Designed and modeled solar cooker

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Designed and Modeled Solar Cooker

by

by Chimbaugona Mkandawire Submitted to the Department of Mechanical Engineering in Partial Fulfillment

of the Requirements for the Degree of

Bachelor of Science at the

Massachusetts Institute of Technology

May 1994

The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part.

Signature of Author . . . ...

Certified by . . . ..

Accepted by . . . ...

Signature redacted

Department of Mechanical Engineering May 6, 1994

Signature redacted

David Gordon Wilson Professor of Mechanical Engineering Thesis Supervisor

Signature redacted

Peter Griffith Chairman, Department Thesis Committee

I

MASSACHUSETTS INSTITUTE

OF TFrHNOIOGy

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DESIGNED AND MODELED SOLAR COOKER

by

CHIMBAUGONA MKANDAWIRE

Submitted to the Department of Mechanical Engineering on May 6, 1994 in partial fulfillment of the requirements for the Degree of Bachelor of Science in

Mechanical Engineering

ABSTRACT

A solar-cooker design is presented and modeled. A solar concentrating mirror is used to capture sunlight energy and store it in eight thermal-storage modules. These modules contain lithium nitrate, or a similar salt, as the active storage medium, and they are stored in a well-insulated housing. The charging time needed to bring eight modules to 250 degrees Centigrade is predicted to be 5.1 hours. The estimated time it takes for eight modules to dissipate 90% of their stored energy while in the housing is 37 hours. The designed solar-collector appears to meet all of the customer-interpreted needs.

Thesis Supervisor: Dr. David Gordon Wilson

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ACKNOWLEDGMENTS

The first set of props goes out to my family. It was my mother's idea for me to do my thesis on a solar powered oven. It was my father who urged me to go to MIT. Second, I would like to thank all of my brothers at Chi Phi. Life is never dull with forty close friends looking after you when you are away from home. The next set of props go out to those involved with my project, specifically Dave Wilson, Ben Matteo & Taffy. Dave Wilson is a great man with many great accomplishments. Currently, he is embarking on a new era in his life. For the four years I have known him, I can say that very few deserve what he has been given. Props to Ben for his zeal to find that perfect fusible salt, and props to Taffy for being Taffy.

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INTRODUCTION

BACKGROUND

Deforestation is a major problem in underdeveloped third-world countries. Many of these nations have laws to protect their trees, but laws do not mean a great deal if no law enforcement exists. Many nations cannot afford law enforcement at this level, nor can they afford to replant all the missing trees protected under law.

To submit a reason why deforestation exists, I shall focus on the underdeveloped third-world nation Malawi. Malawi has a population of nearly 8.5 million people. Of those 8.5 million, 85% live in rural areas. These areas lack electricity, running water, and gas power. So, as one can plainly see, 85% of the population cannot get heat to cook or warm their homes outside of burning wood.

PROBLEM STATEMENT

A solar cooker is one viable solution. The solar cooker I investigate was designed by Professor David Wilson at the Massachusetts Institute of Technology. The solar-cooker has to meet the following criteria: it must be able to heat to a specified initial temperature and retain most of its heat for at least four hours, it must be relatively inexpensive, it must be easy to assemble and use in a third-world environment, and it must meet as many customer-interpreted needs as possible. These interpreted needs are guidelines of how members of the Malawian community go about in preparing their food.

The customer-interpreted needs are the following. The person cooking is accustomed to sitting throughout the duration of cooking. The heat produced from cooking should also provide warmth to those cooking the meal. There should be limited smoke damage to the eyes. Cooking is done primarily in the evening hours when the sun is not very potent. The solar cooker should be able to accommodate round- or flat-bottomed pots with a ten-inch radius.

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OTHER APPROACHES AND PAST WORK

One of the earlier approaches to designing a solar cooker was developed by the VITA Group. The VITA solar-cooker could provide heat only when the sun had its strongest presence; therefore, none could cook in the evening hours. The VITA solar-cooker design did not account for many of the customer-interpreted needs. The person cooking had to stand throughout the duration of cooking a meal. The pot used with the VITA solar cooker had to be a custom-made pot. These are the primary drawbacks to why the VITA solar cooker did not fair well in societies similar to those of Malawi.

The concept of using a solar-concentrating mirror to heat individual modules containing a fusible salt or other thermal-storage medium was originally developed by Wilson in 19871. These individual modules would store energy during periods of high insulation. From this time until the modules were ready to be used by the cook, the modules would be stored in a thermally insulated container. Afterwards, the modules could be used for heating pots, pressure cookers or possibly an oven. All of the possible devices needing a module would also be insulated. Approximate calculations indicate that the modules would be useful during a period of at least eight hours after heating.

1_D.

Wilson, Modular Stored-Heat Concentrating Solar Cooker: Concept Memo and Preproposal.

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METHOD

DESIGN

The design of the solar cooker is shown in figure 1 (from original sketches by David Gordon Wilson). From figure 1, one can see that the solar cooker is made of eight parts: a fresnel mirror, HDPE insulation, an outside casing, an inner casing, a cooking cover, a tilting frame, a nesting spring and thermal storage modules.

The fresnel mirror is a solar concentrating mirror capable of capturing up to sixty percent of the sun's irradiance2_{. The mirror is made of aluminized mylar on plywood.}

The HDPE insulation is foam whose thermal conductivity is 0.042 B.T.U. per hour per square foot per degree Fahrenheit.

The outside casing of the solar cooker could be made from an ordinary plastic trash receptacle. The cooking cover is a modified trash-can lid designed to house a ten-inch-diameter stew-pot. The inner casing of the solar cooker is made of steel or aluminum. Its primary function is to contain the thermal heating modules and the nesting spring. The inner casing also buffers the modules from the insulation, allowing more heat to be retained during heat dissipation. The inner casing is two feet long, has an inner diameter of eight inches and a thickness of one half inch.

The tilting frame tips the solar cooker at different angles; thus, a person can change the angle of the fresnel mirror to match the angle of incidence of the sun's rays. The stand of the tilting frame telescopes, allowing different angles. The stand is made of aluminum or plastic.

The nesting steel spring allows easy loading and unloading of the thermal-storage modules. The spring chosen for the solar cooker must have a spring constant between 2800 and 2900 Newtons per meter. See Appendix B for derivation of spring constant.

2

C. Wyman, J. Castle, F. Kreith, A Review of Collector and Energy Storage Technology for Intermediate Temperature Applications. Solar Energy, vol. 24, pp. 538 (1980).

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The design of the thermal-storage module is shown in figure 2 (adapted from an original by David Gordon Wilson). From figure 2, we can see that the module is made of two different structures: an outside casing and a latent-heat material. The outside casing is made of steel and the latent heat material is probably LiNO3. The solar cooker houses a

total of eight thermal-storage modules. The top surface of each module is curved to allow for flat- or round-bottomed pots. Each module contains 1450 milliliters of LiNO3.

-- SUN'S RAYS ,'FRESNEL MIRROR - -- COOKING COVER -:- HEATING MODULES - --- _{INNER CASING} --- -- - *FOAM INSULATION ---- --- OUTER CASING NESTING SPRING -- TILTING FRAME -- '4--- TELESCOPING STAND

Figure 1. Figure la (above) shows the solar cooker during heating phase whereas figure lb (top of

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(figure lb above, figure 2a below)

8"

-WELD

RADIATION RECEPTION FINS

STEEL CASING Figure 2. Figure 2a (above) shows a blown-up

compatibility of the top surface with respect to modules stack on top of each other.

ROUND-BOTTOMED POT

ON HEATING MODULE

FLAT-BOTTOMED POT

ON HEATING MODULE

heating module. Figure 2b (below left) shows the pot shapes. Figure 2c (below right) shows how

mD 2"1 STEEL CASING _FUSIBLE (LITHIUM NITRATE) 4 SUPPORTS

GROUND

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MEETING THE OBJECTIVES

Ease of assembly and use

An important objective of the solar cooker is to be easily assembled in a third-world environment. An easy-to-assemble product must incorporate as few advanced manufacturing techniques as possible. The proposed solar cooker design has limited the fastening process to welding and snap-fit. Welding is needed only for the assembly of each thermal storage module.

The assembly of the solar cooker is rather simple. The outer casing is evenly filled with foam. This process stops when the height of the foam equals the difference between the outer casing and the inner casing. Once the inner casing is placed inside the outer casing, the process of putting foam into the outer casing restarts. Next, the nesting spring can be placed inside the inner casing. Following, the thermal storage modules are placed inside the inner casing and above the spring. The solar cooker can then be fastened to the cooker cover and the fresnel mirror, in that order respectively. The cooker is fully assembled, and the stand may be attached if an angle is needed for receiving solar radiation. The use of the solar cooker can be split into two different phases. The first phase of use is the heating phase, the second phase is the cooking phase. The fully assembled solar cooker mentioned above is ready to commence the heating phase. During this phase, one must use the tilting frame to align the solar cooker properly with the sun.

To start the cooking phase, a ditch must be dug into the ground if a ditch does not exist. As shown in figure 1b, the ditch should be able to easily accept the solar cooker. With the tilting frame in place, the solar cooker can be tilted into its hole in the ground. Once the solar cooker is in ground, the fresnel mirror is removed and the stew pot may be carefully placed inside its designated area for cooking. The stew pot should be filled with cooking water prior to placement inside the solar cooker. This action avoids pouring water onto a rapidly heating surface which will evaporate much of the water as it makes contact

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with the hot surface. This ends the transition phase between heating and cooking; afterwards, the cooking phase commences.

After cooking is complete and the day is over, the fresnel mirror is refastened to the solar cooker. The solar cooker is then lifted out of the ground and placed onto the tilting stand in preparation for the next day's heating phase.

The thermal storage modules are assembled by welding two separate pieces together. From figure 2, we can identify the weld line. To assemble a module, 1450 cubic centimeters of LiNO3 must be evenly dispersed inside the top piece. Afterwards, the

bottom piece is clamped to the top piece. Now, both pieces can be welded together. Thermal storage modules may be assembled in third-world countries with welding resources. If welding is not available to certain third-world countries, or the cost of manufacturing a module is too high, the modules would have to be made somewhere else.

Interpreted needs

All the customer-interpreted needs were meet with this solar-cooker design. The user of the solar cooker is not required to stand throughout the daily heat-cycle of the machine. There are only three actions requiring the cook to stand by the machine. The first happens when the tilting frame has to be adjusted. This needs only occur once an hour, but the cook may adjust the tilting frame as many times as he or she pleases. The next time the cook has to stand during operation of the solar cooker is during the transition between heating and cooking phases. The last time the cook needs to stand during solar-cooker operation is when the solar solar-cooker is being removed from the ground.

There is only one interpreted need that the solar-cooker design does not incorporate. That need is the ability of the solar cooker to warm those in its presence. There is a way to side-step that need. As each module cools to below its useful cooking temperature, it can be removed and used like hot-water bottles. Towards the end of the day, these modules will be somewhere near 68 degrees Fahrenheit.

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There should be virtually no smoke damage to the eyes. The design of the solar cooker sends most of the dissipated heat from the thermal-storage modules into the ground and stew pot. The only harm people need to protect their eyes from is that of boiling water. The harmful smoke produced by wood fires is entirely absent during use of the solar cooker.

The solar cooker separates the cooking stage from the heating stage. These stages are analogous to dissipating a battery and charging a battery, respectively. This thermal-energy battery stores heat during the day and dissipates heat in the evening. The benefit of a thermal battery allows cooking take place at night instead of during the day.

The design of each module allows for round- and flat-bottomed stew pots. The radius of curvature for each module is slightly larger than that of ordinary stew pots with round bottoms. This allows each module to accept flat- or round-bottomed stew pots. From figure 2b, it is seen that either flat- or round-bottomed pots will produce air pockets. The fact that many pots placed in the solar cooker will have air pockets is not a big concern. Air is a very good heat conducting agent, so the heat that enters these air pockets will eventually enter the stew pot. The contact resistance, due to the air pockets, is too small to be significant; therefore, the solar cooker heats flat- or round-bottomed pots rather well.

DOES IT WORK?

To test to see if the proposed design would work, I first modeled a thermal battery. This thermal battery was used to model the charging and dissipating stages of the solar cooker.

Thermal battery

The thermal battery consists of all the thermal-storage modules, the inner casing, the nesting spring, and the air pockets located throughout the inner casing. In this entire region of space, the temperature is uniform; thus, the volume of the thermal battery is the

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volume of the inner casing. The space outside of this cylindrical thermal battery is occupied by either insulation or the stew pot.

The thermal battery derives its properties from the latent-heat material, lithium nitrate. Therefore, the mass of the thermal battery, the latent heat of the thermal battery and the heat capacity of the thermal battery are those respective properties of the total amount of

LiNO₃_.

Thermal-charging model

The thermal charging of the module is modeled with simple heat conduction. Equation (1) shows how the change of thermal energy of the thermal battery is related to the temperature change and the latent heat of storage of the thermal battery.

AEtb=ptbvLNQ(qbAT + AH) (1)

AT=Tes -Tamb (2)

AEtb is the difference in energy caused by the temperature difference. Ptb is the density of

LiNO3, vLiNO3 is the volume of LiNO3, and ctb is the heat capacity of LiNO₃. ctb

normally changes with respect to the changing temperature of the material involved. To simplify calculations, the mean heat capacity over the range of temperatures from 0 degrees Celsius to the desired temperature was used in place of ctb. AT is the temperature difference that occurred during heating. AHf is the latent heat of fusion of LiNO3.

Equation (2) relates AT, the temperature difference, to Tamb, ambient temperature, and desired temperature, Tdes. The comparison of (1) and (2) shows that the change in energy

of the thermal battery is directly related to the desired final-temperature of the

thermal-storage modules.

The change in energy derived in equation (1) is directly related to the amount of time needed to achieve a temperature change from direct sun irradiance. Equation (3)

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theat AEtb (3)

lscelsun

In equation (3), I1 is the peak irradiance of the sun during the day, Tlsec is the efficiency of the solar concentrating collector. theat is the amount of time required to heat the thermal battery for a temperature difference AT. The comparison of (1), (2) and (3) shows that the time needed to heat the thermal battery is directly related to the desired final-temperature of the thermal-storage modules.

Thermal-dissipation model

The thermal dissipation of the thermal battery is modeled as heat transmission through pipe insulation3 _{. The thermal battery is modeled as a pipe with a diameter of nine}

inches. The foam insulation is modeled as pipe insulation with a nominal thickness of four inches and a thermal conductivity of 0.042 B.T.U. per hour per square foot per degree Fahrenheit. The resulting heat loss per square foot per degree Fahrenheit per hour is 0.15 B.T.U. per square foot per degree Fahrenheit per hour.

Equation (4) relates the heat loss and temperature difference of the thermal battery to the amount of time it takes for the battery to lose 90% of its original energy.

tool :0.9*AFb*SA*AT (4)

0.15

t.,0 1 is the amount of time needed to dissipate the thermal battery to 10% of its initial value.

SA is the surface area of the thermal battery (inner casing). From comparing (1), (2) and (4), the time needed to cool down the thermal battery to 10% of its initial value is indirect and direct relation to the desired final-temperature of each thermal-storage module.

3

T. Baumeister, (editor) Mark's Mechanical Engineers Handbook. McGraw-Hill, Inc., New York, NY, 1958, p. 4-107

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CONCLUSIONS

For the thermal battery charging stage, the following values where obtained. The change of energy related with heating the battery from the ambient 15 degrees Celsius to the desired 250 degrees Celsius is 12.7 megajoules. The time necessary to reach this higher energy state is 5.1 hours.

For the thermal battery dissipation, the following values were determined. The time needed to discharge the battery to 90% of its initial value is 37 hours. The temperature at this energy state is still 250 degrees Celsius. See Appendix A for the full derivation of all these values.

RECOMMENDATIONS

More accurate models are in order. These calculations are only rough estimates. With a more accurate model, a prototype can be assembled and tested. This is only the tip of the iceberg.

Aside from the model, it is vital to search for food-safe latent-heat compounds. In case a crack occurs in one of the modules, the material leaking-out must be safe for contact with human skin at ambient temperatures and must not be toxic if ingested. Thermal-expansion models should be done to estimate the average life of a module is before failure. The end-users need some sort of indication when a module has failed, either by a bad smell or other indication. The end-users normally will not be able to locate any cracks with their naked eye, so it's recommended that they temporarily immerse each module in water once a month. They can search for tell-tale signs of material failure in the modules on a regular basis.

Some parts of the solar collector cannot be manufactured in any third-world country and may need subsidized manufacture by third-world governments or first-world agencies . The end-user may only have to pay the cost of one or two of the parts to the

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solar collector. Nearly all the end-users will not be able to pay for the fresnel mirror, or the cost of welding the heating module, or the cost of lithium nitrate.

This project has only revealed a portion of puzzle involved with solving the problems of deforestation. With more discovery, one can eventually see how important an inventions such as this can be to third-world countries. A manufacturable and marketable solar cooker can affect the poverty and malnutrition problems of any third-world nation. Over a period of a century, the repercussions of curing poverty and malnutrition results in a better overall education of a nation, increased life expectancy, and increased standards of living. These improved attributes open the doorway for any nation to the first world.

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REFERENCES

1. D. Wilson, Modular Stored-Heat Concentration Solar Cooker: Concept Memo and

Preproposal. (1987).

2. C. Wyman, J. Castle, F. Kreith, A Review of Collector and Energy Storage Technology

for Intermediate Temperature Applications. Solar Energy, vol. 24, pp. 517-540

(1980).

3. T. Baumeister, (editor) Mark's Mechanical Engineers Handbook. McGraw-Hill, Inc., New York, NY, 1958.

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APPENDIX A

DERIVATION OF THERMAL BATTERY MODEL

Derivation of thermal charging model

AEtb=PtbvLiNO3(CtbAT + AHR) (1)

AT=Tes - Tamb (2)

Estimated volume of fusible salt in eight modules: 1.1 6e-2 cubic meters. Density of Lithium Nitrate: 2380 kilograms per cubic meter.

Mean specific heat of Lithium Nitrate: 385 Joules per kilogram per degree Celsius. Latent Heat of Fusion of Lithium Nitrate: 367.6 kilojoules per kilogram.

Desired Temperature: 250 degrees Celsius. Change in Energy: 12.7 megajoules

theat= AEtb (3)

iscelsun

Efficiency of solar concentrating collector: 50%

Peak Irradiance of sun: 1372.7 joules per square meter.

Derivation of thermal dissipation model

0.15 B.T.U. * 4.89 ft2 _{* 400 F} _(A1)

ft2 OF hour

too_ = 0.9*A~b*SA*AT (4)

0.15

Equation (Al) equals the heat loss of the thermal battery. The expression in (Al) equals

85.96 joules per second. By comparing (Al) to (4), we see that the surface area of the

thermal battery is 4.89 square feet. The temperature difference was estimated to be 400 degrees Fahrenheit.

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APPENDIX B

DERIVATION OF SPRING CONSTANT

The force felt by the spring is equal to its spring constant multiplied by the deformation of the spring, F = kx. To determine what k, the spring constant, was equal to, I replaced F with the mass of one module. x would then naturally be the height of one module.

Mass of Lithium Nitrate in one module:

(2490)(1.45e-3) = 3.61 kg. Mass of Steel in one module:

(7769)(1.54e-3) = 11.3 kg. Mass of one module:

11.3 kg + 3.61 kg = 14.9 kg. Weight of one module:

(14.9)(9.8) = 146 N.

Deformation of spring: 0.051 m. Spring constant:

Designed and modeled solar cooker

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