the other groups, this can not be completely answered because the model

was never tested or built for that matter. Even so, the testing of the design can either be through

simulation and then through physical tests or vice-versa. This will be addressed in detail in the following

paragraphs.

In modeling a collector, a sequence of tasks needs to be performed. First of all, the variables and

constants must be determined to decide which equations are appropriate. Next, with the aide of Matlab or

Excel, the variables need to be calculated. From there, dimensions of the collector are determined. Free-sketches, CAD drawings, SolidWorks, or ProE provide visual aide to what the design looks like. Finally

simulations are done or the design is tested experimentally.

2http://www.thermotechs.com/Drain%20Down.htm


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2.4.1 F-Chart

Since time is an issue and annual testing is not what our schedule allows, a simulation is the best

alternative. The simulation program researched was the F-Chart. The F-Chart takes in many variables,

see Figure 2 for a typical window of variables used in this method.

Figure 2: Screenshot of F-Chart Simulation Program

Once the calculations of the collector are found ie the flow rate, the heat transfer coefficient, the collector

and solar tank area, etc, the F-Chart can be used. Once all these variables are put into this program, F.

the annual heating load can be found. The following equations are used to determine F. X represents the

collector loss and Y represents collector gain.

After plugging in for the above variables, f. the monthly fraction heating load, can be found by the

following equation.

The next step is to find F. The fraction Fis the sum of the monthly solar energy contributions divided by

the annual load.


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F determines the percentage of the total energy used over the year to heat domestic water.

The F-Chart is a practical way to test our model without having to perform yearly experiments. It is known

to be only 2.5 percent off from monitored results. The only disadvantage to this approach is that it under-

predicts thermal performance in mountainous regions. Still, this is more desirable than over-prediction.

Overall, testing the design through simulation is by far the superior way to get data in a clear cut manner.

Below are some classic examples of graphs done by the F-Chart Method.

Figure 3: Graphs Depicting F-Chart Method


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3. Design and Modeling of Closed Loop Thermosyphon System

3.1 Thermosyphon FunctionalityA thermosyphon system is a passive solar water heater in which the flow of the working fluid is circulated

by natural convection. As the working fluid in the solar collector heats, it becomes less dense and rises

naturally into the tank above. Meanwhile, the cooler working fluid flows down the pipes to the bottom of

the collector with help from gravity, enhancing the circulation. Having a system that is self regulating

eliminates the need for a pump and this is advantageous since thermosyphons can be used in countries

where access to electricity is limited3.

3.2 Design considerations:In order to achieve a low cost, yet effective solar collector certain assumptions and decisions had to be

made while choosing the components that make up the thermosyphon. The thermosyphon consists of a

solar collector plate attached to the tubing that contains the working fluid. This working fluid is usually the

water that needs to be heated and thus and open loop system is implemented if it is to be used in mild

climate areas. However, if freeze protection is needed the thermosyphon can use an antifreeze solution

as its working fluid. In this case, the system is closed loop, so the working fluid passes through a heat

exchanger in the storage tank (which is placed above the solar collector plate in order to achieve flow) to

heat the actual water. In the following section these components are described in more detail as well as

the decision making process for materials and design.

3.3 Solar Collector PlateThe design process for the solar collector plate was centered around three important factors: maximum

efficiency, minimum cost and ease of construction and maintaince. From the available types of designs

3 In Afghanistan only 4% of the population has electricity in their homes


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of solar collector plates the flat plate collector seems to meet these two specifications. A collector plate

can vary in many ways and in the following sections explain the exact nature of this systems plate and

design decisions made with regard to it.

3.3.1 The Absorber Plate

The absorber plate is the means by which energy from the sun can be used for domestic use. Collectors

that are employed in water heating usually use metal absorber plates, due to metals excellent thermal

conductivity and its ability to withstand high temperatures. For the above considerations, the absorber

plate for this design is made from copper sheet, due to its high thermal conductivity and ease of

implementation.

The absorber needs to have a darkened surface to help it collect the incoming energy. Black paint was

used in this design since it can both withstand high temperatures; it has high absoptance levels (94%)

and is readily available in the countries of interest.

3.3.2 GlazingIn order to minimize the losses due to convection at the top of the absorber, glazing was added to the

design. Since glass is an available resource in both Afghanistan and Tajikistan, the glazing will be glass

and not plastic film. Since working with large pieces of glass can be challenging, it is necessary to size

the collector according to standardized sizes of glazing in order to heat the necessary amount of water.

Thus, the collector was sized according to standard area according to the available glass sheet (the area

of one panel for this design is 1.85m2).The glass needs to be tempered in order to withstand possible

environmental hazards that may cause the glass to break. In addition, it is important for the glazing to

have a high transmittance factor, which is determined by the iron content of the glass. The glass that was

chosen for this design is 1/8 inch thick and has an iron content of 0.01% and a 91% transmittance. Single

versus double glazing was considered, but after taking cost into account, the increase in prices compared

to the slight efficiency increase (see Appendix 3) for double glazing [1] made single glazing a better

option. Since the cost of low iron content glass is fairly expensive respective to other aspects of the

design, the prices of the glass were heavily considered when making decisions regarding glazing.

Essentially, lower iron content glass and double glazing would produce the most efficient system; it is not

cost effective enough to justify a relatively small increase in efficiency.

3.3.3 Tubing and flow pattern

In order to achieve the goal of heating water, the energy absorbed by the plate must be conducted to a

liquid flowing through the collector plate. Thus, the absorber plate is soldered onto the flow tubes, which

contain an antifreeze mixture of ethanol and water. This design usescopper flow tubes in the absorberplate, due to their high thermal conductivity and superior corrosion resistance. Attaching copper flow

tubes to a copper absorber plate ensures that soldering will result in bonds with good mechanical and

thermal properties. In general, the tubes can be oriented in a parallel or a series flow pattern, and a

choice based on feasibility and efficiency must be made. Thus, due to construction and maintenance

considerations the best flow pattern was determined to be a parallel pattern (see Figure 4).


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Figure 4: Parallel Flow Pattern

This pattern was chosen mostly due to its ease of construction; specifically the connections only require is

T couplers and couplers with center stop. In addition, there was additional concern in choosing a series

flow pattern with a thermosyphon, in that a series orientation may not produce appropriate flow for the

system to function properly.

The design was modeled employing header and footer tubes with a 1.5 inch outer diameter and parallel

tubes of a .5 inch copper piping. These tubes will be supported by inch wooden blocks. In addition, 3

inches of clearance will be left between the sides of the box and the header and the footer pipes. The

array of the parallel pipes is free floating and is going to be supported by risers (wood blocks 1 inch x 1

inch x 4 inches) placed every 10 inch along these pipes.

The efficiency of the plate depends on the surface area of the working fluid in contact with the plate, the

distance between the tubes, and the thickness of the copper sheet. This efficiency also depends on the

losses due to convection that occur at the top of the absorber. The efficiency increases with the increase

in surface area of the working fluid in contact with the absorber plate. This area can be increased by

having the absorber plate consists of fins soldered together that were bent around the vertical parallel

tubes as discussed later in the construction section.

In addition to glazing, the tube spacing and sheet thickness for the collector plate is a major factor when

determining the efficiency of the plate. The tube spacing and the copper sheet thickness were determined

by comparing the efficiencies based on the following graph:


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Figure 5: Plate Efficiency Factor [1]

To maximize efficiency a copper sheet of 0.02inch thickness was chose with a tube spacing of 4 inch

center to center.

It should be noted, that although these decisions were made to make proper and effective use of

available materials to maximize the output of the collector plate, these sizing considerations can be

changed due to different circumstances, as well as to improve efficiency. In order to model the

effectiveness and behavior of a solar water heater, these decisions were made based on available

literature as well as cost considerations.

3.3.4 Housing and Insulation

The main purposes of the collector housing is to provide protection from the outside elements and to

minimize loss from the absorber plate. The housing must be solid enough to support the glazing system,

thus the frame of the housing will be made of locally available wood. The wood block risers are separated

by the insulation materials by a 0.375 inch plywood layer. Between the tubing and the plywood layer the

insulation is achieved by a 1 inch layer of dead air. To prevent heat loss through the back of the collector

a layer of locally constructed boussilage will be used. This mixture consists of a mix of clay, water, straw

and horsehair and was found to be a local housing material in the region. The thermal conductivity

coefficient was computed as a weighted average, and found to be 0.1381. This layer of insulations was

modeled using local materials, and can thus be changed according to the availability. Specifically, sheep

wool is a locally available material, and can be used to decrease the loss from the collector since its

thermal conductivity is almost 4 times smaller than that of the boussilage.

To prevent losses due to convection out the back of the housing, the collector plate should be placed at

an angle equal to the latitude of the location. To achieve this, the collector will be mounted on a stand

which is 1 m high with a wall containing 2 layers of brick enclosing dead air.


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Other design and construction considerations for the solar collector:

In order to prevent back-flow during the night a one-way valve needs to be placed along the tubes

that connect the storage tank and the solar collector;

During the summer the antifreeze might achieve boiling temperatures in which case a pressure

release valve needs to be implemented in the design to make sure that the antifreeze doesnt

burst the pipes.

When installing the glazing 1/4 inch of frame should support the glass on all sides leaving 3/8

inches to hold the glass at the edge. Also, 1/8 inch is left on all sides of the glass for expansion

and contraction of the glass and box and one inch clearance is left between the glass and the

absorber plate

When painting the absorber plate with black paint multiple layers are better than one thick layer.

After the collector is build it must be baked in the sun to dry out any moisture in the box and to

cure the paint; if the moisture is not removed from the box, condensation will occur on the glassand the efficiency will decrease.

3.4 Working FluidSince freeze protection must be implemented in the thermosyphon, the working fluid needs to be an

antifreeze solution. Most solar collectors use an ethylene-glycol mixture as antifreeze. However, this

solution is very toxic, expensive and needs to be replaced every 2-3 years which makes maintenance

troublesome. To eliminate the toxicity element from this design three non-toxic different were analyzed.

These included propylene glycol, potassium formate and ethanol (see Appendix 2). The antifreeze

solution needs to provide low freezing points and high boiling points as well as achieving cost efficiency

and maintenance. Of the three options, the propylene-glycol and the potassium formate showed very lowfreezing point (up to -50 oC) and high boiling points (148.8 oC), but are expensive (~20$/gallon). Pure

ethanol is rather cheap ~2.5$/gallon exhibits very low boiling temperatures (78.5oC). To implement an

ethanol antifreeze system, it can be mixed with water to increase the boiling point. By analyzing the

weather extremes in Central Asia, a 40.5% ethanol-water mixture is within the needed limits. The boiling

point for 40.5% mixture is 84oC and the freezing point is -24oC (detailed calculations of these parameters

together with graphs showing the dependence of these temperatures on the percentage of ethanol can be

found in Appendix 1).

3.5 Storage TankThe storage tank needs to hold the water to be heated for 1.5 days for a family of 7 people. In addition to

storing water, the storage tank also serves as a countercurrent heat exchanger. Since the size of the heat

exchanger depends on the mass flow rate, the sizing for the storage tank can be found in the heat

exchanger sizing section. The storage tank is a steel box (1/8 inch thick steel sheet) of the required

dimensions. Around this would be layers of boussilage in brick structure so the tank is positioned above

the collector plate.


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3.6 Governing EquationsNomenclature:

A =area of the solar collector (m

2

)Am = area of ethanol-water mixture in contact with absorber plate (m

2)

N = number of tubes in collector (-)

NG= number of glass covers (-)

L= length (m)

Lct =length of connecting tubes (m)

T = temperature (oC)

k = coefficient of thermal conductivity (W/mK)

PD = the density of power emitted by the sun

= viscosity (kg/ms)

= surface emissivity

C= specific heat (kJ/kgK).

m =mass flow rate (kg/s)

Indices:

c =collector

p=plate

g=glass

m=mixture

t= storage tank

a = ambient

s = surface

o or i = outlet and inlet of collector, respectively

Constants:

= Stephan-Boltzmann constant = 5.67E-08 (W/m2K4 )

g= acceleration of gravity= 9.81 (m s-2)

3.6.1 Heat Transfer in the Solar CollectorAssumption: Power emitted by sun: constant at 750 (W/m2 )

This equation is a balance of energy inputs and outputs within absorber plate. The energy input is thatfrom the sun and energy outputs are the re-radiated heat that is reflected off the surface of the plate, the

energy conducted to the working fluid (antifreeze) and heat losses out the backside of the collector.

LossantifreezeradiatedreSunQQQQ

++=

=

layers layer

layer

SaS

mmixtureD

k

L

TTA

L

TTAkTAAP

)()( 24


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Ub=energy loss through the back

Ue= energy loss through the edges

An empirical equation for Ut was developed by following the basic procedure of Hottel

and Woertz (1942) and Klein (1975).

G

g

p

wp

ampamp

w

e

amp

mp

Gt

NfN

Nh

TTTT

h

fN

TT

T

C

NU

++

++

+++

+

+

=

133.012)00591.0(

))((1

1

22

,,

1

,

,

where:

Tp,m = mean plate temperature (K)

C = 520(1-0.000051

2

) for 0

o

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