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Acknowledgements
We would like to thank the following people who gave their time, assistance and consideration during this training period. Firstly, we are extremely grateful to our supervisor Dr. Kenneth Ip who has provided support, advice and constructive comments throughout. We would also like to thank Mr. Jonathan Gates for his help and the continuous supply of information during all this period. Finally, thanks are also due to Dr. Andrew Miller for his kindness and the good times spent in Rouen, and to Ms Michele Terrier who made possible this exchange with the University of Brighton.
Page Acknowledgements 1
Content 2 Abstract 4
Page Appendix 55 Glossary 67 References 68 Bibliography 69
Abstract The aim of this project was to determine the experimental set-up for the measurement of thermal storage system using phase change materials. The report covers solar panels and phase change materials and the operating principles behind them. A solar thermal storage system using phase change material is proposed and background heat transfer equations and total cost established. A method of experimental measurement is proposed in order to measure the performance of the proposed system.
I. Introduction
During our second year in thermal engineering at the IUT (University Institute of Technology) situated in Rouen, Normandy, are required to enter into a period of training. The duration of this period is ten weeks, and is usually done in a company or industry. However we chose to do this period in a university in England, in order to improve our English and apply the theory learnt at the IUT. The institute that we chose was the University of Brighton, which is situated in the south of England, in East-Sussex. This university, was last year declared "University of the year" by the Sunday Times. The University of Brighton offers courses in the following areas:
The University has four different sites:
The department that we carried out our period of training in was the School of the Environment situated in the Cockcroft building, at the Moulsecoomb site under Dr. Kenneth Ip’s supervision and in collaboration with Jonathan Gates, a MPhil/PhD student. The aim of our studies was to propose an experimental set-up for the measurement of thermal performance of a solar thermal storage system. An effective solar thermal storage system must form an integral part of a solar heating system for without this maximum utilisation of solar energy is not possible. Thermal storage can also address the problem in trying to match supply to demand were maximum solar availability occurs during the day, but maximum demand occurs at times when there is a little if any solar availability. This project forms part of a current research to develop and analyse the performance of such a system for use in domestic buildings.
The report is organised into chapters which correspond with the objectives of the project. The first part of the report covers solar energy, the different ways to store energy, and Phase Change Materials (PCMs). The second part covers system design including description of the system, identification of components, PCM selection, all of which should allow a model of the system to be built. The third part details the heat transfer equations, for each part of the system. The final part of the report details the experimental set-up, which describes the parameters to be measured, the measurement procedure and the cost of the system.
Keywords: PCM, solar panel, latent heat storage, heat transfer energy, latent energy.
II. Solar Heating 2.1. Solar Energy At the 1992 conference on climate change, the United Nations Inter-governmental panel concluded that a 60% reduction in the use of fossil fuel would have to be made in order to freeze the level of CO2 emissions by the year 2005 [1]. This has a tremendous implication on the way in which fuel is currently being used, placing greater emphasis on the use of alternative, renewable energy sources. This will have a large impact on the way buildings are operated as currently they account for over 50% of fuel consumption, with heating and lighting residential buildings responsible for 60% of emissions [1].
Solar power has enormous potential for use in residential buildings for approximately 30000 times as much solar energy reaches the earth than is actually needed to meet human demand [2]. It is also a clean source of energy in that it does not produce any CO2 and it is totally renewable. However there are several major problems with harvesting solar energy; it’s availability is unpredictable, intermittent and is often subject to interruptions due to changes in weather. Due to this and the fact that for approximately for half of the 8760 hours per year any location is in darkness [3], a form of thermal storage is required to match supply with demand.
2.2. Solar collectors
A solar collector is made up of the following elements: An opaque body which absorbs the solar radiation by getting overheated, A thermal heat transfer fluid, Thermal insulation (back and sides) A transparent cover (fore face exhibited to the radiation) A heat exchanger called absorber plate
In each collection device, the principle that is usually used is to expose a dark surface to solar radiation so that the radiation is absorbed then, a part of the radiation absorbed in this way is transmitted to a fluid: air or water by means of a heat exchanger. Concerning this heat exchanger, all solar energy systems using indirect water heating require one or more exchangers; heat exchangers influence the effectiveness with which collected energy is made available in domestic water. They also separate and protect the potable water supply from contamination when non-potable heat transfer fluids are used. Like transport fluid selection, absorber plate selection considers thermal performance, cost effectiveness, reliability and safety, and the following characteristics: Heat exchange effectiveness Pressure drop, operating power, and flow rate Physical design, design pressure, configuration, size, materials, and location in the system Cost and availability Thermal compatibility with system design parameters such as operating temperatures, flow rate, and fluid thermal properties.
Actually, there are two main different sorts of collectors: Flat-plate and evacuated-tube collectors.
Flat-plate collectors
A flat-plate collector is the most important type of solar collector since it does not require a lot of maintenance and is really simple to design. Moreover, the flat-plate collector can be used for applications where temperatures are set between 40° C and 100° C. Which make it suitable for space heating applications. A schematic diagram of a liquid flat-plate collector is shown in Fig.1.
A flat-plate collector consists of an absorber plate on which the radiation of the sun falls after having come through one transparent cover made of plastic or glass either single or double-glazed. The absorbed radiation is transferred to a liquid via the absorber plate and it is this energy gain which is the most useful. The remaining part of the radiation absorbed in the plate is lost by convection to the surroundings, and by conduction through the back and edges. The transparent cover helps in reducing the losses by convection and a selective coating can reduce the amount of lost to the surroundings. The liquid most commonly used is water, although oil can be used.
Evacuated-tube collectors The evacuated-tube collector is the other form of solar collector
These are typically more efficient at higher temperatures than flat-plate collectors. In an evacuated-tube collector, sunlight enters through the outer glass tube and strikes the absorber, where the energy is converted to heat. The heat is transferred to the liquid flowing through the absorber. The collector consists of rows of parallel transparent glass tubes, each of which contains an absorber covered with a selective coating. The absorber typically is of tin-tube design, although cylindrical absorbers also are used.
Evacuated-tube collectors are generally more efficient on an all year round basis as they can still operate under cloudy conditions, however they are considerably more expensive than flat-plate collectors -around 80%- and if the vacuum seal fails then they become inefficient. A solar selective coating absorbs the solar radiation and converts it into thermal energy that is transported from inside the inner tube to an application.
Flat-plate collectors for heating air
However, there is also another sort of collector, whose construction is rather similar to the one of a liquid flat-plate; this is the conventional flat-plate collector for heating air. The only difference in its construction concerns the passages through which the air flows. A schematic diagram of such one collector is shown below in Fig.3.
However, it needs ductwork which can take up considerable amount of space and if we need to store, it needs to use either a rock-bed or water for storage which again takes up space.
A thermal application: water heating
Of all the solar thermal applications, solar hot water heating is the most popular and may be the most economically viable. A diagram of a simple natural circulation system is shown in Fig.4.
The two main elements of this system are the liquid flat-plate collector and the storage tank that is located above the level of the collector. When the water in the collector is heated by solar energy, it flows automatically to the top of the water tank and it is replaced there by cold water from the bottom of the tank. Hot water for use is withdrawn from the top of the tank, and cold water enters automatically at the bottom. The main disadvantage with a thermosiphon system is that the storage vessel needs to be located higher than the collector which means the collector may have to be sighted on the ground or on a porchroof.
Finally, in Fig.5 is shown a pumped system because this is one as this, that we will use.
When designing a solar heating system, it is important to consider the local climatic conditions. The most important climate variable(s) is (are) the solar irradiation (and the local ambient temperature). The plane where we will install our panel is inclined around 30° (what is the typical inclination for solar collector in the United Kingdom). The solar irradiation on such an inclined plane varies about 950 kWh/m2 per year in the North of the UK (Scotland) to about 1250 kWh/m2 per year in the South West (see Fig.6).
Fig.6 Variations in annual mean values of solar irradiation on a 30° inclined plane in the UK (kWh/m2)
(Source European Solar Radiation Atlas-1984)
Concerning the design of active solar system for the UK, there is also an important point, it is the fact that the monthly solar irradiation varies between the summer and the winter months. For an installation in Brighton, the seasonal variations for a surface in the South of England are shown below in Fig.7
Fig.7 Monthly distribution of annual solar irradiation received at 30° South in the South of England
(Source European Solar Radiation Atlas-1984)
2.3. Energy transfer
The energy collected by the solar collector is transferred to the heat transfer medium via the absorber plate. This heat is transferred to a storage tank or vessel.
This transfer occurs either by free circulation or by forced circulation
Transfer by water free circulation.
In these installations, the transfer of energy is based on the difference in density between hot and cold water. Water entering at bottom of the collector is heated by the sun which reduces its density and causes it to expand it to rise to the storage tank which must be situated at least 60 cm above the collector. Due to thermal stratification, hot water remains at the bottom of the tank, from which the solar collector is fed.
Transfer by forced circulation.
In addiction to the elements used in the previous system, this system uses a circulation pump driven by a temperature regulation. The role of the circulation pump is to enable a faster transfer of the heat absorbed by the heat transfer fluid from the solar collector. The utilisation of this pump also enables the system to be shut down if the water in collector is not hotter than that inside the tank.
The role of the regulating thermostat is to compare the two temperatures (at the solar panel exit and in the storage tank) and to drive the pump solely when the first temperature is higher than the second one (usually 5-10° C). In practice, the regulators available on the market enable the user to independently set the temperature difference.
III. Phase Change Materials
3.1. Energy storage: an introduction
Energy storage is a fundamental requirement of all solar energy systems. Storage can either be thermal or chemical.
Thermal storage can either take the form of sensible heat storage where energy is stored by raising the temperature of a storage medium, for instance water or rock, or latent heat storage where energy is stored by altering the physical state of the storage medium, which can be solid-solid, liquid-gas or solid-liquid. The most common form of sensible heat storage in dwellings is the incorporation of thermal mass in a building’s structure to act as a heat store.
However there are several disadvantages with sensible heat storage; it is often difficult to judge the correct thermal mass required for space heating requirements and energy cannot be stored or released at a constant temperature. This method of storage is also inefficient as it takes less energy to raise the temperature of a material than it requires to change a solid or crystalline structure into a liquid.
Consequently to store the same amount of energy, significantly larger quantities of storage medium are required for sensible heat stores in comparison to latent heat stores. This is illustrated by the fact that the sensible heat capacity of concrete is approximately 1.0 kJ/kg [4], compared with calcium chlorine, which during phase transition, can store or release 190 kJ/kg [5]. Due to the large volume of material required, sensible heat storage is not suitable for retrofit applications and does not conform to the current trend for lightweight structures.
Furthermore, these systems take up a lot of space and have weight penalties which can have major cost implications in commercial property. The use of latent heat storage is ideally suited where space is at a premium, such as refurbishments as larger amounts of energy can be stored per unit volume in comparison with sensible heat storage, which results in large space savings. Another major advantage with latent heat storage is that heat is stored under isothermal conditions, which means they can deliver or store energy at a constant temperature. The use of latent heat storage is especially suited to the storage of solar energy where it can result in high solar collection efficiency, which can mean that solar collector area can be reduced by 30% [5].
So as to explain what a Phase Change Material is, we must show the example of water, the most simple and used of them. Alternatively, water in a liquid state cooled to the point of crystallisation (0° C) will discharge heat. This process is similar at the other phase (100° C) with boiling resulting in heat storage and condensing resulting in heat discharge.
Latent heat storage and discharge for water at 100° C is termed latent heat of vaporisation and heat storage and discharge at 0° C is termed latent heat of fusion, this is that latent heat which will only be considered during our study. The principle of latent heat storage using phase change materials (PCMs) can be incorporated into a thermal storage system suitable for use in dwellings, where roof-mounted solar panels are used to collect the available solar energy during the day, which is then stored in the PCM for later use. The water phase changes are shown in the schematic diagram in Fig.6
Fig.6 Water Phase changes By comparing the values of steel, copper, water and a typical PCM compound called sodium sulphate; we can see that steel and copper exhibit the lowest heat of fusion for such high melting points.
Characteristics of steel, copper, ice and sodium sulphate
(Source IHVE Guide. Unit and miscellaneous data)
By measuring density values we can also see that larger volumes of space are required. Although ice has the optimum set of readings, the melting temperature is far too low to be useful as a means of heat storage.
It is clear that the PCM exhibits the optimum qualities, it provides a minimal amount of volume for its heat of fusion as well as having a low melting point. That’s why PCM can be used as heat storage. Now, we have to identify the required PCM to integrate in our proposed heating system.
This chapter reviews the characteristics of suitable PCMs for use in buildings and the methods of storage and control. There are several types of PCMs but the three most common groups of PCMs are organic compounds, inorganic compounds and eutectics.
3.2. Organic compounds
These are compounds based on paraffin where the melting temperature of the material varies in relation to the amount of carbon atoms it possesses. Pure paraffins contain 14-40 C-atoms, whereas paraffin waxes contain 8-15 C-atoms [6]. Organic PCMs offer several advantages in that they possess a wide range of melting points, are non toxic, non corrosive, non hygroscopic, chemically stable, compatible with most building materials, have a high latent heat per unit weight, melt congruently and most importantly exhibit negligible supercooling which has plagued some inorganic compounds [5]. Some disadvantages of organic PCMs are; high cost which has led some researchers to investigate technical grade organic [7], low density, and low thermal conductivity in comparison to inorganic compounds, although this can be addressed by the addition of a filler with a high thermal conductivity or the use of aluminium honeycombs or matrixes [8].
They are also subject to substantial changes in volume upon melting, which can result in the material detaching from the sides of it’s container when it freezes, which can affect the heat transfer process. Flammability is often sighted as a potential disadvantage with organic PCMs, however some authors argue that their low vapour pressure presents little risk of fire, and they exhibit unstable characteristics notably large volume changes during liquefaction and solidification and low thermal conductivity.
Organic Phase Change Materials
(Source- CIBS Guide C3 Heat transfer (1976)) 3.3. Inorganic Compounds
These mainly consist of chemicals such as hydroxides or oxides, which have been diluted in an acid solution and are termed as salt hydrates or molten salt. The advantages that salt hydrates offer are; low cost in comparison to organic PCMs, they have a high latent heat per unit mass and volume, they possess a high thermal conductivity compared to organic compounds and offer a wide range of melting points from 7-117° C [9]. However, they can also suffer from loss of water when subjected to long-term thermal cycling due to vapour pressure, although the use of airtight containerisation can prevent this. Problems with corrosion have also been experienced with salt hydrates. The major drawback with salt hydrates is that they can degrade over time due to a process known as decomposition. This is where the PCM melts incongruently and produces two separate parts, an aqueous phase and a solid phase, which possesses different densities, consequently the denser solid phase settles at the bottom of the container and this process is irreversible.
Many salt hydrates exhibit this weakness. Attempts at addressing this problem have centred on using thickening agents with varying degrees of success. However Merks observed that whilst Glauber’s salt thickened with attapulgite clay withstood thermal cycling better than an un-thickened, solution its thermal storage capacity still declined over time [5]. However, the problem with this sort of compounds occurs from repeated phase change cycles during solidification, the salt hydrates melt incongruently. This result is in a compound of a lower hydrate of the same salt [3]. That is to say that the original compound is no longer the same and a lower heat of fusion results.
Inorganic Phase Change Materials 3.4. Eutectics
A eutectic PCM is a combination of two or more compounds of either organic, inorganic or both which may have a more interesting melting point to their individual and separate compounds. They behave themselves as salt hydrates. The main problem with these compounds is the cost, actually some two or three times greater than organic or inorganic.
Eutectics Phase Change Materials
(Source- CIBS Guide C3 Heat transfer (1976))
Phase transition temperature
It is essential that the output of heating system is not less than the overall temperature required to melt the PCM permitting the desired heat transfer to take place. Those compounds with the lowest congruent melting points are therefore more desirable.
IV. System design
This project proposes to realise a model of a heating system. The heat in this system is obtained by a solar panel and the storage of this heat will be done in phase change material, sandwiched inside two pipes, surrounding a water pipe. In the end, the model will be install in a laboratory, inside the university. The laboratory is for the moment used for another field of studies. Before all we had to make the measurement of the size of the laboratory, in order to propose a schematic drawing of a possible model. The pictures below show the laboratory, in its current condition.
Above, picture of the laboratory, one of the entrances.
Above, picture of the laboratory, other view.
The photo below, is a photo of the roof, where the solar panel will be installed.
4.2.System dimension and layout 4.2.1. Laboratory’s schema For this part we have taken the measures of the room size and made a schema of he laboratory; in order to after make the drawings of the implantation of the model inside the laboratory’s room.
4.2.2. Layout of the model
4.2.3. Isolation box
Monitoring the temperature of the internal space is vital in the case of space heating. In our case, the model we propose will be install in a room inside a laboratory of the university. This room has big dimension, and those dimensions could have an influence on the parameters we would like to measure. Indeed, if the size of the room is too big it can happen that the temperature is not uniform and then it exists a temperature gradient inside the room. Furthermore, we can not measure easily the airflow, which flows cross the PCM pipes. So to measure the real impact of the PCM, and the heat exchanged, we need to have a less big room around the PCM pipes. In order to do that, we propose to build a sort of box around the system. This box will be insulated, so as to have a room isolate from the rest of the laboratory’s room. We propose to install this insulated box like in the schema below.
We propose also, a simply way to build this box, but this is just a guide to do it. First built a frame in wood, to have the skeleton of the room. After that, put plasterboards at the outside surface of the wood frame, screwed on the post of the frame. Then, put insulation behind the plaster boards, inside and between the frame Posts. Finally put the rest of the plasterboards inside the room, screwed on the posts of the frame. You have a room, insulate, to protect your system from the outside, and the laboratory’s room.
4.3. Identification of components
4.3.1.Components for the system
For the most important part of the system, we can use a copper pipe for the water flow. But for the size of the pipes we must take care about the implantation of the system, indeed it could be installed under the floor, so the pipes could pass through some joists. The size of the pipes in this case is regulated, the maximal diameter for the holes made inside the joists is 0.25 times the width of the joist. [appendix A.1] For the Phase Change Material we need nine meters of plastic pipes. We take a nominal diameter of 36mm (UPVC Class E), to have a mean internal diameter of 32mm. As the pipes of PCM will be the bigger ones, a diameter of 36 mm leads to have a joist with a minimum width of 150 mm. Which is not too big and could be correct for a lots of situations. [appendix B.1] We take fifty meters of copper pipes, with a nominal diameter of 15mm, That is to say a mean internal diameter of 14mm. For the pipes around the Phase Change Material we need to take plastic pipes, because of the corrosion of the copper by the Phase Change Material chosen. Actually, the PCM in our case is Salt Hydrate, which are efficient but corrosive to the plastic. The length of plastic pipes we need is nine meters, with a nominal diameter of 15mm, to have a mean internal diameter of 11mm for this part. [appendix B.1]
To isolate the system, if it need, we can use valves. The valves we chose are Gate valves and have a diameter of 15mm. [appendix B.1]
Pipes or ducts need not to be insulated if they contribute to the useful heat requirement of a room or space. In this project, the aim is to give to the PCM the largest possible quantities of heat, so we need to insulate the pipes to avoid the heat loss by the water, while it circulates inside the pipes. We insulate the water pipes, with an insulation of 15mm for the diameter and 25mm for the thickness. [appendix B.1]
We need a pump to make the water circulate, with a flow of one meter per second up to five meters per second. However we are limited for the choice, indeed we do not need a heavy pump if we consider the size of the water pipe, but the problem there is that the water needs to go up to 12 m easily. So we need to take a pump with a big head capacity. The choice of pump was made after consulting manufacturer catalogues. [appendix B.2]
Applications Water circulation in commercial heating and air conditioning systems. Options Single or twin head. Temperature range: Pressure rating: Pump connections: -10 to +130°C 6 Bar 1.25"BSP to 80mm
We need to known the size of the isolation room in the laboratory to make the choice of the fans. By calculation, we found eighty cubic meters. We take a fan, which can deliver a volume of air, equal to two hundred cubic meters per hour with a velocity, which can change. We place the fan as the schema below shows it.
The choice of fan was made after consulting manufacturer catalogues. [appendix B.3]
Fan CC-CCI
The CCI fans are acoustically insulated by a double internal wall made up of a double sheet perforated metal structure full of 50 mm of mineral wool; by the way, they are one of the quietest fans in the market.
4.3.2 Components for the measurement
We need thermocouples to make the measurement of the temperature, at different places. The range of temperature we have is –20ºC (just in case) up to 100ºC. So we can take a thermocouple type T which have a range of –250ºC to 395ºC. The choice of thermocouples was made after consulting manufacturer catalogues. [appendix B.4]
We need a device to store and make the acquisition of the data obtained by the measures, a data logger is the more useful device to make this acquisition. We have chosen the following data logger, because it is expendable, and it offers a lot of different input. See appendix B.5 Expandable Data Logger HHP34970A
modules internally
each channel
readings and five instrument configurations
outputs available Intuitive front panel
pacing scans and timestamping readings
Universal input channels In all, the HP 34970A can measure and convert 11 different types of input signals which eliminates the need for expensive external signal conditioning. These signal types are: • temperature with thermocouples, RTDs, and thermistors B, E, J, K, N, R, S, T
• DC and AC voltage 100mV, 1V, 10V, 100V, 300V • 2 and 4 wire resistance 10W to 100MW in 7 decades • frequency and period 5Hz, 10Hz, 40Hz, 300kHz • DC and AC current 10mA, 100mA, 1A
COMMON SPECIFICATIONS DC CHARACTERISTICS Offset voltage ` <3uV, 6 uV for 34902A Initial closed channel R <1W , <0.2W for 34903A Channel/channel isolation >10 W AC CHARACTERISTICS Bandwidth 10 MHz Capacitance (HI-LO) <50 pF
Capacitance (LO-Earth) <80 pF Volt-hertz limit 108
OTHER T/C CJC accuracy 0.8°C Switch life (no load typ.) 100M Rated resistive load (typ.) 100W Operating temp. range 0 to 55°C Storage temp. range -20 to 70°C Humidity (non-condensing) 40°C / 80% RH
ACCURACY SPECIFICATION ±(percent of reading + percent of range) over one year, for example by each input type VDC 10v 0.0035 + 0.0005 VAC (10hz – 20kHz) 10v 0.0600 + 0.04 Resistance 1W , 0.0100 + 0.001 Frequency 40Hz-300kHz 0.01 DC current 100mA 0.050 + 0.005
True RMS AC current 1A 0.10 + 0.04
Thermocouple Type k ±1°C
Amplicon Liveline Ltd. Centenary Industrial Estate Hollingdean Road Brighton BN2 4AW United Kingdom. Tel: - 01273 570220 & Fax: - 01273 570215
We need a water flowmeter, in order to have the value of the water flow inside the water pipes. The value of the water flow is used in the equations to have the amount of the heat exchanged inside the water pipes. So we take a flowmeter which can be fixed on a pipe of 13mm for the diameter. The choice of water flowmeter was made after consulting manufacturer catalogues. [appendix B.6]
We need an air flowmeter, to measure the airflow passing cross the PCM pipes. Indeed to calculate the heat took from the PCM, we need the temperature at inlet and outlet of the insulated room, and the airflow. The choice of air flowmeter was made after consulting manufacturers catalogues. [appendix B.7]
4.4. PCM and solar panel selection
Latent heat of fusion per unit of volume of selected phase change materials Organic compounds:
Eutectics: Inorganic compounds: Density
High density is important because more heat can be stored in a given volume. However, density increase is often accompanied by a decrease in heat of fusion since the substance becomes self-insulated.
Safety
The material must not be dangerous, flammable or toxic, and must be disposable.
By reading this table and seeing the chart, it appears that the best Phase Change Material to choose is the Calcium chloride hexahydrate. Actually, it is a good compromise between a low Phase transition temperature and such an important latent heat of fusion, moreover, there is absolutely no danger in using this PCM and it is one of the cheapest.
4.4.2 Solar panel selection
A Flat-plate collector was selected for the following reasons:
V. Heat transfer process
We have to take into consideration for the heat transfer, that the transfers are not the same for each situation. That is why this chapter is divided into different parts describing the different situations we have in this project.
5.1. Heat transfer for a pipe
The first part describes the heat transfer for a pipe in two situations, firstly the heat loss along the pipe when the water circulates inside the tube. And then the situation, when a fan is blowing air on the pipe, for recovering the heat transmitted by the pipe. In our case, the heat is recovered from the PCM.
5.1.1. Heat loss along the length of a pipe
Assumptions:
The heat loss from the pipe is by convection to the room air and by radiation exchange with the walls. Hence,
The heat loss per unit of pipe length is then,
The convection coefficient may be obtained thanks to:
where,
with,
See appendix C, table C.1 for the values of n, a, b to obtain Pr and Gr.
5.1.2. Cylinder in a cross flow
When the pipes are under the airflow blown by the fan, the air after the pipe is warmer than the air just outside of the fan. So during the passage under the pipe, there is a transfer of heat between the pipe and the air.
The equation describing the heat loss is the same form as before:
So per unit of length,
The only difference is for the convection coefficient, because the Nusselt number is expressed in another form which dependant on the blown air.
Where U¥ is the air velocity.
We have a different expression for the Nusselt number as the case may be.
See appendix B, table B.2 for the values of C and m.
Where all properties are evaluated at T¥ , except Prs, which is evaluated at Ts. If Pr£ 10, n= 0.37; if Pr> 10, n= 0.36. See appendix C, table C.3 for the values of C and m.
5.2. Radial heat transfer
The pipe, considered in the following equations, is formed by two concentric pipes. Water flows through the smaller inner pipe and the outer pipe contains a Phase Change Material. (See figure below)
For the equations we consider a little part of the pipe, so we have:
Where i, o, s subscripts for inlet, outlet, surface Tm is the mean temperature of the fluid
Assumptions: The flow is fully developed Incompressible flow
Now for the radial heat transfer we take a "slice" of a pipe and then a little part of this slice,: Temperature of the inside surface
The governing radial heat transfer equations for a unit section along the length of a concentric pipe containing phase change material are then:
with
m : mass [kg]
5.3. Heat transfer during the phase change
The storage mechanism for all solid-liquid PCM is the same. Once the melting temperature of a PCM is reached it changes phase from crystallisation to fusion. This is called the charge period, as during this stage considerable quantities of latent heat are stored. The PCM will continue to store heat all the time it is at or above it’s melting point, or until it’s saturation point is reached. When the temperature falls below the melting point of the material it will begin to discharge the stored latent heat, which it needs to do in order to crystallise and change phase from liquid to solid.
When phase change occurs the latent heat effect is significantly greater than the sensible heat, hence the radial temperature distribution within each thin layer of the phase change material is assumed to be uniform. This temperature uniformity is further maintained by subdividing the phase change material into thinner layers.
At phase change temperature Tphc, the heat energy is used for the phase change process.
If Qlhtmax > Qlht >0
Tpcm = Tphc
Where, Qlht : latent heat content of the phase change material [J. kg-1] Qlhtmax : maximum latent heat capacity of the phase change material [J. kg-1] Tpcm: temperature of the phase change material [K] Wpcm : rate of heat flow to the phase change material [W.kg-1]
5.4. Equation for the solar panel
For the solar panel it is assumed that there are no heat losses through the back and the sides of the panel, and the air temperature at the front of the solar panel is inclusive of the sky temperature and the sky velocity. The basic equation for the quantity of energy released from the solar panel (to the water passing through) is calculated using the following formula:
Q=F. [I.(t.a)-U.(Ti-Ta)]
Where Q is the quantity of energy released from the collector per meter squared of area.
The constants of the equations are:
The variable of the equation is: Ti the temperature of the water entering the collector. This value varies because of the initial temperature of the water when the heating system is first activated and its heat loss to the PCM pipe once the collector is working.
VI. Experimental set-up
6.1. Parameters to be measured Normally, so as to calculate the heat loss along the length of the pipe (equation (1)), we need three temperatures:
But, due to the fact that the pipes will be enough isolated (thickness=25mm) in order to reduce at the maximum the heat loss by the pipes, it is only necessary to measure the temperature at the exit of the solar panel and at the entrance of the PCM so as to determine the loss of energy in the pipe by using the equation (14). What we also need so as to calculate the quantity of energy is the water flow rate, that’s why we have to use a flowmeter which we will install just after the pump. Concerning the cylinder in a cross flow, to use the equation describing the heat loss (8) we need two thermocouples in order to measure the temperature of the pipe surface (Ts) and the temperature of the ambient air (T¥ ). But there is also a parameter which is necessary to know, it is about the air velocity called U¥ . Actually, we must know this velocity so as to calculate the Reynolds number (10) in order to find the convection coefficient (3). Given that a box will be installed around the PCM pipes, it is now possible to measure the global energy got back by air, so as to do that, we need two temperature acquisitions: one at the exit of the fan, and another one at the exit of the box. We can consider thanks to the size of the box and to the blown air velocity that there will not be any temperature gradient. For the radial heat transfer equations, several points must be taken into consideration more particularly the mean temperatures of the fluid at the inlet and outlet of the pipe (14) for the quantity of heat.
In view of the fact that it is relatively hard to determine mean temperatures, we will use two thermocouples (one for the inlet and the other one for the outlet) situated at the middle of the pipe, corresponding to the ray of the pipe, what gives such a good rough estimate while temperature at the middle of the tube and temperature of the inside pipe must be really close. Concerning the radial heat transfer in the strict sense of the word, four temperatures are useful, it is about the temperature of the inner (16) and outer plastic pipe (18), the temperature inside the PCM (17), and the temperature of the outside surface (19). About the solar panel equation (21), the only variable is the temperature of the water entering the collector, therefore the only thing we will have to carry out is to note down the measurement done by a thermocouple situated inside the pipe just before the solar panel. For an additional calculation, we can use the equation concerning the quantity of heat (14), in order to determine the quantity of heat absorbed by the water passing through the solar collector, for that we can input another thermocouple at the exit of the solar panel so as to have a the two necessary temperatures for the calculation; the water flow rate remaining the same as the one measured before. We propose in order to see the temperature evolution inside the PCM, to take several measurements on the same pipe. These measurements consist in the acquisitions of water temperature and the temperature of the PCM at different depths. This representation is proposed in the figure below.
6.2 Measurement procedure All the equations written below are simpler than the ones given in the fifth chapter which are too theoretical for such an application. We do not need these complicated equations so as to obtain a quiet good approximation of the real heat exchanges.
The aim of this measurement is to characterize for a given duct the heat loss per unit length of copper pipes (Q/L) with a determined |