Solar Oven Report 10/26/16

Team #9 (S.A.C.K. Squad)

Team Members: Sydney Hambrick, Ashley Schantz, Clare Cronin, & Kohl Anderson

1

Abstract

This project is the experimentation of design variables of a solar oven device that was made

of simple materials at a low cost. It would include: cardboard, tape, aluminum foil, and mylar

sheets. We would design the solar oven with certain limitations to the design to not allow the

oven to be too big and that would allow it to be similar in performance index compared to other

teams in the class. Our team chose which variables to change that would improve our numbers

the most to allow it to be more effective. So, our team allowed the window size to be larger

which caused the oven chamber depth to be not as deep as it could be. This allowed the reflectors

to have a greater size with the M/L ratio of 3 to allow the length be higher so that it would cause

the G multiplier variable to be greater increasing the predicted value. We found out that

increasing the reflector size would increase the value instead of increasing the insulation

however with increasing the insulation it allowed the temperature to not be lowered so quickly

when the sun goes away, we hypothesized during our first test. In our final design compared to

the test design we made the insulation thicker however didn’t change other dimensions besides

the outer oven chamber dimensions. We thought it to be safe to have the same window size with

the oven chamber depth to have the best insulation to allow the biscuit to cook all around quicker

than just on the top.

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Table Of Contents

INTRODUCTION……………………………………………………………………………….3

DESIGN THEORY AND ANALYTICAL MODEL…………………………………………..4

DESIGN REQUIREMENT……………………………………………………………………10

DESIGN

DESCRIPTION……………………………………………………………………....11

DESIGN JUSTIFICATION…………………………………………………………………....14

TEST PROCEDURE……………………………………………………………………….…..15

TEST RESULTS…………………………………………………………………………….….16

TEAM DYNAMICS…………………………………………………………………………....20

DESIGN CRITIQUE AND SUMMARY……………………………………………………...21

REFERENCES………………………………………………………………………………….22

APPENDICES…………………………………………………………………………………..23

EXCEL PREDICTION MODEL FOR FINAL OVEN DESIGN…………………...23

PI DETAIL SHEET…………………………………………………………………….29

DISSECTION NOTES…………………………………………………………………31

EXPERIMENTAL DATA COLLECTION SHEETS………………………………..33

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Introduction

Upon beginning this project, the team’s motivation was to explore solar radiation and the

engineering behind solar cooking. Hoping to learn how to create an efficient, functioning solar

oven of our own, we took on the challenge. We were expected to explore what variables would

affect the temperature that the oven chamber could reach as well as how to minimize the

performance index. Our main motive for building a solar oven was definitely for the learning

experience. As future engineers it is important to familiarize ourselves with situations and

problems that could be encountered later in life. This project gave us an opportunity to build on

our own something that is actually used throughout the world. In developing countries, solar

cooking is extremely important as it is an inexpensive solution for people unable to have hot

meals everyday. As sunlight has no cost, the energy source for the oven has no cost. The only

cost involved with solar cooking is the initial cost of the oven itself. The use of solar cooking

also reduces the need for firewood or fuel to cook.

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Design Theory and Analytical Mode

The mathematical model of the oven uses the formula

T io = T ambient + (U × A + U × A )sb sb w w

I × A × τ × a × sin(Θ + β) × Go wn

s

This is a model accounting for a box within a box. The area between the boxes is filled with

insulation material and the temperature that is measured by the model is that of the inner oven

chamber at thermal equilibrium and accounts both for the energy absorbed and the energy lost as

the oven is heated by the solar energy. The initial consideration in the creation of the oven is the

ambient temperature (Tambient) in oC. This is a variable that is not under human control but affects

the internal temperature as it is the state of equilibrium for the box without the addition of the

reflectors and insulation. Therefore the higher the ambient temperature is the higher the internal

oven temperature (Tio) can reach in oC. The following variables are more closely related to each

other a join together to form a larger equation than that of the Tambient and, as such, form a large

fraction. The numerator of this function corresponds to the energy collected from solar power or

factors that increase the retention and the denominator contains the variables of heat loss. The

first consideration is the solar power density (I o ) in W/m2. This is then multiplied by the area of

the window (Aw) in m2 that is “seen” by the sun to calculate the solar power intercepted by the

window of the internal oven chamber. The Aw is a function of the length (L) and width (W) of

the window. The area of the window that is “seen” by the sun is actually a function of the angle

of the window in respect to the sun, however. By using a right triangle with base y and L for the

hypotenuse, the formula becomes

sin(θ β) y = L × s +

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Once all of these expressions are confined the result is

A sin(θ β) P incident to window = I o × w × s +

is a variable out of the control of the designers as it is the angle at which the sun’s rays hit theθs

earth. is the angle of the box with respect to the ground and is a design variable. To maximizeβ

the power incident to the window the oven should be aligned so that This results β 0 .θs + = 9 o

in the equation which creates the highest power incident to the windowin(θ β) s s + = 1

possible. Next the power transmitted through the window into the oven cavity which is measured

by the optical transmission coefficient of the window ( ) and the number of window layers usedτ

(n). The next factor in the equation for the power contained in the oven is the absorption factor of

the cavity wall (a). Both of the cavity wall and the heat transfer should be as close to equalling 1

as possible so as to decrease the heat energy lost through through the box.

The final variable in the numerator is the gain term (G). The G is a function of the geometry of

the reflectors and is equal to the M/L ratio times the lid angle ( . The lid angle is uniquely ) Ω

determined for each M/L ratio and is the value at which the reflection of sunlight fully enters the

window and still fils the window.

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The addition of reflectors causes the power incident seen by the window to change from W y ×

to have the additional projected area of light seen by the window which equals The W . x ×

addition of the constant for the reflectivity of the mirror ( r ) makes the equation

W (y r x) P incident to window = I o × × + ×

The r values have already been experimentally determined and are given in Table 3

This is an extension of the original equation for the numerator of the equation. Substituting in the

expressions for x and y results in the equation

W [L sin(θ β) r M sin(a)] P incident to window = I o × × × s + + × ×

W L sin(θ β) r sin(a)] P incident to window = I o × × × [ s + + × LM ×

A [sin(θ β) r sin(a)] P incident to window = I o × w × s + + × LM ×

Then we apply the other variables associated and fare left with the expression for the total power

absorbed using a reflector

A [sin(θ β) r sin(a)] P incident to window = I o × w × a × τ n × s + + × LM ×

Therefore, given the original equation without reflectors we are able to find where the second

half is the gain from the reflectors and is therefore multiplied by the number of reflectors ( N )

and with the formula for the triangles to make a trapezoidal shape.(Cunningham, Solar Oven

Basics)

1 sin(a)]G = sin(θ + β)s

[sin(Θ + β) + N × r × ×sin(a)]s LM

× [ + LM ×

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[ ] 1 sin(a)]G = 1 + sin(θ + β)s

4 × r × ( ) × sin(a)LM

× [ + LM ×

r ( ) sin(a) G = 1 + 4 × × LM × 1 sin(a)] × [ + L

M ×

(Cunningham, Solar Oven Design Project Guidelines)

Heat is lost through two sources, the sides and window. The equation for the loss of heat through

the sides and bottom of the inter chamber is the overall heat transfer coefficient for the sides and

bottom of the interior oven chamber ( ) in W/m2 * oC multiplied by the area of the sides and U sb

bottom of the oven chamber ( ). This heat loss is from conductive loss as the interior oven as A sb

the oven chamber is in contact with the insulation which allows for heat to be transferred out of

the oven through the sides and bottom of the external oven chamber. The equation of the heat

loss through the window is the overall heat transfer coefficient for the window ( ) in W/m2 * U w

oC multiplied by the area of the window ( ) and all of these are design variables. The heat A w

loss through the window is through a combination of conductive and convective heat loss as the

heat is transferred out through the window as well as through the gap in the window allowing for

the air to pass out of the chamber and thermal energy to escape from the inner oven chamber.

These variable come together to form the bottom part of the equation (

Overall the heat loss of the entire oven is also affected by radiation as A U A ). U sb × sb + w + w

the heat is also lost through radiation increasing the heat transferred out of the oven. The U w

values are correlated to the number of windows used and the temperature inside of the oven. The

more windows the lower the coefficient of heat transfer, while the temperature inside of the U w

oven increases the coefficient in a positively correlational manor.

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The is a function of the thermal conductivity of the lining of the sides and bottom of the U sb

oven. The function modeling this is in which the k values are the .. U sb = x 1k 1 + x 2

k 2 + x 3k 3 + . + x n

k n

thermal conductivity for the nth material and kn is the thermal conductivity of the nth material.

Using the formula for the heat equilibrium of the internal oven the following graphs of the heat

are created. They are then plotted with the empirical temperatures found in Table 1 and the

intersection of these two graphs specifies the predicted temperature for each oven construction.

(Cunningham, Solar Oven Basics)

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Design Requirements:

Within the design and construction of the solar oven a number of constraints where applied to the

project. These constraints limited the number of options afforded in the construction of the oven.

These rules are as follows:

1. The internal oven chamber volume must equal 1000 cm3

2. The length(L) of the internal oven chamber window and height(h) of the internal oven

chamber must be at least 5cm

3. The window opening must be square

4. The oven must have convenient access to the internal oven chamber

5. The oven must be equipped with a rack that is able to hold a biscuit off of the oven walls

6. A digital thermometer must be placed inside of the oven, but the plastic housing must

remain outside of the oven and the reflector field

7. Design is focused on optimizing the Cost-based Performance Index

( ) and the Solar Oven Throw Down Performance IndexI P cost = CostT − T actual ambient

( )I P SOTD = T actualT − T + 1| actual predicted |

8. Maximum M/L ratio of 3

9. Oven must reach over 100oC

10. Focusing lenses and parabolic designs are not allowed

(Cunningham, Solar Oven Design Project Guidelines)

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Design Description

While designing the solar oven we first started with the solar oven excel document to change

the variables to around so that we can see the change in the predicted values for the test. It

allowed us to realize what affected the change in temperature dramatically. Since we had the

design restrictions like oven chamber window being a square, the chamber beging 1000 cm^3,

M/L ratio being 3 at highest, only two layer of mylar, a certain amount of cardboard, and other

options. So our group decided on a width and thought it optimal since it allowed the chamber to

be deep enough for the rack and to cook the biscuit. The dimensions were 14 cm for width and

length and the oven depth would be 5.1 cm. Then we decided to do M/L ratio of 3 so that it

allowed the G value to be highest it could be so that it was more effective in reflecting the sun

into the chamber. Our design of the reflectors were trapezoidal reflectors that would have a

greater surface area than the square reflectors and that the length of the reflectors were 42 cm

and the aluminum foil of the reflectors we tried to have the smoothest of reflector foil however it

came out wrinkled. We had two mylar sheets so that it magnifies the sun and having insulation

thickness of 15.5 cm of newspaper to allow the temperature to stay constant when the sun

disappears or some lack of heat. On the first oven we had the cardboard cut out each side so they

were each individual piece so that it was connected with tape on each edge. While on the second

oven we tried to optimize the cardboard while keeping it in biggest pieces so that it would limit

the amount of tape on the edges and that the heat would not leak out the edges on accident for the

outer oven chamber wall.

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Design Justification:

The design of the oven was based on simultaneously maximizing temperature and the

Performance Index ratio. This was done by using two mylar sheets as the addition of an

additional sheet more than halves the Uw value. The reflectors were chosen to maximize the heat

gain by created the largest allowed M/L ratio and as such had a ratio of 3. Newspaper was used

for the insulation as there was no cost associated with it other than the weight with a thermal

conductivity of 0.064 W/m*oC.. Cardboard was chosen as the walls as it has a low thermal

conductivity for the cost with a conductivity of 0.064 W/m*oC. The only change between the

final oven and the prototype was a 5.5 cm increase in the insulation size. This was the result of

an improved usage of the cardboard which allowed for more usable cardboard from the same

size sheet.

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Test Procedure

In order to align our solar oven with the sunlight, we used a backpack to prop it up at the

angle needed. We stuck the thermometer through the outer chamber into the inner chamber to

read the temperature of the inner chamber. During the second test, we placed a biscuit in the

inner chamber as well to demonstrate the fact that the oven gets to a reasonable temperature to

actually cook food. The ambient temperature was recorded as well as the IO. During the oven

tests, we recorded the temperature every five minutes for fifty minutes. We were able to see the

constant increase in temperature over time.

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Test results

In the first solar oven test we did not do it inside of a class session since that day was

rained out and we were told to do it on our own by the next class session. Our first test day was

on a saturday with the outside temperature being around 33 degrees Celsius allowing the Io value

to be higher since the sun was out without any obstructions. There was no wind to interfere with

the temperature. However at one point during the test one large cloud came into our line of

sunlight stopping the energy transferring into the oven chamber. This allowed us to notice that

our insulation for the chamber was not strong enough to allow the chamber to stay hot for long,

we also noticed this when opening the chamber. For the test we set up the oven in a clear

opening with a direct line of sight to the sun, using a backpack as a pivot to tilting the oven

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towards the sun at the proper angle. We then let the oven sit there for about a total of forty

minutes keeping an eye on the temperature as it rose steadily. The first high value we got was

around 150 degrees celsius while at the end of the day our high was 193 degrees celsius allowing

it to be close to our predicted value. To get to the highest values during the test it took about

seven minutes to get from the starting heat to the highest to level out. Since the during the test we

had a cloud block the sun it caused the heat to go down for a while then when the cloud moved

out of the way the temperature went to its highest point. During the test though we realized that

the duct tape that was holding the reflector panels onto the oven chamber was weakening in

strength to the point where it was peeling off from the melting of the adhesive. It caused us to

hold the reflectors on ourselves or to put more duct tape on in the end causing the seal for the

reflector lid with the oven chamber to be tighter allowing the temperature to increase to the

highest peak. While testing the oven there were other groups around us that were testing at the

same time so we discussed the rate at which their oven chambers went up. It allowed us to

compare and see if our chamber was working properly. Meanwhile with the Io values during the

testing phase on the first test it was at the highest value of the day and during that time it stayed

constant so that it didn’t change dramatically. On the second test day the Io value was high

however it was at a decreasing value during the test so that the highest temperature we could get

would be decreasing and not constant.

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For the second solar oven test was at 3:30 on October 20th. The temperature outside was

32.5 degrees Celsius and the sky had a minimal about of clouds in it which allowed the Tio to be

higher. There was a small amount of wind to affect the temperature. At some points people

would walk by or stand in front of our oven momentarily stopping the energy transfer to the oven

chamber. Our insulation was so well compacted that it was bursting out of the outer oven

chamber. In order to solve this problem, we continually had to reinforce our seams with more

duct tape. We propped our oven up on a backpack so that our oven chamber was directly in the

line of the sunlight. We then proceeded to record the temperature for every five minutes for fifty

minutes. Our final temperature was 147.1 degrees Celsius which was not as close to our

predicted as we would have liked. We noticed the duct tape attaching our reflectors to the rest of

the chamber started to melt, so we had to reinforce the tape with more duct tape. We were also

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able to compare the rate of our temperature increasing with other groups around us which

allowed us to notice if anything was going wrong with our oven.

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Team Dynamics

Overall, we all worked equally on every part. No one did one entire piece alone, each

member worked together on whatever needed to be completed at the time. As our schedules did

conflict a few times, not everyone was always present at all times, however whenever a meeting

was missed, it was also made up. Although everyone may have not contributed to the same

things, equal work was still done. Specifically Kohl was in charge of the excel and was helped

by Sydney. Ashley was in charge of the construction of the box with Clare working as her

assistant. Sydney was in charge of the measurements of the solar oven. No conflicts arose

throughout the project given the interpersonal relationship that was developed throughout the

course of the project.

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Design Critique and Summary

Given the experience of the two tests performed as well as the ability to observe the test

designs of the other teams. First of all, after seeing the results of the Solar Oven Throw Down,

we were exposed to an abundance of new ideas. We could have optimized the window size by

creating a trapezoidal prism with the inner chamber of the oven or covered the outside of the

inner chamber with aluminum foil to increase the temperature. Also, on our final oven, our

window construction melted during the throw down which greatly affected the temperature of

the oven in the end. Additionally, the conditions on the two test days were not the same which

also made a difference. However, it is difficult to critique our two ovens in depth without having

built more ovens. There needed to be more than just two ovens to really create a trend and

redesign a better oven. We would suggest to future teams to maximize the M/L ratio. The

dynamic of our team, as mentioned above, was very effective and efficient. We have compatible

personality types which assisted with the design process. The only downfall to how well our

team gets along is that occasionally we converse too much which can distract us from the work,

but completing the project on time was never an issue.

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References

Cunningham, Brian. Solar Oven Basics.

Cunningham, Brian. Solar Oven Design Project Guidelines.

Cunningham, Brian. Solar Oven Excel Guide.

Cunningham, Brian. Solar Oven Report Guidelines.

Cunningham, Brian. Solar Oven Team Prediction Model.

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Appendices

Solar Oven Excel numbers and Graph

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25

Test 2 One Mylar Sheet

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Test 2 Two Mylar Sheets

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Test 1 One Mylar Sheet

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Test 1 Two Mylar Sheets

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PI Detail Sheet

Solar Oven cost breakdown: First Oven

Materials:

Specific material Amount used Cost basis Cost for amount used

Duct tape 29 yds $0.07/yd $2.03

Box cutter N/A N/A $5.47

Newspaper 5 newspapers $0.00 $0.00

Aluminum foil 26.5 ft2 $0.19/ft2 $5.04

Black Paper 3 $0.03/sheet $0.09

Cardboard 4 m2 $1.75/m2 $7.00

Mylar 2 sheets $0.25/sheet $0.50

(1) TOTAL MATERIAL COST:

$20.13

(2) Transportation cost:

Weight of oven: 3.0 lb

X $.20/lb = $0.60

(3) Labor cost: fixed at $5.00 per team

Total oven cost: add (1) + (2) + (3) = 25.73

Performance Index:

Tambient = 33.5 degrees C

Tactual = 193.0 degrees C

Cost-Based PI = 6.20 SOTD PI = 14.8

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Solar Oven cost breakdown: Second Oven

Materials:

Specific material Amount used Cost basis Cost for amount used

Duct tape 37 yds $0.07/yd $2.57

Box cutter N/A N/A $5.47

Newspaper 6 newspapers $0.00 $0.00

Aluminum foil 26.5 ft2 $0.19/ft2 $5.04

Black Paper 3 $0.03/sheet $0.09

Cardboard 4 m2 $1.75/m2 $7.00

Mylar 2 sheets $0.25/sheet $0.50

(1) TOTAL MATERIAL COST:

$20.67

(2) Transportation cost:

Weight of oven: 4.9 lb

X $.20/lb = $0.98

(3) Labor cost: fixed at $5.00 per team

Total oven cost: add (1) + (2) + (3) = 26.65

Performance Index:

Tambient = 32.5 degrees C

Tactual = 147.1 degrees C

Cost-Based PI = 4.30 SOTD PI = 3.03

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Dissection Notes

Before Disassembly:

● Box is a box within a box. Trapezoidal reflectors.

● M/L ratio of 3

● Reflectors come off

● 2 Mylar sheets

Outside Dimensions:

● _____ by 34 ½ cm

● Height: 16 cm

● Window is 14 by 14 cm

Used black duct tape to tape corners together

Omega was 105 degrees

There were four reflectors - trapezoidal - they met at corners, foil is very smooth.

M/L = 3

Correct Omega angle

Thermometer put between Mylar and window, not stuck through the box

Used tin foil rack, reflectors removed for access

Books/Backpacks to create angle

Lots of black duct tape

Internal:

❏ Covered in black paper, really smooth

❏ Chamber was 14 by 14 by 5.1 cm, insulation thickness 10.5 cm, dimensions uniform

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❏ Cardboard, black duct tape, black paper, exterior edges has black tape sealing it

❏ Used 2 Mylar sheets, there isn’t much gap at all, maybe 3 or 4 mm

❏ Newspaper packed pretty tightly

❏ Black duct tape used to put oven together

❏ Lots of newspaper, whole exterior of chamber covered in black tape

After Disassembly:

➔ Strengths- tin foil very smooth, lots of insulation, measurements accurate

➔ Weaknesses- Mylar sheets were too close, heavy, rack cutting it close on chamber height

➔ Large reflectors and good insulation make good oven

➔ Use black tape to seal everything together, use largest window area possible

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Data Collection Sheet