manufacturing of a food dehydrator and modeling of the drying process in matlab

A Graduation Project Report

MODELING OF THE DRYING IN A FOOD DEHYDRATOR

By

TUGAY TANIK

D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g

F a c u l t y o f E n g i n e e r i n g a n d A r c h i t e c t u r e

Y e d i t e p e U n i v e r s i t y

J u n e 2 0 1 5 , I s t a n b u l , T u r k e y

MODELING OF THE DRYING IN A FOOD DEHYDRATOR

By

TUGAY TANIK

DATE OF APPROVAL: 12 June 2015

APPROVED BY: TUGAY TANIK

Assoc. Prof. Dr. HOJIN AHN

Thesis Supervisor

D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g

F a c u l t y o f E n g i n e e r i n g a n d A r c h i t e c t u r e

Y e d i t e p e U n i v e r s i t y

J u n e 2 0 1 5 , I s t a n b u l , T u r k e y

ACKNOWLEDGEMENT

I would like to thank my advisor, Assoc. Prof. Dr. Hojin AHN. Without his help and

attention, this would have never been possible.

I would like to thank my parents, who have encouraged me to do my best in school

and life.

I would also like to thank my friend Cüneyt ÖZNAM, who has helped me during the

manufacturing of the prototype and experiments.

Tugay TANIK

III

Modeling of the Drying in a Food Dehydrator TANIK

Dept. of Mech. Eng., Yeditepe Univ. IV

ABSTRACT

Plant foods can produced in certain seasons of the year in limited amount. These foods

have a life time depending on the storage conditions. Foods completed their life rot and

become inconsumable. Food drying is one of the methods to prevent rotting and to extend the

ability to consume food. Also food drying is used to change structure of the food for using it

as dry food in different fields. Drying can be made naturally by the sun and wind, but if a food

dehydrator machine which can control the temperature and flow rate of the air is used, drying

occurs in less time and in more hygienic conditions than natural drying.

In this project, a food dehydrator which is suitable for home use was designed and

food drying in this food dehydrator was modeled. In the design, unlike standard dryer designs,

when some of the air which is heated for using in drying is thrown out, some of the heated air

is not thrown out and it is recycled to the system. So, desired temperature in the system is

provided with less power consumption in less time because that all of the unsaturated hot air

is not thrown out and a part of it is used again.

Design of the food dehydrator was drawn as 3D model in SolidWorks software. Then

first prototype was produced. Drying process in the food dehydrator was modeled via

MATLAB software. Parameters affecting the drying as; amount of the air entering the dryer,

amount of the air recycling in the dryer, heater power and fan flow rate capacity were varied

via MATLAB model and results were observed in virtual environment. Based on these

results, some improvements was made on the prototype. At the same time, temperature

sensors, humidity sensors, thermocouples, voltmeter, orifice and pressure sensors were

connected on the prototype and experiments were performed. Then data obtained from

experiments were collected. These data were compared with the data obtained from

MATLAB to observe the consistency. Finally, ideal drying time and drying cost were

determined and prototype was formed with improving.


Dept. of Mech. Eng., Yeditepe Univ. V

ÖZET

Bitkisel besinler senenin belirli mevsimlerinde, belirli miktarlarda üretilebilirler. Bu

besinlerin saklama koşullarına bağlı bir ömürleri vardır. Ömrünü tamamlayan besinler çürür

ve tüketilemezler. Çürümeyi önlemek ve besinlerin tüketilebilme süresini uzatmak için

besinleri kurutmak kullanılan yöntemlerden biridir. Ayrıca besinlerin yapısını değiştirip başka

alanlarda kuru gıda olarak kullanmak için de kurutma işlemi yapılır. Kurutma işlemi güneş ve

rüzgâr ile doğal olarak yapılabildiği gibi, sıcaklık ve hava akışının kontrol edilebildiği

kurutma makinelerinde daha kısa sürede, daha sağlıklı koşullarda ve kontrollü bir şekilde

yapılabilir.

Bu projede, evde kullanıma uygun bir gıda kurutucusu tasarımı yapılmış ve bu

kurutucu içerisinde gerçekleşecek kuruma olayı modellenmiştir. Yapılan tasarım standart

kurutucu tasarımlarından farklı olarak, kurutmada kullanılan sıcak havanın bir kısmı dışarı

atılırken, bir kısmı sisteme döndürülerek tekrar kullanılmaktadır. Henüz doygun hale

gelmemiş sıcak havanın tamamı atılmayıp, bir kısmı tekrar kullanıldığı için sistem içerisinde

istenen ideal sıcaklık değeri daha az güç tüketerek, daha kısa sürede sağlanmaktadır.

Tasarım SolidWorks programı ile 3 boyutlu olarak modellenmiş ardından ilk prototip

üretilmiştir. Kurutucu içerisinde gerçekleşen besinin kuruma olayı MATLAB programı ile

modellenmiştir. Yapılan MATLAB modeli ile kurutmayı etkileyen; kurutucuya giren hava

miktarı, kurutucu içerisinde tekrar kullanılan hava miktarı, ısıtıcı gücü ve fan debisi gibi

parametreler değiştirilerek sanal ortamda ki sonuçlar gözlemlenmiştir. Bu sonuçlara

dayanarak prototipte bazı geliştirmeler yapılmıştır. Aynı zamanda prototip üzerine bağlanan

sıcaklık sensörleri, nem sensörleri, ısıl çiftler, voltmetre, orifis ve basınç sensörleri ile, yapılan

deneylerden elde edilen veriler toplanmıştır. Bu veriler, MATLAB’ de oluşturulan modelden

alınan veriler ile karşılaştırılıp tutarlılıkları incelenmiştir. Sonuç olarak uygun kurutma zamanı

ve uygun kurutma maliyeti belirlenmiş ve yapılan iyileştirmeler ile prototip son halini

almıştır.


Dept. of Mech. Eng., Yeditepe Univ. VI

TABLE OF CONTENTS

TITLE PAGE…………………………………………………………………………………...I

APPROVAL SHEET.………………………………………………………………………....II

ACKNOWLEDGEMENT ...…………………………………………………………………III

ABSTRACT…………………………………………………………………………………..IV

ÖZET…………………………………………………………………………………..............V

TABLE OF CONTENTS…………………………………………………………………..…VI

LIST OF FIGURES…………………………………………………………………......…....IX

LIST OF TABLES……………………………………………………………………........…XI

1. INTRODUCTION .............................................................................................................. 1

2. LITERATURE SURVEY ................................................................................................... 3

2.1. Patent Research……………………………………………………………….……....3

2.2. Theory…………………………………………………………………………………5

3. SYSTEM DESIGN AND MODELING OF THE PROTOTYPE .................................... 18

4. PRODUCTION OF THE PROTOTYPE .......................................................................... 21

4.1. Production of the case ................................................................................................ 21

4.2. Production of the chassis ........................................................................................... 22

4.3. Production of the trays ............................................................................................... 23

4.4. Production of the door ............................................................................................... 23

4.5. Procurement of the fan, heater, and controller .......................................................... 24

4.6. Assembly of the orifice meter.................................................................................... 26


Dept. of Mech. Eng., Yeditepe Univ. VII

4.7. Assembly of the prototype ......................................................................................... 28

5. DEVELOPMENT OF THE PROTOTYPE ...................................................................... 29

5.1. Production of a new heater ........................................................................................ 29

5.2. Changing the fan system ............................................................................................ 32

5.3. Changing the controller and power supply………………………………………….33

5.4. Adding shelves and trays ........................................................................................... 33

6. IMPROVEMENT OF THE SOLIDWORKS DRAWING ............................................... 34

7. EXPERIMENTAL SETUP ............................................................................................... 35

8. RESULTS OF THE EXPERIMENTS .............................................................................. 39

9. MATLAB PROGRAMMING .......................................................................................... 41

9.1. Problem Statement ..................................................................................................... 41

9.2. MATLAB codes ........................................................................................................ 42

9.2.1. Program #1: Determination of the ideal drying process…………………..…...42

9.2.2. Program #2: Calculation of the Vaporization Rate……………………….……44

9.2.3. Program #3: Vaporization Rate Depending on Water Activity …………….…45

10. MATLAB RESULTS ....................................................................................................... 48

10.1. The differences of the Prototype from the Standard Food Dehdrator ........................ 48

10.2. Finding the Ideal Drying Case ................................................................................... 48

10.3. Estimation of the Experimental Result ...................................................................... 52

10.4. Vaporization Rate Calculation ................................................................................... 52


Dept. of Mech. Eng., Yeditepe Univ. VIII

11. CONCLUSION ............................................................................................................. 54

12. APPENDICES ............................................................................................................... 56

13. REFERENCES .............................................................................................................. 71

13. BIOGRAPHY ................................................................................................................ 73


Dept. of Mech. Eng., Yeditepe Univ. IX

LIST OF FIGURES

Figure 1: Mike Moles' Food Dehydrator .................................................................................... 4

Figure 2: Moisture Content vs time curve .................................................................................. 5

Figure 3: Drying rate vs moisture content curve ........................................................................ 6

Figure 4: The adiabatic saturation process ................................................................................. 8

Figure 5: Operating principle of the system ............................................................................. 18

Figure 6: Hand Sketch of the prototype.................................................................................... 19

Figure 7: 3D model of the prototype ........................................................................................ 19

Figure 8: Cross-section view of the prototype.......................................................................... 20

Figure 9: Parts of the prototype ................................................................................................ 20

Figure 10: Disused computer cases .......................................................................................... 21

Figure 11: Insulation coating in the case .................................................................................. 21

Figure 12: Grinding of the corners ........................................................................................... 22

Figure 13: Chassis of the prototype .......................................................................................... 22

Figure 14: Galvanized steel trays ............................................................................................. 23

Figure 15: The door of the dryer with air outlet hole ............................................................... 23

Figure 16: Disassembly of the broken hairdryer ...................................................................... 24

Figure 17: Components of the broken hairdryer ...................................................................... 24

Figure 18: Renovated hairdryer mechanism ............................................................................. 25

Figure 19: Fixing of the fan and heater .................................................................................... 25

Figure 20: Opening the hole with hole saw drill ...................................................................... 26

Figure 21: Assembly of the orifice with the frame ................................................................... 26

Figure 22: Rasping of the pressure taps.................................................................................... 27

Figure 23: Measuring of the orifice pipe diameter ................................................................... 27

Figure 24: Completed Prototype .............................................................................................. 28

Figure 25: SolidWorks drawing of the completed prototype ................................................... 28


Dept. of Mech. Eng., Yeditepe Univ. X

Figure 26: Nonflammable material cutting .............................................................................. 29

Figure 27: Frame plate forming ................................................................................................ 30

Figure 28: Locker plate............................................................................................................. 30

Figure 29: Curled up nichrome wire......................................................................................... 31

Figure 30: Porcelain Terminal .................................................................................................. 31

Figure 31: The heater unit ........................................................................................................ 32

Figure 32: A pair of fan ............................................................................................................ 32

Figure 33: Settlement of fans and heater .................................................................................. 33

Figure 34: The power supplies connected in series .................................................................. 33

Figure 35: Dimensions of the Prototype ................................................................................... 34

Figure 36: The cross-section view of the prototype ................................................................. 34

Figure 37: Disassembly of the prototype .................................................................................. 34

Figure 38: Location of the thermocouples and sensors ............................................................ 35

Figure 39: Thermocouples and sensor locations at the point 3 and 4....................................... 35

Figure 40: Thermocouple ends ................................................................................................. 36

Figure 41: 20 Channel Multiplexer .......................................................................................... 37

Figure 42: The Sensiron SHT75 sensor .................................................................................... 37

Figure 43: The data acquisition board ...................................................................................... 38

Figure 44: OMEGA PX274 differential pressure transmitter .................................................. 38

Figure 45: Experimental Set-up ................................................................................................ 38

Figure 46: Relative Humidity Result of the 96W Full Open Strawberry Test ......................... 40

Figure 47: Relative Humidity Result of the 96W Full Open Strawberry Test ......................... 40

Figure 48: Model of the problem .............................................................................................. 41

Figure 49: Algorithm of the vaporization rate .......................................................................... 44

Figure 50: Water Activity & Moisture Content Graph for Mercerized Cotton [24] .................. 46

Figure 51: Water Activity & Moisture Content Graph at 55˚C ................................................ 46


Dept. of Mech. Eng., Yeditepe Univ. XI

Figure 52: Precaution Code for Water Activity........................................................................ 47

Figure 53: Change of the Drying Time Depending on the Heater Power Change ................... 50

Figure 54: Change of the Drying Cost Depending on the Heater Power Change .................... 50

Figure 55: Change of the Drying Time Depending on the Inlet Air Flow Rate Change.......... 50

Figure 56: Change of the Drying Cost Depending on the Inlet Air Flow Rate Change ........... 51

Figure 57: Change of the Drying Time Depending on the Fan Flow Rate Change ................. 51

Figure 58: Change of the Drying Cost Depending on the Fan Flow Rate Change .................. 51

Figure 59: Vaporization Rate with constant water activity ...................................................... 52

Figure 60: Vaporization Rate with instant water activity changes ........................................... 53

LIST OF TABLES

Table 1: Location of the thermocouples and sensors ............................................................... 36

Table 2: Result of the Wet Towel Drying Test ........................................................................ 39

Table 3: Result of the Strawberry Drying Test......................................................................... 39

Table 4: Program #1.1 Specifications....................................................................................... 42

Table 5: Program #1.2 Specifications....................................................................................... 42

Table 6: Program#2 Specifications........................................................................................... 45

Table 7: Program#3 Specifications........................................................................................... 45

Table 8: Result of the Program#1.1 Depending on the Power Change .................................... 48

Table 9: Result of the Program#1.1 Depending on the Inlet Air Flow Rate Change ............... 49

Table 10: Result of the Program#1.1 Depending on the Fan Flow Rate Change..................... 49

Table 11: Estimation of the Experimental Result ..................................................................... 52

Table 12: Total Mass of the Evaporated Water ........................................................................ 53


Dept. of Mech. Eng., Yeditepe Univ. 1

1. INTRODUCTION

Most of the plants does not produce food continuously. They produce food in a specific

season once each year. Therefore, plant foods must be consumed in the season or preserved

for eating during the off season. If the food is not stored under the suitable conditions, it rots.

Rotting is caused by growth of bacteria on food. To prevent rotting, the food must be rendered

an unfavorable environment survival of the bacteria. The bacteria which decay the food

usually cannot stay alive at high temperature, extreme cold or bone dry environment. Because

the foods lose their structural features, nutritional properties and taste at high temperature,

freezing or drying process are used for preserving food. While frozen foods remain the same

as in the season; form, taste and nutritional properties of the dried food change. Generally,

dried food are not use in the same manner as fresh state of it. Food drying can also be used to

obtain different product. Therefore, dry food industry has occurred.

Food can be dried naturally by spreading the ground outdoors with the help of the sun

and wind. This method has been applied since ancient times. The sun and wind are good and

costless sources. However, they are unreliable. Drying cannot be controlled exactly. Another

method to dry food is using oven or food dehydrator. This method is more costly than solar

drying, but drying temperature, air velocity and drying time can be controlled with these

machines.

Several types of food drying system have been produced. Some of these are cyclone

drying, drum drying and freeze drying systems. These systems which include too large and

expensive equipment are applied in the industry. In these systems, especially in freezing

drying, food properties are maintained substantially. Besides, changes in the form, surface and

taste are minimized. However, these systems are not practical for domestic use. People who

want to dry food at home need small and inexpensive food dryers which have low operating

costs. In the market, there are this type food dryers. Prices of them vary between 50$ and

1000$ depending on capacity and power. Their power consumption are between 125W and

1000W, and 1 𝑚2drying costs are between 0.7$ (1.87 TL) and 0.9$ (2.4 TL). [1]



In this project, a food dehydrator which is suitable for domestic use was designed. In

the design, all of the heated air is not thrown out, a part of it is returned back to system. So,

desired temperature in the system is provided with less power consumption in less time

because that all of the unsaturated hot air is not thrown out and a part of it is used again.

In the experiments, initially, wet towel pieces were used for drying because towel

pieces can be wetted repeatedly without any cost. Drying process in the dehydrator was

modeled based on the towel with the help of MATLAB software. Then, the strawberry was

selected as fruit to be dried. Before drying, strawberries were finely chop to extend the drying

surface area. Also, a model was formed for strawberries in MATLAB. Parameters of the

drying such as; flow rate of fresh air, flow rate of air mixture (flow rate of fan), drying

temperature and heater power were varied and various drying time and drying cost values

were obtained from MATLAB.

According to information which is gained from calculations in MATLAB, a new

heater and fan system was made, flow rate of the fans were adjusted, shelves and trays were

added the system. Then, some tests were made with developed prototype and result of it was

compared with result of the model which was formed in MATLAB to examine the

consistency. Consequently, ideal drying time and drying cost value were determined.



2. LITERATURE SURVEY

This report focus on two main issues. They are manufacturing of a food dryer prototype

which has special air circulating system and modeling of the food drying in the food dryer via

MATLAB. Therefore, literature survey of the report is divided into patent research about

design and theory about drying.

2.1. Patent Research

After some patent researches, a patent of the food dehydrator which has similar air

circulation system to ours, was found. This is Mike Moles’ patent of “Continuous air flow

dehydrator and method for improved energy efficiency” [2] . Detailed information about the

patent is as follows:

Title of the patent: Continuous airflow dehydrator and method for improved

energy efficiency

Publication number: US20070240328 A1

Publication type: Application

Application number: US 11/406,111

Publication date: Oct 18, 2007

Filing date: Apr 18, 2006

Priority date: Apr 18, 2006

Inventors: Mike Moles

Original Assignee: Mike Moles



According to Mike Moles, this food dehydrator increases the energy efficiency and

decreases the costs and air pollution with different air circulation design. In this design, air

inlet to the air tunnel is closed and heated air is drawn from the drying chamber by the

recirculating fan. So, the air is heated again and the required power of the heater is decreased.

Also, a filter provides to remove moisture and contaminants from the recycled air. A diversion

hood provide to direct the recycled air.

Figure 1: Mike Moles' Food Dehydrator

Mike Moles’ dehydrator is more complicated than ours. It has more components such

as; filter, recirculating fan and diversion hood. This design was developed for industrial

usage. However, in this project, an inexpensive food dehydrator design was aimed for

domestic usage. Therefore, simplified of the design in this patent was used in this project.



2.2. Theory

In this project, drying process of a food in a dehydrator was modeled in MATLAB.

Therefore, some researches about drying, drying mechanism, drying methods and drying

calculations.

“Drying is a complex operation involving transient transfer of heat and mass along with

several rate processes, such as physical or chemical transformations, which, in turn, may

cause changes in product quality as well as the mechanisms of heat and mass transfer.

Physical changes that may occur include: shrinkage, puffing, crystallization, glass transitions.

In some cases, desirable or undesirable chemical or biochemical reactions may occur leading

to changes in color, texture, odor or other properties of the solid product.” [3]

“Drying of foods implies the removal of water from the foodstuff. In most cases, drying

is accomplished by vaporizing the water that is contained in the food, and to do this the latent

heat of vaporization must be supplied. There are, thus, two important process-controlling

factors that enter into the unit operation of drying:

-Transfer of heat to provide the necessary latent heat of vaporization,

-Movement of water or water vapor through the food material and then away from it to

effect separation of water from foodstuff.” [4]

The drying process

“Drying is normally carried out by heating the solid in air so that the water evaporates

into the air. The drying process may be followed via a graph of moisture content vs time.

Figure 2: Moisture Content vs time curve



In a typical drying curve there are three distinct zones:

Zone A is a warming up period.

Zone B is the constant rate drying period. During this period, the drying curve is a

straight line.

Zone C is the falling rate period. During this period, the last of the moisture is being

removed and the rate of drying falls as the moisture content falls. The moisture content

will eventually fall to a constant value. This is known as the equilibrium moisture

content.

If tangents to the drying curve are drawn, the drying rate can be measured at various

points on the drying curve and a graph of drying rate vs moisture content drawn.

Figure 3: Drying rate vs moisture content curve

In Figure 3,

Point A represents the end of the warming up period

Point B represents the critical moisture content. This is the moisture content when the

drying changes from constant rate drying to falling rate drying

Point C represents the equilibrium moisture content.



Drying mechanisms

Constant rate drying occurs when the solid material is completely covered with a layer

of water. Drying occurs by evaporation from the surface of the water layer and the rate is

governed purely by the temperature and moisture content of the drying air.

When sufficient water has evaporated so that a layer of water no longer covers the

surface of the solid, water has to migrate from the interior of the solid by diffusion before it

can evaporate from the surface of the solid. Under these circumstances, as the water content

of the interior falls, the rate of diffusion to the surface falls and, hence the rate of evaporation

falls due to the need to overcome capillary forces and diffusion resistance.” [5] [6]

In addition, evaporation occurs at the liquid vapor interface, when the vapor pressure is

less than the saturation pressure of the liquid at a given temperature. In other words, “drying

does not occur at all if the relative humidity of the environment is 100 percent. In this case,

there is no transformation from the liquid phase to the vapor phase, and the two phases are in

phase equilibrium.” [7]

“Before proceeding to the basic principles, it is useful to note the following unique

features of drying which make it a fascinating and challenging area for R&D:

• Product size may range from microns to tens of centimeters (in thickness or depth)

• Product porosity may range from zero to 99.9 percent

• Drying times range from 0.25 sec (drying of tissue paper) to five months (for certain

hardwood species)

• Production capacities may range from 0.10 kg/h to 100 t/h

• Product speeds range from zero (stationary) to 2000 m/s (tissue paper)

• Drying temperatures range from below the triple point to above the critical point of the

liquid

• Operating pressure may range from fraction of a millibar to 25 atmospheres



• Heat may be transferred continuously or intermittently by convection, conduction, radiation

or electromagnetic fields

Clearly, no single design procedure that can apply to all or even several of the dryer

variants is possible. It is therefore essential to revert to the fundamentals of heat, mass and

momentum transfer coupled with a knowledge of the material properties (quality) when

attempting design of a dryer or analysis of an existing dryer.” [8]

Drying calculations

In this report, drying process in the produced dehydrator was modeled as considering

about basic heat and mass transfer knowledge. Also, some thermodynamics knowledge as

gas-air mixtures and air conditioning was used. Used principles and formulas are given as

follow:

Mass balance:

Figure 4: The adiabatic saturation process

The mass flow rate of dry air remains constant:

�̇�𝑎1= �̇�𝑎2

= �̇�𝑎 (1)



The mass flow rate of vapor in the air increases by an amount equal to the rate of

evaporation �̇�𝑓:

�̇�𝑤1= �̇�𝑓 = �̇�𝑤2

(2)

Or

�̇�𝑎𝜔1 + �̇�𝑓 = �̇�𝑎𝜔2 (3)

Thus,

�̇�𝑓 = �̇�𝑎(𝜔2 − 𝜔1) (4)

�̇�𝑓: Mass flow rate of the vapor

�̇�𝑎: Mass flow rate of the dry air

𝜔1: Specific humidity of the unsaturated (inlet) air

𝜔2: Specific humidity of the saturated (outlet) air

“Mass flow rate is the mass of a substance which passes per unit of time.

Its unit is kilogram per second in SI units, and slug per second or pound per second in US

customary units. The common symbol is �̇� (pronounced "m-dot").” [9]

�̇� = lim∆𝑡→0

∆𝑚

∆𝑡=

𝑑𝑚

𝑑𝑡 (5)

“Specific (absolute) humidity (𝜔) (or moisture content) is ratio of the mass of water

vapor in air to the total mass of the mixture of air and water vapor.” [10]

𝜔 = 𝑚𝑣

𝑚𝑎=

𝑃𝑣𝑉/𝑅𝑣𝑇

𝑃𝑎𝑉/𝑅𝑎𝑇=

𝑃𝑣/𝑅𝑣

𝑃𝑎/𝑅𝑎= 0.622

𝑃𝑣

𝑃𝑎=

0.622𝑃𝑣

𝑃−𝑃𝑣 (kg water vapor/kg dry air) (6)



Where;

𝑚𝑣: Mass of the water vapor

𝑚𝑎: Mass of the dry air

𝑃𝑣: Vapor pressure

𝑃𝑎: Dry air pressure

𝑃: Total (atmospheric) pressure

In the calculations of the report specific humidity was used as depending on the

relative humidity:

𝜔 = �̇�𝑣

�̇�𝑎= 0.622

∅𝑃𝑠𝑎𝑡@𝑇

𝑃−𝑃𝑠𝑎𝑡@𝑇 (7)

Where;

∅: Relative humidity

𝑃𝑠𝑎𝑡@𝑇: Saturation pressure at temperature “T”

“Relative humidity (∅) is the amount of moisture in the air compared to what the air

can "hold" at that temperature. When the air can't "hold" all the moisture, then it condenses as

dew.” [11]

∅ = 𝑃𝑣

𝑃𝑠𝑎𝑡@𝑇 (8)

According to “Equation 8”, vapor pressure is;

𝑃𝑣 = ∅𝑃𝑠𝑎𝑡@𝑇 (9)



Energy Balance

�̇�𝑖𝑛 = �̇�𝑜𝑢𝑡 (Since �̇� = 0 𝑎𝑛𝑑 �̇� = 0) (10)

�̇�𝑎ℎ1 + �̇�𝑓ℎ𝑓 = �̇�𝑎ℎ2 (11)

If there is a heater in a system which heats inlet air ( �̇� ≠ 0);

�̇�𝑎ℎ1 + �̇� = �̇�𝑎ℎ2 (12)

Where;

ℎ1: Enthalpy of the inlet air

ℎ2: Enthalpy of the outlet air

�̇�: Power of the heater [kJ/sec = kW]

Enthalpy is defined as a thermodynamic potential, designated by the letter "H", that

consists of the internal energy of the system (U) plus the product of pressure (P)

and volume (V) of the system: [12]

𝐻 = 𝑈 + 𝑃𝑉 (13)

𝐻 = 𝐻𝑎 + 𝐻𝑣 = 𝑚𝑎ℎ𝑎 + 𝑚𝑣ℎ𝑣 (14)

Dividing by 𝑚𝑎 gives:

ℎ =𝐻

𝑚𝑎= ℎ𝑎 +

𝑚𝑣

𝑚𝑎ℎ𝑣 = ℎ𝑎 + 𝜔ℎ𝑣 (15)

Where;

𝐻: Total enthalpy

ℎ: Specific enthalpy

ℎ𝑣 ≅ ℎ𝑔: Vapor specific enthalpy

ℎ𝑎 = 𝑐𝑝𝑇: Enthalpy of dry air



So;

ℎ = 𝑐𝑝𝑇 + 𝜔ℎ𝑔 (16)

Where;

𝑐𝑝: Specific heat (=1.005 kJ/kg˚C for air at room temperature)

“Specific heat is the amount of heat per unit mass required to raise the temperature by one

degree Celsius.” [13]

If “Equation 16” is multiplied by �̇�𝑎𝑖𝑟, energy flow is obtained [14] :

�̇�𝑎𝑖𝑟ℎ = �̇�𝑎𝑖𝑟𝑐𝑝𝑇 + �̇�𝑎𝑖𝑟𝜔ℎ𝑔 (17)

Where;

�̇�𝑎𝑖𝑟: Mass flow rate of the dry air

“For calculating the surface vapor density (𝜌𝑣𝑠), ideal gas law can be used at low

temperatures (below 400 kelvins):

𝑃𝑉 = 𝑛𝑅𝑇 (18)

Where 𝑛 is the number of moles, which is related by density by 𝑛 = 𝑀/𝑚, where 𝑀 is the

mass of water present and 𝑚 is the molar mass of water (18.01528 grams/mole). R is the gas

constant (8.3144621 J/molK)” [15]. Thus,

𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =𝑀

𝑉=

𝑃𝑚

𝑅𝑇 (19)

So vapor density on the surface can be find as follow;

𝜌𝒗𝒔 =𝑎𝑤𝑃𝑠𝑠

𝑅𝑣𝑇𝑠 (20)



Where;

𝑅𝑣 =𝑅

𝑚= 0.462 (The individual gas constant water vapor (J/kg K))

𝑃𝑠𝑠: Saturation pressure of the surface

𝑇𝑠: Surface temperature

𝑎𝑤: The water activity

“Water activity (𝑎𝑤) is defined as the ratio of the equilibrium water vapor pressure of

a foodstuff (𝑝𝑤, kPa) to the saturated vapor pressure (𝑝𝑤𝑜, kPa) at the same temperature.”[16]

𝑎𝑤 =𝑝𝑤

𝑝𝑤𝑜 (21)

For calculating temperature of the drying surface:

𝑇𝑆 = 𝑇∞ −ℎ𝑓𝑔@𝑇∞

𝐶𝑝(𝐿𝑒)2/3

𝑀𝑤

𝑀𝑎𝑖𝑟

𝑃𝑣𝑠−𝑃𝑣∞

𝑃0 (22)

Where;

𝑇𝑠: Surface temperature

𝑇∞: Ambient temperature

𝑀𝑤/𝑀𝑎𝑖𝑟: Molar mass ratio of the water and air (18.015/28.97 = 0.622)

𝑃𝑣𝑠: Saturation vapor pressure

𝑃𝑣∞: Actual vapor pressure

𝑃0: Atmospheric pressure

𝐶𝑝: Specific heat

𝐿𝑒: Lewis number



“Lewis number (Le) is a dimensionless number defined as the ratio of thermal

diffusivity to mass diffusivity. It is used to characterize fluid flows where there is

simultaneous heat and mass transfer by convection.

It is defined as:

𝐿𝑒 =𝛼

𝐷 Where α is the thermal diffusivity and D is the mass diffusivity.

The Lewis number can also be expressed in terms of the Schmidt number and

the Prandtl number:

𝐿𝑒 =𝑆𝑐

𝑃𝑟 ” [17] (23)

“Schmidt number (Sc) is a dimensionless number defined as the ratio of momentum

diffusivity (viscosity) and mass diffusivity, and is used to characterize fluid flows in which

there are simultaneous momentum and mass diffusion convection processes.

𝑆𝑐 = 𝑣/𝐷 (24)

Where;

v: kinematic viscosity or (𝜇/𝜌) in units of (m2/s)

D: mass diffusivity (m2/s).” [18]

“Prandtl number (Pr) is a dimensionless number, defined as the ratio of momentum

diffusivity (kinematic viscosity) to thermal diffusivity.” [19] It can be found in the

thermodynamics tables.

For calculating drying time:

𝑡 =𝑚𝑤𝑎𝑡𝑒𝑟

�̇�𝑣𝑎𝑝𝑜𝑟 (25)



Where:

𝑚𝑤𝑎𝑡𝑒𝑟: Mass of the water which is wanted to dry

�̇�𝑣𝑎𝑝𝑜𝑟: Vaporization rate of the water in the body

Vaporization rate of the water can be found as follow:

�̇�𝑣𝑎𝑝𝑜𝑟 =𝑆ℎ̅̅̅̅ 𝐷

𝐿𝑐𝐴(𝜌𝑣𝑠 − 𝜌𝑣∞) (26)

Where:

D: Mass diffusivity

𝜌𝑣𝑠: Saturation vapor density

𝜌𝑣∞: Actual vapor density

A: Total surface area of the occurred drying

Lc: Characteristic Length

Sh: Sherwood Number

“Sherwood number (Sh) (also called the mass transfer Nusselt number) is a

dimensionless number used in mass-transfer operation. It represents the ration of the total rate

of mass transfer to the rate of diffusive mass transport alone” [20]

mass ch LSh

D

(27)

Where:

ℎ𝑚𝑎𝑠𝑠: Mass transfer coefficient

𝐿𝑐: Characteristic length

D: Mass diffusivity



Correlation:

0.466 1 30.683RedSh Sc (28)

Where:

Sc: Schmidt Number

Re: Reynolds Number

“Reynolds number is defined as the ratio of inertial forces to viscous forces and

consequently quantifies the relative importance of these two types of forces for given flow

conditions.” [21]

Re cd

V L

v

(29)

Where:


v: kinematic viscosity

𝑉∞: Air velocity

Air velocity can be found as:

𝑉 = 𝑄/𝐴𝑐 (30)

Where:

Q: Volumetric flow rate

𝐴𝑐: Cross sectional area of flow

“Nusselt number (Nu) is the ratio of convective to conductive heat transfer across

(normal to) the boundary.” [22]



cd

hLNu

k

(31)

Where;


k: Thermal conductivity

h: Specific enthalpy

Correlation for40 Re 4000d

:

0.466 1 30.683*Re *Prd dNu (32)

Where:

𝑅𝑒𝑑: Reynolds Number

𝑃𝑟: Prandtl Number

According to all knowledge in this part, the problem was discussed and modeled with

the formulas given above.



3. SYSTEM DESIGN AND MODELING OF THE PROTOTYPE

In this project, a food dehydrator which can reuse the some of the air which is heated

and used from the system, was designed. According to this design, the fresh air goes into the

food dryer with the help of the fans. Then, it was heated by a heater and it passes through the

trays. Then, some of the humid air exits to the ambient and some of the humid air was

recycled to the system to mix and use with the fresh air. (Figure 5)

Figure 5: Operating principle of the system



Before manufacturing of the prototype, some hand sketches were made, then prototype

was modeled in the SolidWorks as 3D model as shown in Figure 7. So, any assembly errors

or unexpected costs were avoided during the production of the prototype.

Figure 6: Hand Sketch of the prototype

Figure 7: 3D model of the prototype



The cross-section view was taken to understand the position of the components in the

prototype as shown in Figure 8.

Figure 8: Cross-section view of the prototype

Trays, chassis, case, and door of the prototype were shown in Figure 9.

Figure 9: Parts of the prototype



4. PRODUCTION OF THE PROTOTYPE

4.1. Production of the case

For case of the prototype, a disused desktop computer case with the dimensions of 40

cm in length 20 cm in width and 41.5 cm in height was used. Computer components in the

case and front panel of the case were disassembled. Side panels with grid were replaced by

panels without grid.

Figure 10: Disused computer cases

Inside the case was coated with glass wool insulation with aluminum foil which has 1

cm thickness, for reducing heat loss from case walls.

Figure 11: Insulation coating in the case



4.2. Production of the chassis

Steel square tubes (1 x 1 cm) were welded each other so, two fame were made for

chassis of the dryer. To prevent damages on the glass wool, corners of the frames were

rounded via grinding machine.

Figure 12: Grinding of the corners

For shelves, 2 x 2 cm steel square tubes were cut longitudinally so, two L-profiles were

obtained from one square profile. 6 pieces L-profiles were fixed on the frames reciprocally

with screws. So, 3 shelves were obtained.

Figure 13: Chassis of the prototype



4.3. Production of the trays

To provide double-sided drying on trays, 3 pieces galvanized steel screen wires were cut

in 15 x 25 cm as shown in Figure 14.

Figure 14: Galvanized steel trays

4.4. Production of the door

Two sheet metal were cut with snips from a side panel of a disused computer case and

one of them (17 x 25 cm) was fixed on the chassis for mounting of fans and heater. Other

sheet metal (20 x 29.5 cm) was fastened in front of the case with two hinges for using as door.

To keep door closed, a magnet was used. The air outlet hole with 7 cm diameter was opened

middle of the door via hole saw drill.

Figure 15: The door of the dryer with air outlet hole



4.5. Procurement of the fan, heater, and controller

A broken hairdryer which has three levels of fan speed and three levels of heater power

options was obtained.

Figure 16: Disassembly of the broken hairdryer

Broken part of the hairdryer was not necessary for food drying, so broken part was

removed. The handle of the hairdryer was cut properly to use controller of the hairdryer as

control panel of the prototype.

Figure 17: Components of the broken hairdryer



Figure 18: Renovated hairdryer mechanism

Fan and heater were fixed on the shelf which is above trays via plastic clamps.

Figure 19: Fixing of the fan and heater

To take out the control panel and electric cable from inside the case, a hole was opened

at the top of the case via hole saw drill. After control panel and electric cable were taken out,

the hole was closed.



Figure 20: Opening the hole with hole saw drill

A sheet metal (20 x 12 cm) was cut and it was fastened on the chassis with screws and

nuts to close the top of the door. Air inlet hole with 7 cm diameter was opened on this sheet

and an orifice meter which was provided by supervisor was mounted on it with screws.

4.6. Assembly of the orifice meter

Figure 21: Assembly of the orifice with the frame



Before mounting of the orifice, orifice was disassembled. When the orifice was

disassembled, burr was observed around the holes of the pressure taps in the orifice. To avoid

error of the pressure measurement, around the holes of the pressure taps were rasped as show

in Figure 22.

Figure 22: Rasping of the pressure taps

Diameter of the orifice pipe was measured as 47.5 mm and diameter of the hole on the

orifice plate was measured with a caliper as 24.5mm.

Figure 23: Measuring of the orifice pipe diameter



4.7. Assembly of the prototype

Finally, orifice was assembled, trays were placed on the shelves on the chassis and

chassis was put in the case. So prototype was completed as shown in Figure 24.

Figure 24: Completed Prototype

Some arrangements were done on the SolidWorks drawing, and model was completed.

Figure 25: SolidWorks drawing of the completed prototype



5. DEVELOPMENT OF THE PROTOTYPE

When the prototype was operated with lowest heat level, obtained heat from heater of

the hairdryer was observed as higher than expected heat amount. Also, energy consumption of

the hairdryer was high. Therefore, all component of the hairdryer; heater, fan, controller and

electronic circuit were not used and removed.

5.1. Production of a new heater

For heating the air, a new heating element was produced. A nonflammable material was

cut with utility knife. So, housing of the heater with the dimensions of 10 cm in length, 17 cm

in width, 7.5 cm in height and frame which holds the heater wire were formed.

Figure 26: Nonflammable material cutting



For passing the heater wire from inside the frame, 6 holes which have 1 cm diameter

were opened on the frame plate with hole saw and hammer as you can see in Figure 27.

Figure 27: Frame plate forming

For fixing the wire which passing through in the frame plate, locker plate was made.

Figure 28: Locker plate



5 meter flat nichrome wire was provided by adviser. It was curled up until it is 1.5

meter. Then it was wrapped around the nonflammable frame plate and fixed with locker plate.

Figure 29: Curled up nichrome wire

The resistance of the nichrome heater wire was measured as 14 Ohms with a

multimeter.

Two ends of the nichrome wire were fixed with heatproof porcelain terminal.

Figure 30: Porcelain Terminal



All components of the heater were placed in the housing and fixed. The position of the

wire was adjusted in the heater. So, heater was formed as you can see in Figure 31.

Figure 31: The heater unit

5.2. Changing the fan system

For ventilation system, 4 pieces 12 Volt DC fans which have 8 mm diameter were used.

Fans were lined up in twos in the air duct.

Figure 32: A pair of fan



Figure 33: Settlement of fans and heater

The fans and heater unit was placed on the chassis and fixed. For supplying power to

the fans and heater unit, electric cable system was installed. The fans was connected in series

a power supply, heater unit was connected another power supply couple.

5.3. Changing the controller and power supply

To provide required power for heater, two power supplies which have 30V and 5A

capacity were connected as series. Also a power supply (30V/5A) provides power for fans.

Voltage and current were controlled with buttons on the power supplies. So, fan speed and

heater level were adjusted.

Figure 34: The power supplies connected in series

5.4. Adding shelves and trays

To increase the drying capacity of the prototype and to use the heated air more

efficiently, the number of the shelves and trays was increased to 5 from 3.



6. IMPROVEMENT OF THE SOLIDWORKS DRAWING

After the development of the prototype, also SolidWorks drawing of the prototype was

improved depending on the changing parts.

Figure 35: Dimensions of the Prototype

Figure 36: The cross-section view of the prototype

Figure 37: Disassembly of the prototype



7. EXPERIMENTAL SETUP

After the prototype was completed, to conduct the experiments, an experimental set-up

was prepared. To measure the temperature, humidity and pressure values; 12 thermocouples,

5 temperature-humidity sensors and 1 pressure sensor were located as shown in Figure 38.

Figure 38: Location of the thermocouples and sensors

Location of 8 thermocouples and 1 sensor at the point 3 and point 4 are shown in

Figure 39.

Figure 39: Thermocouples and sensor locations at the point 3 and 4

7

3 4

Thermocouples

Sensor



Table 1: Location of the thermocouples and sensors

Location Number of Thermocouples and Sensors

1 1 Thermocouple and 1 Sensor


3 4 Thermocouples

4 4 Thermocouples and 1 Sensor



7 1 Differential Pressure Sensor

In Table 1, number of the thermocouples and number of the sensors and their locations

are shown.

In a thermocouple, there are two different conductors which do not contact each other.

To measure the temperature, conductors on the one end of the thermocouple must contact

each other. So, one end of the thermocouples was soldered as shown in Figure 40.

Figure 40: Thermocouple ends



The solderless end of the thermocouples were connected to a 20 channel multiplexer as

shown in Figure 41.

Figure 41: 20 Channel Multiplexer

Then, 20 Channel multiplexer were installed into the Agilent data acquisition

instrument which was connected to the computer with USB cable. Agilent software was used,

to take and save temperature data.

To measure humidity and temperature, The Sensirion SHT75 digital sensor was used.

Figure 42: The Sensiron SHT75 sensor

The sensors were connected to the data acquisition board as shown in Figure 43. The

data acquisition board send the data to computer and UDAQ software show and save the

measured humidity and temperature values.



Figure 43: The data acquisition board

To measure the pressure on the orifice a differential pressure transmitter (OMEGA

PX274) was connected to orifice.

Figure 44: OMEGA PX274 differential pressure transmitter

Finally, experimental set-up was completed as shown in Figure 45.

Figure 45: Experimental Set-up



8. RESULTS OF THE EXPERIMENTS

After the experimental setup was completed, some experiments were conducted on the

prototype by the project mate. These experiments are divided into two parts as wet towel tests

and strawberry tests. In the initial tests, wet towel pieces were dried to control the system,

then pieces of the sliced strawberries were dried in the prototype. 4 tests were made with wet

towel pieces and 3 tests were made with strawberries.

In the three tests of the wet towel, openness of the outlet air hole was changed as full

open, 1/2 open and 1/3 open. In the final test of the wet towel, outlet hole was open but air

mixing hole was closed. Result of the tests were shown in Table 2.

Table 2: Result of the Wet Towel Drying Test

Test Type

(Towel)

Power

(W)

Heat Loss

(W)

Time

(min)

Evaporated

Water (g)

Flow Rate of the

Inlet Air (L/s)

Full Open 125 36 105 156,78 0,81

1/2 Open 125 38 117 156,37 0,78

1/3 Open 125 43 116 136,53 0,72

Mix Closed 125 41 138 135,50 1,44

According to Table 2, in the test with full open outlet, the most water was vaporized at

the least time.

Table 3: Result of the Strawberry Drying Test

Test Type

(Strawberry)

Power

(W)

Heat Loss

(W)

Time

(min)

Evaporated

Water (g)

Flow Rate of the

Inlet Air (L/s)

Full Open 96 43 167 97,54 0,79

1/2 Open [1] 96 41 155 97,50 0,77

1/2 Open [2] 125 48 174 162,49 0,74

In the Table 3, the most evaporated water is seem as in 1/2 open test with 125W heater

power. However in this test, drying air temperature increased about 63˚C and strawberries

were dried overly. In 1/2 open test with 96W heater power, drying air temperature stayed low

for drying. So, strawberries softened. The best drying was obtained in the full open test with

96W heater power.



In this report to compare the results of the experiment with MATLAB codes, data of the

96W full open strawberry test was taken from the project mate.

Figure 46: Relative Humidity Result of the 96W Full Open Strawberry Test

Temperature changes in Figure 46 and relative humidity changes in Figure 47 were used

in the MATLAB code and results were compared with each other.

Figure 47: Relative Humidity Result of the 96W Full Open Strawberry Test

05

1015202530354045505560

0 2000 4000 6000 8000 10000

Tem

per

atu

re (

˚C)

Time (s)

Temperature vs Time

T1

T2

T3

T4

T5

T6

05

1015202530354045505560

0 2000 4000 6000 8000 10000

Rel

ativ

e H

um

idit

y (%

)

Time (s)

Relative Humidity vs Time

H1

H2

H4

H5

H6



9. MATLAB PROGRAMMING

9.1. Problem Statement

Food drying process in the prototype was modeled with MATLAB. While The

MATLAB program was coding, Figure 48 was considered as model of the problem.

Figure 48: Model of the problem

The system was divided into 3 parts. Then the cases between the each part were

modeled in The MATLAB with the help of the heat transfer and mass transfer subjects. The

cases at the points and between the points are:

At the point 1, the air incoming from ambience combines with recycled air.

Between the points 1-2, air velocity is increased with fans to provide forced

convection. Also temperature of the air is increased with heater to increase

moisture holding capacity of the air.

Between the points 2-3, heat and mass transfer occur. Surface temperature of

the food is increasing. Water in the food is evaporated and water vapor is

moved by the air. Water content of the air increases. Temperature of the air

decreases.

At the point 3, a part of the air is thrown out, other part of the air is returning in

the system.



9.2. MATLAB Codes

9.2.1. Program #1: Determination of the ideal drying process

To determine the ideal drying cost and drying time, two programs were coded

depending on the different parameters. Parameters of the first one are; temperature of the air

passing over the food (T2 in Figure 48), flow rate of the inlet air, and flow rate of the fan.

Parameters of the second program are; power of the heater, flow rate of the inlet air, and flow

rate of the fan. The programs consist of 1 main code and 8 function codes. Functions are

called from main code or other function codes. To solve the problem 3 different iterations run

in the program.

Table 4: Program #1.1 Specifications

Program #1.1 Estimation of Experiment Result (Steady-State)

Parameters 𝑄ℎ𝑒𝑎𝑡𝑒𝑟, �̇�𝑎𝑖𝑟 , �̇�𝑎𝑖𝑟,𝑜

Resulting 𝑇1, 𝑇2, 𝑇3, 𝑇𝑠, 𝜔1, 𝜔2, 𝜔3,

∅1, ∅2, ∅3, �̇�𝑣𝑎𝑝𝑜𝑟 , 𝑡𝑑𝑟𝑦, 𝑐𝑜𝑠𝑡

Table 5: Program #1.2 Specifications

Program #1.2 Estimation of Experiment Result (Steady-State)

Parameters 𝑇2, �̇�𝑎𝑖𝑟 , �̇�𝑎𝑖𝑟,𝑜

Resulting 𝑄ℎ𝑒𝑎𝑡𝑒𝑟, 𝑇1, 𝑇3, 𝑇𝑠, 𝜔1, 𝜔2, 𝜔3,

∅1, ∅2, ∅3, �̇�𝑣𝑎𝑝𝑜𝑟 , 𝑡𝑑𝑟𝑦, 𝑐𝑜𝑠𝑡

In the problem shown in Figure 48; 𝑇1, 𝑇2, 𝑇3, 𝜔1, 𝜔2, 𝑎𝑛𝑑 𝜔3 are unknowns. To find

these 6 unknowns, necessary 6 equation was obtained from mass and energy balance

equations as follows:



Mass balance:

�̇�𝑎𝑖𝑟𝜔1 = �̇�𝑎𝑖𝑟0𝜔∞ + (�̇�𝑎𝑖𝑟 − �̇�𝑎𝑖𝑟0

)𝜔3 (1)

𝜔1 = 𝜔2 (2)

�̇�𝑎𝑖𝑟𝜔3 = �̇�𝑎𝑖𝑟𝜔2 + �̇�𝑣𝑎𝑝𝑜𝑟 (3)

Energy balance:

�̇�𝑎𝑖𝑟ℎ1 = �̇�𝑎𝑖𝑟0ℎ∞ + (�̇�𝑎𝑖𝑟 − �̇�𝑎𝑖𝑟0

)ℎ3 (4)

�̇�𝑎𝑖𝑟ℎ2 = �̇�𝑎𝑖𝑟ℎ1 + 𝑄ℎ𝑒𝑎𝑡𝑒𝑟 (5)

�̇�𝑎𝑖𝑟ℎ3 = �̇�𝑎𝑖𝑟ℎ2 − 𝑄 + �̇�𝑣𝑎𝑝𝑜𝑟ℎ𝑔@𝑇𝑠

Where; 𝑄 = �̇�𝑣𝑎𝑝𝑜𝑟ℎ𝑓𝑔@𝑇𝑠 (the energy absorbed from the food)

So,

�̇�𝑎𝑖𝑟ℎ3 = �̇�𝑎𝑖𝑟ℎ2 + �̇�𝑣𝑎𝑝𝑜𝑟ℎ𝑓@𝑇𝑠 (6)

The enthalpy unknowns in above equations were used find temperature unknowns with

this equation:

ℎ = 𝑐𝑝𝑇 + 𝜔ℎ𝑔@𝑇 (7)

However, as seen, the temperature cannot be left alone in above equation because

enthalpy of water vapor (ℎ𝑔@𝑇) is dependent with temperature. Therefore, to find the

temperature from enthalpy, iterations were made.

“The enthalpy of water vapor (ℎ𝑔@𝑇) could be found in “Table-A4” (Thermodynamics:

an Engineering Approach, McGraw-Hill) or it could be determined approximately from

ℎ𝑔@𝑇 = 2500.9 + 1.82𝑇 (𝑘𝐽

𝑘𝑔) 𝑇 𝑖𝑛 °𝐶 (8)

in the temperature range -10 to 50 °𝐶 with +0.1 and -0.6 kJ/kg errors.” [22]



However in the calculations, graph of the ℎ𝑔@𝑇 table was drawn and equation of it was

found as:

ℎ𝑔(𝑇) = −0.000000024703951 𝑇4 − 0.0000031198158 𝑇3 − 0.00031842659 𝑇2 +

1.834738 𝑇 + 2500.985 (9)

Therefore, more accurate result were gained.

At the continuation of the solution, all formulas in the theory part of the report were

used and they were shown in MATLAB codes (Main1.m, Main2.m, Iter1.m, Iter2.m,

Tsurface.m, P_sat.m, find_T_from_h.m, enthalpy_hf.m, enthalpy_hg.m,

enthalpy_hfg.m, denthalpy_hg.m) added in the appendices.

9.2.2. Program #2: Calculation of the Vaporization Rate

To calculate the vaporization rate and total evaporated water during drying process with

using data which obtained from the experiments, another program was coded. The algorithm

of this program was shown in Figure 49.

Figure 49: Algorithm of the vaporization rate



This program called as “vap_rate.m” imports all temperature, relative humidity and

mass flow rate values of the inlet air from an excel worksheet which was formed by

experiments. Then, it finds the saturation pressure, specific humidity, water vapor enthalpy

and specific enthalpy at the all 6 points and it exports mass flow rate of the recycled air, mass

flow rate of the air passing through the fan and mass flow rate of the water vapor to an excel

worksheet for each time. Then, every values are marked and held on the graph.

Table 6: Program#2 Specifications

Program #2 Vaporization Rate Calculation

Parameters 𝑇1, 𝑇2, 𝑇3, 𝑇𝑠, ∅1, ∅2, ∅3, �̇�𝑎𝑖𝑟,𝑜

Resulting �̇�𝑣𝑎𝑝𝑜𝑟 , �̇�2, �̇�𝑎𝑖𝑟

This code is iterated for each time so, instant vaporization rate graph is obtained. If

equation of this graph is found and integrated for all points, approximate total amount of the

evaporated water during drying can be found.

9.2.3. Program #3: Vaporization Rate Depending on Water Activity

This program is a mixture of Program #1 and Program #2. It uses same data used by the

Program #2 and finds vaporization rate and total mass of the evaporated water as Program #2.

Also it uses some equations used by the Program #1. However, Program #3 considers about

water activity changes in real time. Therefore, this program gives more accurate results about

vaporization rate and total mass of evaporated water than Program #1 and Program #2.

Table 7: Program#3 Specifications

Program #3 Vaporization Rate Calculation depending on water activity

Parameters 𝑇1, 𝑇2, 𝑇3, 𝑇𝑠, ∅1, ∅2, ∅3, �̇�𝑎𝑖𝑟,𝑜

Resulting �̇�𝑣𝑎𝑝𝑜𝑟 , �̇�2, �̇�𝑎𝑖𝑟



To use the water activity in this program, a water activity-moisture content at different

temperature graph for mercerized cotton was obtained from a scientific article. (Figure 50)

Figure 50: Water Activity & Moisture Content Graph for Mercerized Cotton [24]

In the project, drying process is requested to be performed at about 55 ˚C. So the water

activity & moisture content graph at 55 ˚C was redrawn based on Figure 50.

y = 3708,3x6 - 6115,9x5 + 3845,2x4 - 1117,1x3 + 132,4x2 + 0,8111x

0

0,2

0,4

0,6

0,8

1

0 0,1 0,2 0,3 0,4 0,5

Wat

er A

ctiv

ity

Moisture Content (kg/kg)

55˚C for Mercerized Cotton

Figure 51: Water Activity & Moisture Content Graph at 55˚C



After plotted the graph (Figure 51), the trend line was added to the graph with the

equation. This equation was used in the MATLAB code. However, this equation works only

between 0 and 0.339 moisture content ratio. Over the 0.339 moisture content ratio, this

equation gives the water activity is greater than 1. But, water activity must be between 0 and 1

and it must be 1 for moisture content over 0.339. Therefore, an “if” loop was added the code

to get the water activity as 1 for moisture content over 0.339 as shown in Figure 52.

Figure 52: Precaution Code for Water Activity

So the Program #3 controls the moisture content after each iteration and determine the

instant water activity. So it calculates the vaporization rate in real time and draw vaporization

rate graph. When the equation of the graph is integrated, total mass of the evaporated water is

found. This program called as “vap_rate_wa.m” was given in the appendices.



10. MATLAB RESULTS

10.1. The differences of the Prototype from the Standard Food Dehydrator

To understand the effect of the air recycling (air mixing) system which is not existing

in standard dehydrator, Program#1.1 was run with two different parameters; open air mix hole

and closed air mix hole. Results show that to dry the food in 3 hours with providing the 56 ˚C

drying air on the food requires 53W with open air mix hole. However, to get the same

conditions with the closed air mix hole, about 300W heater power is needed. Also while the

drying cost of the dryer with open air mix hole is 0.0561 TL, the drying cost of the dryer with

closed air mix hole is about 0.2544 TL. This is 4.5 times more expensive. This shows that air

recycling system increases the efficiency.

10.2. Finding the Ideal Drying Case

In this part, to find the ideal drying case, parameters such as; fan flow rate, inlet air

flow rate and power of the heater, were diversified with the Program#1.1 and different values

of the drying time, drying cost and drying temperature were observed.

Table 8: Result of the Program#1.1 Depending on the Power Change

CONSTANT CONSTANT VARIABLE

# Fan Flow

Rate (kg/s)

Inlet Air Flow

Rate (kg/s)

Power of the

Heater (W)

Drying

Time (h)

Drying

Cost (TL)

The Air Temperature

on the food (T2) (°C)

1 0,0088 0,00092 73 2,12 0,055 68,89

2 0,0088 0,00092 63 2,49 0,0556 62,65

3 0,0088 0,00092 53 2,99 0,0561 56,30

4 0,0088 0,00092 43 3,71 0,0565 49,82

5 0,0088 0,00092 33 4,84 0,0566 43,21

According to Table 8, increasing the power of the heater decreases the drying time and

drying cost but increases the drying air temperature.



Table 9: Result of the Program#1.1 Depending on the Inlet Air Flow Rate Change

CONSTANT VARIABLE CONSTANT

# Fan Flow

Rate (kg/s)

Inlet Air Flow

Rate (kg/s)

Power of the

Heater (W)

Drying

Time (h)

Drying

Cost (TL)

The Air Temperature


1 0,0088 0,00110 53 3,26 0,0609 52,27

2 0,0088 0,00100 53 3,11 0,0583 54,34

3 0,0088 0,00092 53 2,99 0,0561 56,30

4 0,0088 0,00082 53 2,85 0,0533 58,91

5 0,0088 0,00072 53 2,69 0,0504 62,09

In the Table 9, when the inlet flow rate is decreased, drying time and drying cost

decreases but drying air temperature increases.

Table 10: Result of the Program#1.1 Depending on the Fan Flow Rate Change

VARIABLE CONSTANT CONSTANT

# Fan Flow

Rate (kg/s)

Inlet Air Flow

Rate (kg/s)

Power of the

Heater (W)

Drying

Time (h)

Drying

Cost (TL)

The Air Temperature


1 0,0110 0,00092 53 2,89 0,0540 54,89

2 0,0100 0,00092 53 2,93 0,0549 55,44

3 0,0088 0,00092 53 2,99 0,0561 56,30

4 0,0080 0,00092 53 3,05 0,0570 56,80

5 0,0070 0,00092 53 3,12 0,0584 57,65

In the Table 10, when the fan flow rate is increased, drying time and drying cost

decrease but, drying temperature decreases. Figure 53 and Figure 54 were drawn with the data

obtained from Table 8.



Figure 53: Change of the Drying Time Depending on the Heater Power Change

Figure 54: Change of the Drying Cost Depending on the Heater Power Change

Figure 55 and Figure 56 were drawn with the data obtained from Table 9.

0

2

4

6

30 40 50 60 70 80

Dry

ing

Tim

e (h

)

Heater Power (W)

TIME (h)

0,05480,05520,0556

0,0560,05640,0568

30 40 50 60 70 80

Dry

ing

Co

st (

TL)

Heater Power (W)

COST (TL)

2,00

2,50

3,00

3,50

0,0006 0,0007 0,0008 0,0009 0,001 0,0011 0,0012Dry

ing

Tim

e (h

)

Inlet Air Flow Rate (kg/s)

TIME (h)

Figure 55: Change of the Drying Time Depending on the Inlet Air Flow Rate Change



Figure 56: Change of the Drying Cost Depending on the Inlet Air Flow Rate Change

Figure 57 and Figure 58 were drawn with the data obtained from Table 10.

Figure 57: Change of the Drying Time Depending on the Fan Flow Rate Change

Figure 58: Change of the Drying Cost Depending on the Fan Flow Rate Change

According to above figures, ideal drying time and ideal drying cost were selected as

3 hour and 0.0561 TL (5.61 Krş) in the 3rd case. Then parameters of the ideal case were

applied on the prototype and results were compared with MATLAB results.

0,004

0,024

0,044

0,064

0,0006 0,0008 0,001 0,0012D

ryin

g C

ost

(TL

)

Inlet Air Flow Rate

COST (TL)

2,82,9

33,13,2

0,006 0,008 0,01 0,012

Dry

ing

Tim

e (h

)

Fan Flow Rate(kg/s)

TIME (h)

0,0520,0540,0560,058

0,06

0,006 0,008 0,01 0,012

Dry

ing

Co

st (

TL)

Fan Flow Rate (kg/s)

Drying Cost (TL)



10.3. Estimation of the Experimental Result

The Program#1.1 was run to estimate the result of the 96 Watt full open strawberry

test. Then, results were compared with each other in Table 11.

Table 11: Estimation of the Experimental Result

T1

(˚C)

T2

(˚C)

T3

(˚C)

Ø 1

(%)

Ø 2

(%)

Ø 3

(%)

Drying Time

(h)

Experiment 49.83 55.30 53,80 22 16 18 3

MATLAB 50.41 56.21 53.76 22 17 20 3

According to Table 11, results are very closed each other. The errors are about 1% for

temperature values. For relative humidity (Ø) values, the errors are about 6.25% - 11.11%.

However accuracy of the humidity sensors is also %2 and it cannot show the result in 0.1

sensitivity. So, Program #1 works as expected.

10.4. Vaporization Rate Calculation

To find the vaporization rate and total evaporated water mass, Program #2 and Program

#3 were used with the data obtaining from 96W full open outlet strawberry test. Then Results

were compared each other.

Result of the Program #2:

Figure 59: Vaporization Rate with constant water activity

y = 4E-20x4 - 8E-16x3 + 6E-12x2 - 2E-08x + 4E-05

0

0,00002

0,00004

0,00006

0,00008

0 2000 4000 6000 8000 10000

Md

ot

vap

or

[kg/

sec]

Time (s)

Vaporization Rate with constant water activity(=1)



Result of the Program #3:

Figure 60: Vaporization Rate with instant water activity changes

In the Figure 59, the graph has more straight line than the graph in Figure 60, because

water activity was taken constant. Result of the Program #3 (Figure 60) gives more realistic

vaporization rate & time graph than Program #2, because that it calculates the water activity

instanly.

When the equation of the graph which is obtained from Program #2 ( Figure 59) was

integrated, total evaporated water mass was found as 204.47 g.

When the equation of the graph which is obtained from Program #3 ( Figure 60) was

integrated, total evaporated water mass was found as 95.29 g.

In the experiment, total evaporated water mass was measured as 97.54 g.

Table 12: Total Mass of the Evaporated Water

The Experiment Program #3 Program #2

Mass of the Evaporated Water (g) 97.54 95.29 204.47

According to these result, the Program #2 shows that more water ( about 2 times) was

vaporized than evaporated water in the experiment because water activity was taken as “1”

always. However water activity decreases with time. Therefore, the Program #3 gave more

accurate result with 2.3% errors. Reason of this error is that water activity change was

obtained for mercerized cotton but it was used for strawberry. Therefore, this result with this

error was acceptable.

y = -6E-24x5 + 1E-19x4 - 8E-16x3 + 2E-12x2 - 4E-09x + 1E-05

0

0,000005

0,00001

0,000015

0,00002

0 1000 2000 3000 4000 5000 6000 7000 8000 9000Vap

ori

zati

on

Rat

e [k

g/s]

Time [sec]

Vaporization Rate



11. CONCLUSION

In this project, a special food dehydrator was designed. This food dehydrator has an air

mixing hole unlike standard food dehydrators. This hole provides that the fresh air coming

from the outlet mixes with the heated, unsaturated and reusable recycling air. Therefore,

required energy to heat the air decreases.

After operation system was determined, some hand sketches were made and the model

of the prototype was formed in SolidWorks as 3D. Then prototype was produced with an old

computer case and a hair dryer mechanism. This prototype was not successful because the

hair dryer mechanism provide higher air temperature than desired. So, new heater unit and fan

system were designed and produced.

After the production of the prototype was completed, some experiments were conducted

on the prototype by the project mate. In the experiment, during the drying process some

measurements such as; the temperature measurement at the 6 points, humidity measurement at

the 5 points, pressure measurement on the orifice meter, voltage measurement on the heater

unit were done. The power of the heater, speed of the fans, openness of the air mixing hole

and openness of the outlet hole were changed to observe the effect of them on the drying

process. Then, results of the all experiments were given to me for using in MATLAB

modeling.

The drying process in the designed prototype was modelled in the MATLAB. To find

the ideal drying time and drying cost, to estimate the experimental results and to calculate the

vaporization rate and total vaporized water, three programs were coded in the MATLAB. The

Program #1 was used to find the ideal drying time and drying cost and to estimate the

experimental results. Program #2 and Program #3 were used to calculate the vaporization rate

and total mass of the evaporated water. Difference between Program #2 and Program #3 is

that Program #2 takes the watery activity as “1” and constant, Program #3 calculates the water

activity depending on the moisture content changes instantly.

Firstly, the Program #1 was run to determine the advantage of the special design of the

system. According to the result, air recycling system provides 4.5 times less drying cost than

standard dehydrator designs in the same drying time.



Then, ideal drying time and ideal drying cost were calculated by the Program #1. The

results show that the drying time should be about 3 hour and drying cost is 0.0561 TL. This

drying cost can be expressed as 0.60 TL for drying 1 𝑚2 surface area. This value changes

between 1.87 TL and 2.40 TL for standard food dehydrators. Also this shows the efficiency of

the design.

After the experiments, results of the MATLAB were compared with the results of the

experiments. Temperature and drying time values are same with about 1% error. The relative

humidity values are closed each other with ±0.02 (2%) error. So, it was decided that the

Program #1 is working properly.

To calculate the vaporization rate and total mass of the evaporated water during the

drying, Program #2 and Program #3 were run with the data which was obtained from 96W

full open outlet strawberry test. In the test, total mass of the evaporated water was measured

as 97.54 g via precision scales. The Program #2 calculates the amount of the evaporated water

as 204.47 g. The Program #3 found the total mass of the evaporated water as 95.29 g.

According to results, Program #3 gives more accurate result than Program #2 because it

controls the moisture content and calculates the water activity instantly. There is 2.3% error

between the result of the experiment and result of the Program #3 because to calculate the

water activity change depending on the moisture content, water activity graph for the

mercerized cotton was used. So, Program #3 works as expected.



12. APPENDICES

12.1. MATLAB CODES

Program#1.1

Main1.m:

clear all;

clc;

%%%% full open outlet 96W strw%%%%%

%%%%% Parameters:%%%%%%%

Q = 0.05286; %% power (kW)

mdot = 0.0088; %% for 12V 4 Fan kg/sec

mdot0 = 0.00092; %% kg/sec

%%%%%%%%%%%%%%%%%%%%%%%%%

Tamb = 21.2585; %% C

RHamb = 0.56; %% 50%

Pamb = 99.130; %% Pa

cpair = 1.005; %%

diff = 2.5e-5; %% Diffusivity

Lchar = 0.248; %% meter %% 4A/wetted Perimeter

Tarea = 10*0.25*0.15/2;

Psatamb = P_sat(Tamb);

wamb = 0.622*RHamb*Psatamb/(Pamb-RHamb*Psatamb);

hgamb = enthalpy_hg(Tamb);

hamb = cpair*Tamb + wamb*hgamb;

airdensity = 1.164; %% kg /m^3

flowarea = 0.16*0.08 ;%% m^2

kinvisc = 16.97e-6;

thermdiff = 23.9186e-6;

velocity = (mdot/airdensity/flowarea);

Re = velocity*Lchar/kinvisc; %% <5e5

Sc = kinvisc/diff;

Pr = kinvisc/thermdiff;

lewis = Sc/Pr;

Sh = 0.664*sqrt(Re)*Sc^(1/3); %% 0.6 < Sc < 50

hmass = Sh*diff/Lchar; %% meter / sec

hA = hmass*Tarea; %% meter_cube / sec

w2 = wamb;

h3 = 150;

mwater = 0.09754; %kg

mtowel = 0.105; %kg

icount = 0;

TOL = 1e-8;



while(1)

[f h3 mwater wa] = iter(mwater,mtowel,h3,Q, w2, hA, mdot,

mdot0, hamb, wamb, Pamb, cpair, lewis);

w2new = w2*1.00001;

[f2 h3 mwater wa] = iter(mwater,mtowel,h3,Q, w2new, hA, mdot,


df = (f2-f)/(w2new-w2); %% } (differentiate)

dw2 = -f/df; %% } Newton Method

w2 = w2+dw2; %% }

icount = icount + 1;

if(icount>1000)

disp('EXCESSIVE ITERATION1');

break;

end

if(abs(dw2/w2)<TOL)

break;

end

end

[f h3 mwater wa] = iter(mwater,mtowel,h3,Q, w2, hA, mdot, mdot0,

hamb, wamb, Pamb, cpair, lewis);

Iter1.m:

function[f h3 mwater wa] = iter(mwater,mtowel,h3,Q, w2, hA, mdot,


wa=0.86; %%%average water activity

h1 = (mdot0*hamb + (mdot-mdot0)*h3)/mdot; %%%%%4

h2 = Q / mdot + h1; %%%%%5

T2 = find_T_from_h(h2, w2, cpair);

Psat2 = P_sat(T2);

RH2 = w2/(w2+0.622)*Pamb/Psat2;

Pvap2 = RH2*Psat2;

Ts = Tsurface(T2, Pvap2, Pamb, cpair, lewis);

Psatsurf = P_sat(Ts);

denssurf = wa*Psatsurf/0.462/(Ts+273.15);

dens2 = Pvap2/0.462/(T2+273.15);

mdotvap = hA*(denssurf - dens2);

drytime = mwater/(mdotvap*3600); %hour

kWh = Q*drytime; %kWh

cost = kWh*0.354; %TL



hfsurf = enthalpy_hf(Ts);

h3 = h2 + mdotvap*hfsurf/mdot; %%%%%6

w3 = w2 + mdotvap/mdot; %%%%%3

w1str = (mdot0*wamb + (mdot-mdot0)*w3 )/mdot; %%%%%1

w1 = w2;

f = w1-w1str;



RH1 = w1*101.325/(P_sat(T1)*0.622*(1+w1/0.622));

RH2 = w2*101.325/(P_sat(T2)*0.622*(1+w2/0.622));

RH3 = w3*101.325/(P_sat(T3)*0.622*(1+w3/0.622));

disp('T1 T2 T3 ');

disp([T1, T2, T3]);

disp('w1 w2 w3 ');

disp([w1, w2, w3]);

disp('RH1 RH2 RH3 ');

disp([RH1, RH2, RH3]);

disp('Tsurface mdotvapor (gr/sec)');

disp([Ts,mdotvap*1000]);

disp('Power (W) Dry Time (h)');

disp([Q*1000,drytime]);

disp('kWh Cost (TL)');

disp([kWh,cost]);

disp('-----------------------------');

end

Tsurface.m

function[Ts] = Tsurface(T, Pvap, Pamb, cpair, lewis)

const = 0.622/cpair/lewis^(2/3)/Pamb;

Ts = T*0.9;

icount = 0;

TOL = 1e-8;

while(1)


[hfg] = enthalpy_hfg(Ts);

F = Ts - T + hfg*const*(Psatsurf-Pvap);

Ts2 = Ts*1.00001;

Psatsurf = P_sat(Ts2);



[hfg] = enthalpy_hfg(Ts2);

F2 = Ts2 - T + hfg*const*(Psatsurf-Pvap);

dF = (F2-F)/(Ts2-Ts);

dTs = -F/dF;

Ts = Ts + dTs;

icount = icount+1;

if(icount>100)

disp('EXCESSIVE ITERATION IN TSURFACE');

break;

end

if(abs(dTs/Ts)<TOL)

break;

end

end

P_sat.m

function[P] = P_sat(T)

TK = T+273.15;

P = exp(-6096.9385/TK + 16.635794 - 2.711193e-2*TK + 1.673952e-

5*TK*TK + 2.433502*log(TK))/10;

Denthalpy_hg.m

function[hg, dhgdt] = denthalpy_hg(T)

hg = 2500.895 + T*(1.834738 + T*(-0.00031842659 + T*(-.0000031198158

+ T*(-0.000000024703951))));

dhgdt = 1.834738 + T*(-0.00031842659*2 + T*(-0.0000031198158*3 +

T*(-0.000000024703951)*4));

Enthalpy_hf.m

function[HF] = enthalpy_hf(T)

HF = 0.6446687 + T*(4.16485+T*0.00019215847);

Enthalpy_hg.m

function[hg] = enthalpy_hg(T)

hg = 2500.985 + T*(1.834738 + T*(-0.00031842659 + T*(-

0.0000031198158 + T*(-0.000000024703951))));



Enthalpy_hfg.m

function[hfg] = enthalpy_hfg(T)

hf = 0.6446687 + T*(4.16485 + T*0.00019215847);

hg = 2500.895 + T*(1.834738 + T*(-0.00031842659 + T*(-

.0000031198158 + T*(-0.000000024703951))));

hfg = hg - hf;

Find_T_from_h.m

function[T] = find_T_from_h(h, w, cpair)

T = 40;

icount = 0;

TOL = 1E-9;

while(1)

[hg, dhgdt] = denthalpy_hg(T);

F = cpair*T + w*hg - h;

dF = cpair + w*dhgdt;

dT = F/dF;

T = T-dT;

icount = icount+1;

if(icount>100)

disp('EXCESSIVE ITERATION IN FIND_T_FROM_H');

break;

end

if(abs(dT)<TOL)

break;

end

end



Program #1.2

Main2.m

clear all;

clc;

%%%%% Parameters:%%%%%%%

T2 = 55;

mdot = 0.01374; %% for 12V 4 Fan kg/sec

mdot0 = 0.00094; %% kg/sec

%%%%%%%%%%%%%%%%%%%%%%%%%

Tamb = 20.43; %% C

RHamb = 0.2895; %% 50%

Pamb = 99.130; %% kPa

cpair = 1.005; %%


Lchar = 0.248; %% meter

Tarea = 10*0.25*0.15; %% m^2

Psatamb = P_sat(Tamb);

wamb = 0.622*RHamb*Psatamb/(Pamb-RHamb*Psatamb);

hgamb = enthalpy_hg(Tamb);

hamb = cpair*Tamb + wamb*hgamb;


flowarea = 0.16*0.08 ;%% m^2

kinvisc = 16.97e-6;


velocity = (mdot/airdensity/flowarea);


Sc = kinvisc/diff;


lewis = Sc/Pr;

Sh = 0.664*sqrt(Re)*Sc^(1/3); %% 0.6 < Sc < 50



w2 = wamb;

icount = 0;

TOL = 1e-8;



while(1)

[f] = iter(T2, w2, hA, mdot, mdot0, hamb, wamb, Pamb, cpair,

lewis);

w2new = w2*1.00001;

[f2] = iter(T2, w2new, hA, mdot, mdot0, hamb, wamb, Pamb, cpair,

lewis);

df = (f2-f)/(w2new-w2); %% } (differentiate)

dw2 = -f/df; %% } Newton Method

w2 = w2+dw2; %% }

icount = icount + 1;

if(icount>100)

disp('EXCESSIVE ITERATION in main');

break;

end

if(abs(dw2/w2)<TOL)

break;

end

end

[f] = iter(T2, w2, hA, mdot, mdot0, hamb, wamb, Pamb, cpair, lewis);

Iter2.m

function[f] = iter(T2, w2, hA, mdot, mdot0, hamb, wamb, Pamb, cpair,

lewis);

mwater = 0.157;

Psat2 = P_sat(T2);

RH2 = w2/(w2+0.622)*Pamb/Psat2;

Pvap2 = RH2*Psat2;

hg2 = enthalpy_hg(T2);

h2 = cpair*T2 + w2*hg2;



denssurf = Psatsurf/0.462/(Ts+273.15);

dens2 = Pvap2/0.462/(T2+273.15);

mdotvap = hA*(denssurf - dens2); %kg/h

hfsurf = enthalpy_hf(Ts);

h3 = h2 + mdotvap*hfsurf/mdot ; %%%%%6

h1 = (mdot0*hamb + (mdot-mdot0)*h3)/mdot; %%%%%4

Q = mdot*(h2-h1); %%%%%5

w3 = w2 + mdotvap/mdot; %%%%%3

w1str = (mdot0*wamb + (mdot-mdot0)*w3 )/mdot; %%%%%1



w1 = w2; %%%%%2

f = w1 - w1str;

drytime = mwater/(mdotvap*3600); %hour

kWh = Q*drytime; %kWh

cost = kWh*0.354; %TL




RH1 = w1*101.325/(P_sat(T1)*0.622*(1+w1/0.622));

RH2 = w2*101.325/(P_sat(T2)*0.622*(1+w2/0.622));

RH3 = w3*101.325/(P_sat(T3)*0.622*(1+w3/0.622));

disp('T1 T2 T3 ');

disp([T1, T2, T3]);

disp('w1 w2 w3 ');

disp([w1, w2, w3]);

disp('RH1 RH2 RH3 ');

disp([RH1, RH2, RH3]);

disp('Tsurface mdotvapor (gr/sec)');

disp([Ts,mdotvap*1000]);

disp('Power (W) Dry Time (h)');

disp([Q*1000,drytime]);

disp('kWh Cost (TL)');

disp([kWh,cost]);

disp('-----------------------------');

end



Program #2:

Vap_rate.m

clear all

clc

%%% 156,78gr water was removed

%%% 105 minutes

Pamb = 101.325; %Pa

cpair = 1.006;

%%% Read Temperature from excel %%%

T1a = xlsread('exp','D:D');

T2a = xlsread('exp','E:E');

T3a = xlsread('exp','F:F');

T4a = xlsread('exp','G:G');

T5a = xlsread('exp','H:H');

T6a = xlsread('exp','I:I');

%%% Read Relative Humidity from excel %%%

RH1a = (xlsread('exp','J:J'))/100;

RH2a = (xlsread('exp','K:K'))/100;

%H3a isn't known

RH4a = (xlsread('exp','L:L'))/100;

RH5a = (xlsread('exp','M:M'))/100;

RH6a = (xlsread('exp','N:N'))/100;

%%% Read mass flow rate of the inlet air %%%

mdot1a = xlsread('exp','R:R');

mdot2a = (1:size(mdot1a))';

mdotvapa = (1:size(mdot1a))';


mdot3drya = (1:size(mdot1a))';

w1a = (1:size(mdot1a))';





for i= 1:size(T1a,1)

T1 = T1a(i);

T2 = T2a(i);

T3 = T3a(i);

T4 = T4a(i);

T5 = T5a(i);

T6 = T6a(i);



RH1 = RH1a(i);

RH2 = RH2a(i);

%H3 isn't known

RH4 = RH4a(i);

RH5 = RH5a(i);

RH6 = RH6a(i);

%%% Finding Saturated Pressures

Psat1 = P_sat(T1);

Psat2 = P_sat(T2);

Psat3 = P_sat(T3);

Psat4 = P_sat(T4);

Psat5 = P_sat(T5);

Psat6 = P_sat(T6);

%%% Finding Specific Humidity

w1 = 0.622*RH1*Psat1/(Pamb-RH1*Psat1);

w1a(i) = w1;


w2a(i) = w2;

% w3 = w4


w4a(i) = w4;


w5a(i) = w5;


w6a(i) = w6;

w3 = w4;

%%% Finding hg







%%% Finding enthalpy h







mdot1 = mdot1a(i);



%%% Finding mdot2

mdot2 = mdot1*(h4-h1)/(h2-h4);

mdot2a(i) = mdot2;

%%% Finding mdot3

mdot3 = mdot1 + mdot2;

mdot3a(i) = mdot3;

%%% Finding dry air of mdot3

mdot3dry = mdot3 * (1 - w3);

mdot3drya = mdot3dry;

%%% Finding mdotvap

mdotvap = mdot3dry * ((w2 + w6)/2 - (w4 + w5)/2);

%mdotvap = mdot3dry * (w6 - w5);% gr/4sec

mdotvapa(i) = mdotvap;

%%% Plotting

t=1:size(T1a,1);

plot(t(i),mdotvap,'*')

hold on

end

grid on

xlabel('Number of sample [1sample/4sec]')

ylabel('m_v_a_p_o_r [g/sec]')

title('125 Watt full open // 2h 53m // 156.78 g water')

%%% export data to excel

xlswrite('mdotvap',mdotvapa);

xlswrite('mdot2',mdot2a);




Program #3:

Vap_rate_wa.m

clear all

clc

%%% 97.54 gr water was removed

%%% 168 minutes

Pamb = 101.325; %Pa

cpair = 1.006;

mwater = 0.09754; %kg initial

msolid = 0.02483; %kg constant

%%% Read Temperature from excel %%%

T1a = xlsread('exp','D:D');

T2a = xlsread('exp','E:E');

T3a = xlsread('exp','F:F');

T4a = xlsread('exp','G:G');

T5a = xlsread('exp','H:H');

T6a = xlsread('exp','I:I');

%%% Read Relative Humidity from excel %%%

RH1a = (xlsread('exp','J:J'))/100;

RH2a = (xlsread('exp','K:K'))/100;

%H3a isn't known

RH4a = (xlsread('exp','L:L'))/100;

RH5a = (xlsread('exp','M:M'))/100;

RH6a = (xlsread('exp','N:N'))/100;

%%% Read mass flow rate of the inlet air %%%

mdot1a = xlsread('exp','R:R');


mdotvapa = (1:size(mdot1a))';


mdot3drya = (1:size(mdot1a))';






mdotvapcalca = (1:size(mdot1a))';

Tsa = (1:size(mdot1a))';

waterremoved = 0;

for i= 1:size(T1a,1)

T1 = T1a(i);

T2 = T2a(i);

T3 = T3a(i);

T4 = T4a(i);

T5 = T5a(i);

T6 = T6a(i);



RH1 = RH1a(i);

RH2 = RH2a(i);

%H3 isn't known

RH4 = RH4a(i);

RH5 = RH5a(i);

RH6 = RH6a(i);

%%% Finding Saturated Pressures

Psat1 = P_sat(T1);

Psat2 = P_sat(T2);

Psat3 = P_sat(T3);

Psat4 = P_sat(T4);

Psat5 = P_sat(T5);

Psat6 = P_sat(T6);

%%% Finding Specific Humidity


w1a(i) = w1;


w2a(i) = w2;

% w3 = w4


w4a(i) = w4;


w5a(i) = w5;


w6a(i) = w6;

w3 = w4;

%%% Finding hg







%%% Finding enthalpy h







mdot1 = mdot1a(i);



%%% Finding mdot2

mdot2 = mdot1*(h4-h1)/(h2-h4);

mdot2a(i) = mdot2;

%%% Finding mdot3

mdot3 = mdot1 + mdot2;

mdot3a(i) = mdot3;

%%% Finding dry air of mdot3

mdot3dry = mdot3 * (1 - w3);

mdot3drya = mdot3dry;

%%% Finding mdotvap

mdotvap = mdot3dry * ((w2 + w6)/2 - (w4 + w5)/2);

%mdotvap = mdot3dry * (w6 - w5);% gr/4sec

mdotvapa(i) = mdotvap;

%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%


Lchar = 0.248; %% meter %% 4A/wetted Perimeter

Tarea = 10*0.25*0.15/2;


flowarea = 0.16*0.08 ;%% m^2

kinvisc = 16.97e-6;


velocity = (mdot3/airdensity/flowarea);


Sc = kinvisc/diff;


lewis = Sc/Pr;

Sh = 0.664*sqrt(Re)*Sc^(1/3); %% 0.6 < Sc < 50



mc = mwater/msolid; % moisture content kg/kg

wa = 3708.3*mc^6-6115.9*mc^5+3845.2*mc^4-

1117.1*mc^3+132.4*mc^2+0.8111*mc; %wateractivity

if (mc>0.339)

wa = 1;

end

if (mc<0)

wa = 0.000000001;

end

Pvap2 = RH5*Psat5;




Tsa(i) = Ts;


denssurf = wa*Psatsurf/0.462/(Ts+273.15);

dens2 = Pvap2/0.462/(T5+273.15);

mdotvapcalc = hA*(denssurf - dens2);

mdotvapcalca(i) = mdotvapcalc;

%%%%%%%%%%%%%%%%%%%%%%

%%% Plotting

t=1:size(T1a,1);

plot(t(i),mdotvapcalc,'*')

hold on

mwater = mwater - mdotvapcalc*4;

end

grid on

%%% export data to excel

xlswrite('mdotvap',mdotvapa);





13. REFERENCES

[1] http://www.kitchenstewardship.com/2010/06/18/excalibur-dehydrator-review-

head-to-head-vs-nesco-american-harvest-dehydrator/

[2] http://www.google.com/patents/US20070240328

[3] Handbook of Industrial Drying, Fourth Edition, by Arun S. Mujumdar

[4] http://www.nzifst.org.nz/unitoperations/drying1.htm#basictheory

[5] http://www.gunt.de/download/drying_evaporation_english.pdf

[6] http://sst-web.tees.ac.uk/external/u0000504/Notes/UnitOps/EvapnDrying.pdf

[7], [22] Cengel, Yunus A.,and, Boles, Michael A. (2010). Thermodynamics: an

Engineering Approach, 7th ed. McGraw-Hill

[8] http://staff.sut.ac.ir/haghighi/download/documents/Drying.pdf

[9] http://en.wikipedia.org/wiki/Mass_flow_rate

[10] http://dictionary.reference.com/browse/specific+humidity

[11] http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/relhum.html

[12] Mark W. Zemansky (1968), Heat and Thermodynamics, Chapter 11 (5th edition)

page 275, McGraw Hill, New York.

[13] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html

[14] https://www5.eere.energy.gov/manufacturing/tech_deployment/amo_steam_tool/

equipBoiler?pv=1

[15] http://en.wikipedia.org/wiki/Saturation_vapor_density

[16] Khalloufi , S., Glasson, J. and Ratti, C., Water activity of freeze dried mushrooms

and berries,Department of Food Science and Nutrition Canada G1K 7P4. 2000.



[17] http://en.wikipedia.org/wiki/Lewis_number

[18] http://en.wikipedia.org/wiki/Schmidt_number

[19] http://en.wikipedia.org/wiki/Prandtl_number

[20] http://en.wikipedia.org/wiki/Sherwood_number

[21] http://en.wikipedia.org/wiki/Reynolds_number

[22] http://en.wikipedia.org/wiki/Nusselt_number

[23] Manuel R. Conde, (1997) ENERGY CONSERVATION WITH TUMBLER

DRYING IN LAUNDRIES, M. Conde Engineering



14. BIBLIOGRAPHY

Mujumdar, Aruns S. (2014). Handbook of Industrial Drying, 4th ed. CRC Press

Cengel, Yunus A.,and, Boles, Michael A. (2010). Thermodynamics: an Engineering

Approach, 7th ed. McGraw-Hill

Manuel R. Conde, (1997) ENERGY CONSERVATION WITH TUMBLER DRYING IN

LAUNDRIES, M. Conde Engineering