Nonazeotropic binary refrigerant refrigerator drexel senior design project final report

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Drexel University
Mechanical Engineering Department
Senior Design Final Report Titled:
Binary Refrigerant Refrigerator
Project 25
MEM-493
Samuel Beccaria
Abhinav Duggal
Mathew Smith
Xiaoyi Zhu
May 13, 2015
Advisory: Dr. Bakhtier Farouk

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Abstract
The objectives are to design, retro-fit, and test a domestic refrigerator using a binary mixture
of refrigerants. This concept is motivated by energy savings potential, derived from non-
azeotropic refrigerant mixtures. While a single fluid remains at constant temperature during
constant pressure evaporation/condensation processes, a non-azeotropic mixture undergoes
evaporation/condensation processes at constant pressure over a temperature range, called
temperature glide. The first phase of this project was to select two refrigerants and optimize
their mixture fractions for the refrigeration cycle. Certain restrictions apply on the
availability/production of some refrigerants due to their thermophysical and environmental
properties, like high Global Warming Potential (GWP) and high Ozone Depletion Potential
(ODP). Therefore, refrigerants R-125 and R-134A were selected on basis of low GWP and
low ODP. The optimal mixture fraction was then calculated by using the method of Lagrange
Multipliers and the Exhaustive Search method. Performance of the refrigerator, a Magic Chef
Model MCBR270S mini-fridge, was simulated using the optimized binary mixture in the final
phase of this project. Project stakeholders include consumers, appliance manufacturers, and
government agencies.

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Table of Contents
1. Introduction...................................................................................................................................4
1.1. Problem Statement.................................................................................................................4
1.2. Background ............................................................................................................................4
1.3. Motivation ..............................................................................................................................4
1.4. Refrigerant Selection..............................................................................................................4
2. Methods..........................................................................................................................................5
2.1. Thermodynamic System.........................................................................................................5
2.2. Optimization Method.............................................................................................................7
2.2.1 Fall and Winter terms: Lagrange Multiplier Method...................................................7
2.2.2 Spring term: Exhaustive Search Method.......................................................................8
2.3. Experimental Studies .............................................................................................................9
2.4. Experimental Methods.........................................................................................................10
2.4.1. Generalized Experimental Procedure..........................................................................10
3. Conclusions and Discussions: ......................................................................................................10
3.1. Project Management............................................................................................................10
3.1.1. Team Organization.......................................................................................................10
3.1.2. Project Budget ..............................................................................................................11
3.2. Results of Optimization Procedure......................................................................................11
3.2.1. Fall and Winter Terms: Lagrange Multiplier Results ................................................11
3.2.2. Spring Term: Exhaustive Search Results ....................................................................12
3.2.3. Effect of LSHX on Reverse-Rankine System...............................................................14
3.3. Discussion of Experimental Results.....................................................................................16
3.4. Conclusions and Future Work.............................................................................................17
4. Works Cited and Referenced ......................................................................................................18
5. Appendix A: Reversed Rankine Cycle Analysis .........................................................................22
6. Appendix B: Optimization Procedure.........................................................................................26
7. Appendix C: Lagrange Multiplier Code .....................................................................................27
8. Appendix D: Refrigerant Justification........................................................................................28
9. Appendix E: Daewoo Compressor HFL5Y-1 Datasheet.............................................................30
10. Appendix F: Exhaustive Solution................................................................................................31
11. Appendix G: Exhaustive Solution Equations..............................................................................32
12. Appendix H: Water Calorimeter Test.........................................................................................35

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1. Introduction
1.1.Problem Statement
The objectives of the project are to design, retro-fit, and test a domestic vapor compression
refrigerator that uses a binary refrigerant mixture instead of the more traditional single
refrigerant refrigerators.
1.2. Background
Refrigerators that are currently used in households operate on a single working fluid called a
refrigerant. This refrigerant has to meet a certain safety and thermophysical criteria. The most
ideal refrigerant to use should have low toxicity, low flammability, a high heat of vaporization, a
small specific heat and specific volume and low ozone depletion and global warming potentials.
Unfortunately, single refrigerants either offer poor thermophysical properties, causing little harm
to the environment or offer excellent thermophysical properties, resulting in a high potential risk
to the environment. Using a mix of both is one of the most effective ways to work around this
problem [25], [36], [37], [39].
A mixture of two refrigerants is referred to as a binary mixture of refrigerants, which can
experience one or two states simultaneously- liquid, vapor and liquid-vapor, depending upon
pressure and temperature of the system and the saturation pressure of refrigerants in the mixture.
In most cases this allows for a temperature glide effect (a range of saturation temperature for a
given saturation pressure) that allows the freezer temperature to be reached at a lower pressure
[36]. Additionally, by mixing a refrigerant with poor thermophysical properties that does little
harm to the environment to the refrigerant with excellent thermophysical properties that does a
lot of harm to the environment results in a binary mixture that can have a significantly reduced
potential risk to the environment alongside observing gains in the Coefficient Of Performance
COP [37].
1.3. Motivation
Currently, domestic refrigerators in the United States make use of a refrigerant called HFC-134a
(R-134A, 1,1,1,2-Tetrafluoroethane) as their working fluid, which does not deplete the ozone
layer and has an acceptable set of thermophysical properties. However, R134a has high GWP of
1300. The Kyoto Protocol of the United Nations Framework Convention on Climate Change
(UNFCCC) calls for reductions in emissions of six categories of greenhouse gases, including
hydrofluorocarbons (HFCs) used as refrigerants. From the environmental, economic, social and
ethical aspects, it is urgent to find a better alternative to HFC refrigerant [29]. This has been
further explained in Appendix D.
1.4. Refrigerant Selection
From a wide range of refrigerant pairs, R-125/R-152A and R-125/R-134A were chosen based on
their thermophysical and environmental properties. The latter refrigerants were finally chosen
because of their availability; as with the first choice of refrigerants, R-152A was not readily

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accessible in the United States. Also, there were certain restrictions placed on refrigerant use by
the EPA, which states that- refrigerants more flammable than R-134A cannot be used as a
replacement [30]. According to ASHRAE flammability classification, R-152A belongs to A2
class, which means this refrigerant has a lower flammability limit (LFL) of more than 0.10
kg/m3 at 21°C and 101 kPa and a heat of combustion of less than 19,000 kJ/kg [31]. Thus R-
152A can’t be used, although the binary mixture of R-152A and R-125 may have higher COP.
The mixture of R-125 and R-134A is an acceptable choice which has good thermophysical
properties and is most importantly safe to use.
The refrigerator used for this project, which will be operating with the binary refrigerant
selection is a Magic Chef 2.6 Model MCBR270S mini-fridge. This refrigerator employs the
vapor-compression cycle and makes use of the standard compressor, evaporator, condenser,
liquid suction line heat exchanger (LSHX) and throttling valve components.
2. Methods
2.1. Thermodynamic System
In the fall and winter term the focus of the project was on an idealized Reverse-Rankine cycle
using a binary refrigerant mixture. At the end of the winter term it was decided that a modified
Reverse-Rankine cycle was to be used (a Reverse-Rankine cycle with a LSHX.) It was found
from research that common household refrigerators utilize this modified Reverse-Rankine cycle
which is shown in Figure 1.
FIGURE 1. DIAGRAM OF REFRIGERATION CYCLE STATE POINTS WITH LIQUID-SUCTION HEAT EXCHANGER
The working fluid enters the compressor as a saturated vapor and leaves as a superheated vapor.
Due to the fact that superheated vapor is entering the condenser, state 3 is broken up into states
3a and 3b, where 3a is when the working fluid is a saturated vapor and state 3b is when it is a

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saturated liquid. At state 3b the working fluid leaves the condenser as a saturated liquid and
becomes a subcooled liquid after leaving the LSHX. The working fluid is throttled and leaves as
a saturated liquid-vapor mixture, where it enters the evaporator and partially evaporates. The
remaining evaporation occurs over the LSHX and the cycle repeats as the working fluid leaves
the LSHX as a saturated vapor. It is assumed no heat is lost to the environment during any other
process other than inside the condenser, that there is a constant evaporator load, the pressures
over states 5 to 1 and states 2 to 4 are constant, and that there is isentropic compression. The
qualities of the working fluid remain on or under the liquid-vapor dome on its saturation line
from states 5 to 1 and states 3a to 3b [18], [48]. Figure 2 shows the relative states in Figure 1 on
the T-s diagram for the system where each state, states 1 through 6, are labeled at their respective
quality.
FIGURE 2. T-S DIAGRAM FOR SYSTEM IN FIGURE 1, WITH A BINARY MIXTURE AS THE WORKING FLUID
For a binary refrigerant refrigerator that is utilizing a non-azeotropic mixture the phase change
from a saturated vapor to a saturated liquid, and vice versa, experiences a temperature glide over
the phase change [36]. The temperature glide characteristic for a non-azeotropic working fluid
actually reduces the total energy needed to perform the cycle, hence why implementing this
design is crucial to an increase in the coefficient of performance (COP) of the system [37], [24],
[1]. For a binary mixture working fluid the T-s diagram is better understood by the
accompanying concentration diagram (T-x diagram) shown in Figure 3.

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FIGURE 3. T-X DIAGRAM OF WORKING FLUID THROUGHOUT THE ENTIRE SYSTEM
The T-x diagram shows the non-azeotropic nature of the working fluid at two pressure states, at
720 kPa and at 1510 kPa, the pressure ranges for the refrigerator. The line in the graph represents
an arbitrarily chosen mixture fraction. The working fluid, as it works through the system, rides
along the line, starting at state 1 at a low pressure and going to a higher pressure. As it works
through the system, the mass fractions will always remain the same, but the vapor and liquid
fractions will change from state to state [36]. With these principles of how the system works the
deterministic solution can be set up by creating a system of equations from state to state that
represent the physics of the binary working fluid and its function over specific components.
These equations are detailed in Appendix A.
2.2. Optimization Method
2.2.1 Fall and Winter terms: Lagrange Multiplier Method
The goals of this project were to design, retro-fit and test an optimized domestic vapor-
compression refrigerator that makes use of a binary refrigerant as its working fluid. The fall and
winter term were an exercise in developing the method to find the optimal mass fractions of each
refrigerant, R125 and R134A that minimize the work of compression of the Reverse-Rankine
Cycle. In order to accomplish this task the method of Lagrange multipliers, an optimization
algorithm (shown in Appendix B), was created in MATLAB (shown in Appendix C) and used to
find the mass fractions that guarantee a minimized work of compression with regards to the
objective function in Equation 1.

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𝑊𝑐 = 𝑚̇ �𝑥1 ∗ 189.3 ∗ �1 −
15.45 − log( 𝑃𝑡2)
15.45 − log( 𝑃𝑡1)
� + (1 − 𝑥1) ∗ 245.1
∗ �1 −
15.91 − log( 𝑃𝑡2)
15.91 − log( 𝑃𝑡1)
��
(1)
In Equation 1, mdot is the mass flow rate of the binary mixture, x1 represents the mass fraction of
the refrigerant R125 in the binary working fluid, and Pt1 and Pt2 are the total pressures of the
evaporator side and condenser side respectively. Pt1 and Pt2 are expressed as functions of x1, T1
and T3, and the derivation of the objective function and Pt1 and Pt2 are shown in Appendix A.
The objective function is subject to the constraints shown in Equations 2 and 3 that were derived
from the Reverse-Rankine cycle.
𝜙1 = 𝑄 𝑒 − 𝑚̇ ∗ (ℎ1 − ℎ3) = 0 (2)
𝜙2 = 𝑄𝑐 − 𝑄 𝑒 − 𝑊𝑐 = 0 (3)
The constraint in Equation 2 relates the cooling capacity (heat injected into the system by the
evaporator), to the enthalpies from state 4 to state 1. Since the enthalpy at state 4 is equivalent to
the enthalpy at state 3, due to the nature of the throttling valve, Equation 2 applies. Equation 3
describes the constraint that entails the entire energy balance of the system, where the heat
rejected by the condenser is equivalent to the sum of the heat and work injected into the system.
The condenser, evaporator and heat exchanger equations that relate the temperatures of different
states to one another are shown in Appendix A. The log-mean temperature difference is mainly
used to describe the effect of the energy exchange between fluids in a heat exchanger, however
the full extent of this method is not shown, only the resulting equations from it.
Once the foundations were set for the Lagrange Multiplier method the procedure for obtaining
the optimization result was created. Since constructing a third constraint to accompany the
objective function in Equation 1, which is a function of four variables (and thus could have 3
constraint equations), would be tedious the optimization was done iteratively. As a result of this
a value for the mass fraction of R125 in the mixture was chosen, between 0 and 1, and the
optimization was run to produce the optimal result.
2.2.2 Spring term: Exhaustive Search Method
The Lagrange Multiplier method was explored as an option to find the minimum work of
compression for a modified Reverse-Rankine cycle shown in Figure 1 using R125 and R134A in
mixture. However due to the complexity of the equations the Exhaustive Search method was
explored as an option for optimization.
In order to accomplish the task of the Exhaustive Search method a deterministic system was
created, using a set of 8 equations and 8 unknowns, the formulation of which is shown in
Appendices F and G. With a selected mass fraction of R125, the 8 variables are solved for using
the deterministic system and the work of compression is computed. Then another mass fraction
of R125 is selected and the process is repeated. This is carried over the range of 0 to 1 mass
fraction of R125 and was used to find the mass fraction of R125 and R134A that produced a
minimum work of compression.

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The deterministic system is a system of equations, with a number of variables the same as the
number of equations, and solves the system of equations for the variables present. For the entire
system there are 8 equations and 9 unknowns, however in this case the mass fraction of R125
was assumed, and the system contained 8 residual equations (equations whose value sums to be
0) and 8 unknown variables. These variables were the mass flow rate (𝑚̇ ) and the temperature at
states 1 (T1), 2 (T2), 3a (T3a), 3b (T3b), 4 (T4), 5 (T5), and 6 (T6).
The residual equations were setup using a variety of system balances from the energy balances
and pressure balances derived from the modified Reverse-Rankine cycle. That is, the energy
balances over the evaporator, condenser, the liquid to suction line heat exchanger and the overall
system energy balance were used in conjunction with the assumption that the pressure of the
high-side states were equivalent to one another and the pressure of the low-side states were
equivalent to one another. This system of equations is then used to find the solution of each
variable when the mass fraction of R125 is given. Then using the solved values for T1, T2, T3, etc
the work of compression and the COP can be determined. This is done repetitiously for mass
fractions of R125 ranging from 0 to 1 to obtain the temperature values needed to calculate the
COP of the system when using that mixture.
In order to solve the non-linear system of equations the Newton Raphson method was the
method of choice in order to achieve results. The Newton-Raphson method was used because it
is a numerical method capable of handling the bulk of the system of residual equations that
resulted from attempting to create an optimization of the system. In order to use the Newton
Raphson method an initial guess at what the temperature values and mass flow rate are must be
provided, and have the added stipulation that those values must be very close to the actual value,
otherwise the Newton Raphson method will fail.
2.3.Experimental Studies
The experimental studies that pave the way for the testing procedures are drawn from several
sources. Each one of these sources account for certain aspects, such as measuring temperature,
energy exchange, pressures and work of compression for a binary refrigerant refrigerator. Two
sources are PhD works performed at the University of Illinois, Urbana-Champaign’s Air-
Conditioning and Refrigeration Center, where Dr. Stoecker performed his work. It is important
to note that the United States has set specific procedures and conditions for refrigerator/freezer
performance testing. While a calorimeter test is considered the most accurate for testing these
appliances, other methods from a literature study will be presented [36].
One of these prior works by Launay [21], which was performed under supervision of Dr.
Stoecker, describes experimental testing procedures for NARM based refrigerant systems in
detail. They suggest doing performance testing with a fixed evaporator load for the fridge and
freezer. Power consumption of the fridge, measured during compressor on-cycles, is found from
a watt transducer or power meter. The mass flow rate of refrigerant can be measured using a
mass flow meter placed in the refrigerant circuit [12], [13], [15].
The work by Mohanraj [27] performed on NARM refrigeration systems details testing of the
system performance. Because the primary quantities of interest with respect to refrigerator
system performance are evaporating temperature, condensing temperature, power consumption,
and volumetric cooling capacity, experimental data can be determined from these quantities.

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The evaporating temperature can be measured by placing thermocouples along the tubing of the
evaporator. For the condenser, the temperature of the refrigerant can be measured before and
after entering the tubes. The air stream temperatures can be measured using temperature sensors
at inlet and exit points with air blown over the evaporator. The mass flow rate of the air can be
determined by the size of the fan used to blow the air, usually given in cubic foot per minute
(CFM).
2.4.Experimental Methods
The experimental procedure for designing, building, and testing the domestic refrigerator/freezer
with the optimized binary mixture consists of three main stages: Data Acquisition and Reduction
of Baseline System, Charging and Adjusting System with Binary Refrigerant Mixture, and Data
Acquisition/Performance Testing of Optimized Binary Refrigerant System. Data acquisition and
reduction for the baseline system was discussed in the experimental methods section.
2.4.1. Generalized Experimental Procedure
In order to confirm the theoretical results from simulated cycle data, experimental validations
were required to characterize the baseline refrigerator. The baseline refrigerator charged with R-
134a was tested in the lab using a water calorimetry method along with compressor power data
to estimate system several performance parameters. The criteria considered here was the power
consumption of the compressor, the on-off cycling characteristics of the compressor, and the
system COP.
The power input to the compressor was measured using a plug-in wattmeter. This provided
compressor power consumption during compressor on-cycles. The cycle time of the compressor
was the duration of time the compressor was turned on and provided insight into the total amount
of energy supplied to the system. Temperature cycle information was obtained by observing
when the cabinet temperature reached the upper limit for the thermostat, then cooled as the
compressor was running, and finally shut off at the lower limit of the thermostat. By plotting the
cabinet air temperature data over time, the compressor on-time, off-time, the total cycle time was
determined.
The evaporator load was calculated using a water calorimeter placed inside the refrigerator; this
consisted of a small and thin aluminum container filled with 500 milliliters of water at an initial
temperature of 46.3 ℃. This was placed inside the refrigerator with a thermocouple probe
submersed in the water to measure the temperature. The cabinet air temperature, ambient air
temperature, and compressor power were measured as well; these measurements were recorded
every 30 seconds until the water temperature reached 5 ℃. It is important to note that the
compressor was running the entire time the water calorimeter data was recorded. With the
evaporator load and the compressor power the COP of the refrigerator can be calculated.
3. Conclusions and Discussions:
3.1. Project Management
3.1.1. Team Organization
Weekly meetings were held with the team’s advisor Dr. Farouk on Thursday at 11am in the
Randell building. The group delivered weekly progress report to Dr. Farouk during this meeting

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and updated Dr. Farouk with any questions, comments, and concerns that may have developed in
the past week. Dr. Farouk assigned weekly tasks to the group or to individual member in the
group. Weekly team meetings amongst the individuals were held to work together on the tasks,
which were assigned by Dr. Farouk.
The group has four members. One member was held accountable for scheduling meetings,
keeping meeting minutes, and keeping track of project deadlines and requirements. The group
primarily uses Google drive to store all the work, data, research papers and the meeting minutes.
3.1.2. Project Budget
The budget includes the cost of the refrigerator, refrigerants, and sensory instruments described
in Table 1.
TABLE 1.EXPECTED BUDGETED LIST OF ITEMS
Item Vendor Qty
Unit
Cost
Total
Cost
Magic Chef Mini Refrigerator 2.6 cu ft HomeDepot 1 $139.00 $139.00
R125 USA Refrigerants 25 $9.00 $282.00
Taylor 1443 Digital Thermometer Amazon 1 $10.00 $10.00
Blue LED Temperature Sensor Amazon 1 $16.00 $16.00
Kill-A-Watt Electric Usage Monitor Amazon 1 $19.00 $19.00
Aluminum pan Fresh Grocer 5 $1.50 $7.50
Enviro Safe Can-Tap Gauge Sears 1 $28.00 $28.00
Line Tap Valve Amazon 1 $6.00 $6.00
Grand Total: $507.50
The total budget for this project rests at $507.50. The actual items bought and budgeted for are
listed in Table 2. Since the refrigerator was gifted to the group from Drexel’s IRT it is not
included.
TABLE 2. ACTUAL BUDGETED ITEMS
Item Vendor Qty
Unit
Cost
Total
Cost
R125 USA
Refrigerants
25 $9.00 $282.00
Kill-A-Watt Electric Usage Monitor Amazon 1 $19.00 $19.00
Aluminum pan Fresh Grocer 5 $1.50 $7.50
Grand Total: $308.50
The cost of recharging the refrigerator was also not included in this cost since it was not
budgeted for until the end of the spring term.
3.2. Results of Optimization Procedure
3.2.1. Fall and Winter Terms: Lagrange Multiplier Results
The results of the optimization procedure for the Reverse Rankine cycle utilizing a binary
mixture are shown in Table 3.

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TABLE 3. RESULTS OF OPTIMIZATION PROCEDURE FOR MIXTURE OF R125
Concentration
of R125
0.2 0.4 0.6 0.8 0.9 1
T1 (°C) -79.0 -65 -51.9 -37.2 -29.7 -22.3
T3 (°C) 64.9 60 56.5 52.9 51.0 49.1
𝑚̇ (kg/s) 0.00110 0.00105 0.000997 0.000953 0.000934 0.000918
Wc (kW) 0.111 0.0909 0.0723 0.0549 0.0466 0.0385
Table 3 shows that from 0 % to 100% of R125 in the mixture, the optimization favors R125 over
R134A, which would mean that to optimize the simple vapor-compression cycle with regards to
refrigerant mixture, only R125 should exist in the mixture. This was found to not be the case for
the modified Reverse Rankine cycle analyzed with the Exhaustive Search method.
3.2.2. Spring Term: Exhaustive Search Results
The optimization procedure using the deterministic system and the Newton Raphson solver were
able to produce results for R125/R134A that had a minimum work of compression at 0.15/0.85
mass fractions of R125/R134A. With the Exhaustive Search method used for a system with the
system parameters described in Table 4 the minimum work of compression for R125/R134A was
found to exist at 0.15/0.85 mass fractions respectively, the graph of which is shown in Figure 5.
TABLE 4. DOMESTIC REFRIGERATOR SYSTEM PARAMETER VALUES
System Parameter Value
Qe 50 Watts
UA (Condenser) 0.012 W/K
UA (Evaporator) 0.012 W/K
UA (LSHX) 0.00075 W/K
𝑚̇ of air (Condenser) 0.0045 kg/s

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FIGURE 4. WORK OF COMPRESSION AT VARIOUS CONCENTRATIONS OF R125 (MINIMUM LOCATED AT 0.15.)
The minimum work of compression is located at 0.15/0.85 mass fractions of R125/R134A,
although the location is obscured by the “shallowness” of the minimum point. The COP, in
correspondence with the work of compression, has a maximum value of 2.38 located at 0.15 of
R125, the graph of which is shown in Figure 6.
21.01
20.00
21.00
22.00
23.00
24.00
25.00
26.00
27.00
28.00
29.00
30.00
31.00
32.00
33.00
34.00
35.00
36.00
37.00
38.00
39.00
40.00
0 0.2 0.4 0.6 0.8 1
WorkofCompression(W)
Mass Fraction of R125
Work of Compression vs. Concentration of R125
Work of
Compressio
n vs
Concentrati
on of R125

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FIGURE 5. COP AT VARIOUS VALUES OF R125 IN MIXTURE (WITH A MAXIMUM AT 2.38).
The maximum COP and minimum work of compression corresponding to the mixture fractions
of 0.15/0.85 for R125/R134A offer a 0.5% decrease in the work of compression and a 0.7%
increase in COP with regards to pure R134A. The location of the minimum work of compression
and maximum COP differ between refrigerant mixtures and can also change given specific
system parameters. All system parameters have an effect on the location of the minimum work of
compression, but the LSHX is the component of interest since it has been stated that the LSHX is
what allows the smallest possible work of compression to occur for R125 and R134A.
3.2.3. Effect of LSHX on Reverse-Rankine System
The effect of the LSHX on the system is that it drives the temperature of the working fluid down
before it is throttled and allows for a dry saturated vapor quality of the working fluid to be
present at state 1. This in turn seems to drive the work of compression to decrease further, which
in turn drives the COP of the system to increase. A graph of this concept, with the system
operating at different overall heat transfer coefficients, is shown in Figure 7.
2.380
1.300
1.500
1.700
1.900
2.100
2.300
2.500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
COP(W/W)
COP vs. Concentration of R125
COP vs
Concentration
of R125
Maximum
COP

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FIGURE 6. COP OF THE SYSTEM VS. THE CONCENTRATION OF R125 AT DIFFERENT HEAT TRANSFER
COEFFICIENTS OF THE LSHX
What was encountered in the winter term has been encountered for the deterministic solution of
the optimization problem, that when the LSHX is absent, represented by a 0 overall heat transfer
coefficient, there is no peak in the system, save for the maximum located at 0. However as the
heat transfer coefficient is increased, the maximum COP location is shifted to the right and up,
occurring at 0.15/0.85 and then 0.2/0.8. This means that the system itself could be designed to
accept a specific mixture of R125/R134A that allows it to operate at the maximum COP,
corresponding to a minimum work of compression.
This was done for two other types of refrigerants simply to see if this effect is constant across
refrigerant mixtures. The refrigerants selected were R12 and R114. In Figure 8 are the results of
modifying the overall heat transfer coefficient of the LSHX when the working fluid is R12 and
R114 with different system parameters.
1.300
1.500
1.700
1.900
2.100
2.300
2.500
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
COP
COP vs. Mass Fraction of R125
Uax = 0.0025
Uax = 0.00075
Uax = 0.0
No LSHX

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FIGURE 7. COP VS. MASS FRACTION OF R114 FOR A MODIFIED REVERSE RANKINE CYCLE AND A CHANGING HEAT
TRANSFER COEFFICIENT FOR THE LSHX
What is seen in Figure 7 is that the refrigerants R12 and R114 experience a maxima at around
50/50 mass fraction of R12/R114, despite the presence of a LSHX in the simulation model.
3.3.Discussion of Experimental Results
Analysis of the experimental results obtained from the cabinet air temperature profiles showed a
consistent compressor cycle behavior. The cabinet air temperature with the thermostat setting
fixed at the lowest temperature produced an upper temperature value of -1.89 ℃ and a lower
temperature value of -4.7 ℃. Figure # shows the plot of cabinet air temperature over time. It can
be seen from this plot that the total compressor cycle time is approximately 16 minutes. The
compressor on-time and off-time are approximately 7.5 and 8.5 minutes, respectively. A
refrigerant mixture with better performance would be expected to show a shorter compressor on-
time for a fixed evaporator load and thermostat setting.
2.700
2.800
2.900
3.000
3.100
3.200
3.300
3.400
3.500
0 0.2 0.4 0.6 0.8 1 1.2
COP
COP vs. Mass Fraction of R114
Uax = 1.0
Uax = 0.5
Uax = 0.3
Uax = 0.0
No LSHX

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FIGURE 8. CABINET AIR TEMPERATURE OVER TIME DEMONSTRATING THE COMPRESSOR ON/OFF CYCLES
The water calorimeter test was conducted with a shallow bowl of heated water that was placed
inside of the refrigerator and made to be cooled from its high temperature to a temperature of
5°C using a thermocouple to record the temperature of the water every 30 seconds. The
temperature of the water and the subsequent heat load calculations are shown in Appendix H.
The end result was that the Magic Chef 2.6 cubic feet refrigerator, subject to a heated bowl of
water, had a COP of 0.51 W/W, comparing this with the COP for the refrigerator data shown in
Appendix E this is reasonable. This COP value from the experiment does not match with the
simulated COP value for R134A (0% R125, 100% R134A). This is because of the assumptions
made for the modified Reverse-Rankine cycle do not accurately match the Magic Chef
refrigerator in the lab, which has pressure drops and superheated vapor at state 1.
3.4.Conclusions and Future Work
The optimization due to the Lagrange Multiplier method favored 100% R125 for a Reversed-
Rankine cycle. However for the Exhaustive Search method applied to the modified Reverse
Rankine cycle the optimum occurred at 15% R125 and 85% R134A. The optimum value has not
yet been tested in the refrigerator but in the future the refrigerator should be charged with the
optimum mixture and the model results validated.
A major component of the refrigerator considered in this analysis and almost every domestic
refrigerator on the market is a liquid to suction line heat exchanger. This is a simple heat
exchanger that transfers heat from the hot liquid refrigerant on the high-pressure side to the cold
refrigerant on the low-pressure side. These are used on domestic refrigerators for two main
reasons; the first reason is to increase the refrigeration effect in the evaporator by sub-cooling the
liquid refrigerant before throttling, which reduces the amount of flash gas entering the
evaporator. The heat lost from the liquid side is absorbed by the vapor side, which causes the
refrigerant to enter the superheated state on the suction side. The other reason an LSHX is used
on most domestic refrigerators is to prevent liquid from entering the compressor, which would
eventually cause a burnout.
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
0 20 40 60 80 100 120 140
Temperature(degc)
Time (minutes)
Temperature Data logged Once per Minute (Overnight 4-6-2015)

18
From a thermodynamic standpoint, the LSHX produces two effects on system performance,
which can cause an increase or decrease in efficiency, depending on the refrigerants considered.
The LSHX allows the system to produce the same refrigeration effect at a higher evaporation
temperature. At the same time, superheating the refrigerant vapor before compression reduces
the specific volume, which can cause the compressor to operate less efficiently.
The impact on choice of refrigerants for a non-azeotropic refrigeration system comes from the
performance of different working fluids with respect to the LSHX. For some fluids, such as R-12
and R-134a, the COP increases monotonically with the effectiveness of the LSHX, this is the
ratio of the actual heat transfer to the maximum possible heat transfer. For fluids like R-22 and
R-32, the LSHX is detrimental to system performance because the superheating effect outweighs
the increased refrigeration effect, resulting in an overall decrease in COP.
The COP of the Magic Chef refrigerator was found, from the water calorimeter test, to be 0.52
W/W. For the future, the refrigerator should be charged with the simulated optimal mixture
fraction and charged into the refrigerator, so that the COP could be tested for the optimal
mixture. As well, a non-exhaustive optimization method, for the modified Reverse-Rankine
system, using either the Lagrange Multiplier method or any other optimization method, should
be explored. As well, the refrigerator could be tested at multiple mixture fractions in order to
develop an experimental result for incremental mixture fractions of R125 and R134A. As well,
for simulation modeling purposes pressure drops and superheating at state 1 in the modified
Reverse-Rankine cycle could be accommodated for in order to fully represent to Magic Chef
refrigerator.
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19
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Nonzaeotropic Mixture of Refrigerants," ed University of Illinois at Urbaba-Champaign: Oak
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in the vapor compression cycle," in AIChE symposium series, 1984, pp. 122-127.
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ASHRAE transactions, vol. 91, pp. 241-249, 1985.
[38] W. F. Stoecker, Design of Thermal Systems, 3 ed. New York, NY: McGraw Hill, 1989.
[39] W. F. Stoecker and D. J. Walukas, "Conserving energy in domestic refrigerators through the use
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21
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22
5. Appendix A: Reversed Rankine Cycle Analysis
Figure 9 refers to the system diagram for the Reversed Rankine Cycle T-s diagram.
FIGURE 9. REVERSE RANKINE CYCLE T-S DIAGRAM
The Equations 1, 2 and 3 are derived from the properties of the thermodynamic system. Starting
with the objective function in Equation 1, the objective function stems from the model of
isentropic compression for a single working fluid in Equation 5.
𝑊𝑐 = 𝑚̇ ∗ 𝑐1 ∗ �1 −
𝐴1 − log( 𝑃𝑡2)
�
(5)
Where mdot is the mass flow rate of the working fluid, A1 is the saturated pressure-temperature
constant derived from the method of least squares, Pt2 and Pt1 are the total pressure on the
evaporator and condenser sides respectively and the c constant is derived for a specific fluid
undergoing isentropic compression. These constants are derived specifically for R125 and
R134A. The objective function for a single refrigerant can be modified, using the constants
derived for each refrigerant in mixture, shown in Equation 6.
𝑊𝑐 = 𝑥1 ∗ 𝑊𝑐,125 + (1 − 𝑥1) 𝑊𝑐,134𝐴 (6)

23
Where Wc,125 and Wc,134A are the work of compression associated with each working fluid and x1
is the mass fraction of R125 in solution. Substituting Equation 5 into Equation 6 for the
respective refrigerant mixtures gives Equation 7.
𝑊𝑐 = 𝑥1 ∗ 𝑐1 ∗ �1 −
� + (1 − 𝑥1) ∗ 𝑐2 ∗ �1 −
�
(7)
Equation 7 is then modified by substituting the constant values for R125 and R134A returns the
equation given in Equation 1 which is the objective function that is being minimized. In order to
calculate the pressures, Pt1 and Pt2, the mole fraction of each component must be calculated from
the mass fraction. The relationship between mole fraction and mass fraction is shown in
Equation 8.
𝑦𝑥,𝑛 =
𝑥1
�𝑥1 + (1 − 𝑥1)
𝑀1
𝑀2
�
(8)
The variable yx,n represents the mole fraction at a specific quality (vapor or liquid) and at a
specific state, M1 and M2 are the molecular weights of R125 and R134A respectively. Since the
quality of the mixture is a liquid at state 3, this equation applies to state 3. However since the
quality of the mixture at state 1 is a saturated liquid, Equation 9 must be used to calculate the
mole fraction of liquid at state 1.
𝑦𝑙,1 =
𝑦 𝑣,1 ∗ 𝑃134𝐴,1
�𝑃125,1 − 𝑦 𝑣,1 ∗ �𝑃134𝐴,1 − 𝑃125,1��
(9)
And since yv,1 is equivalent to the mole fraction at that state, equation 7 applies in the calculation
of yv,1 using the mass fraction of R125 in mixture, x1. PR,1 represents the saturated vapor pressure
of each refrigerant, R125 and R134A at states 1, and thus with these relationships Pt1 and Pt2 are
expressed as functions of y1 and T1 and y1 and T3 respectively. From Dalton’s law the
relationship between Pt1 and Pt2 to the mass fraction and the temperatures are shown in
Equations 10 and 11 respectively.
𝑃𝑡1 = 𝑦𝑙,1 𝑃125,1 + �1 − 𝑦𝑙,1� ∗ 𝑃134𝐴,1 (10)
𝑃𝑡2 = 𝑦𝑙,3 𝑃125,3 + �1 − 𝑦𝑙,3� ∗ 𝑃134𝐴,3 (11)
Two more equations for the saturated pressure of each refrigerant R125 and R134A are given in
Equation 12 and 13 respectively, the culmination of a least squares fit of saturated pressure-
temperature data from NIST [need reference].
𝑃125,𝑛 = exp �15.45 −
2446.3
𝑇𝑛
�
(12)
𝑃134𝐴,𝑛 = exp �15.91 −
2810.9
𝑇𝑛
�
(13)
Where PR,n is the saturated pressure for R125 and R134A at states 1 or 3 (where R is R125A or
R134A and n is 1 or 3). Thus by substituting Equations 8, 9, 12 and 13 into Equations 10 and 11,

24
Pt1 and Pt2 can be expressed as functions of x1, T1 and x1, T3 shown in Equations 14 and 15
respectively.
𝑃𝑡1 =
𝑥1 ∗ 𝑃134𝐴,1
�𝑃125,1 − 𝑥1 ∗ �𝑃134𝐴,1 − 𝑃125,1��
∗ exp �15.45 −
2446.3
𝑇1
�
+ �1 −
𝑥1 ∗ 𝑃134𝐴,1
�𝑃125,1 − 𝑥1 ∗ �𝑃134𝐴,1 − 𝑃125,1��
� ∗ exp �15.91 −
2810.9
𝑇1
�
(14)
𝑃𝑡2 =
𝑥1
�𝑥1 + (1 − 𝑥1)
𝑀1
𝑀2
�
∗ exp �15.45 −
2446.3
𝑇3
� + �1 −
𝑥1
�𝑥1 + (1 − 𝑥1)
𝑀1
𝑀2
�
�
∗ exp �15.91 −
2810.9
𝑇3
�
(15)
Having the relationships between Pt1 and Pt2 and x1, T1 and T3 allows the creation of the
objective function as a function of the mass flow rate, mass fraction of R125 in mixture, the
temperature at state 1 and the temperature at state 3. The constraint equations are then defined
over the condenser and over the compressor. Starting with the easiest of the constraints, Equation
2 stems from the energy balance over the evaporator. Since the energy put into the system by the
heating fluid in the evaporator is constant, at 0.05 kW, the enthalpies at each state are left to be
calculated in terms of x1, T1 and T3. The enthalpies at states 4 and 1 must be derived from the
thermodynamic system. The enthalpy at state 4 is known from the throttling valve, where it is
assumed that the expansion is isenthalpic. Thus Equation 16 relates the enthalpy at state 3 and
the enthalpy at state 4.
ℎ3 = ℎ4 (16)
Equations relating the enthalpy of state to a quadratic function of Tn, where n is the state, are
shown for vapor and liquid in Equations 17 through 20 for R125 and R134A respectively.
ℎ125,𝑙,𝑛 = 200 + 1.268 ∗ 𝑇𝑛 + 0.00219 ∗ 𝑇𝑛
2 (17)
ℎ125,𝑣,𝑛 = 333.2 + 0.449 ∗ 𝑇𝑛 − 0.00232 ∗ 𝑇𝑛
2 (18)
ℎ134𝐴,𝑙,𝑛 = 200 + 1.349 ∗ 𝑇𝑛 + 0.00142 ∗ 𝑇𝑛
2 (19)
ℎ134𝐴,𝑣,𝑛 = 398.6 + 0.574 ∗ 𝑇𝑛 − 0.000117 ∗ 𝑇𝑛
2 (20)
Where hR,x,n represents the enthalpy for refrigerant R125 or R134A, the state n, and the quality at
that state, vapor, liquid or liquid-vapor. Liquid-vapor mixtures yield an equation that is a
combination of hR,l,n and hR,v,n dependent upon mixture fraction. Since the quality of state 4 is a
subcooled liquid the enthalpy at that state can be approximated by Equation 21.
ℎ3 = 𝑥1 ∗ ℎ125,𝑙,3 + (1 − 𝑥1) ∗ ℎ134𝐴.𝑙,3 (21)

25
For the sensible heat equation, it is necessary to express T2 and T3’ as functions of T3 and the
temperature of the cooling fluid entering the condenser. The analysis of the condenser requires
that the condenser be analyzed in sections, denoted by Figure 5.
FIGURE 10. MODEL OF CONDENSER ANALYSIS
The sensible heat Equations for the sensible heat of vaporization and the initial sensible heat
them become Equations 22 and 23.
𝑄𝑠,1 = 𝑚̇ 𝑐 𝑝 ∗ ( 𝑇2 − 𝑇3′) (22)
𝑄𝑠,2 = 𝑚̇ 𝑐 𝑝 ∗ ( 𝑇3′ − 𝑇3) (23)
The only additional information needed are the equations for T2 and T3’. These equations are
given in Equations 24, 25 and 26.
𝑇3′ =
𝑇3 − 25 ∗ �1 − exp �𝑈𝐴 ∗ �
1
𝑊1
−
1
𝑊2
��
𝑊1
𝑊2
− 1
(24)
𝑇 𝑚 = 25 − (25 − 𝑇3′ ) ∗
1 − exp �𝑈𝐴 ∗ �
1
𝑊2
−
1
𝑊1
��
𝑊2
𝑊1
− exp �𝑈𝐴 ∗ �
1
𝑊2
−
1
𝑊1
��
(25)

26
𝑇2 =
𝑇3′ − 𝑇 𝑚 ∗ �1 − exp �𝑈𝐴 ∗ �
1
𝑊1
−
1
𝑊2
��
𝑊1
𝑊2
− 1
(26)
Where W1 is the product of the mass flow rate and the specific heat of the working fluid, W2 is
the product of the mass flow rate and the specific heat of the cooling fluid, and the UA is the heat
transfer coefficient of the condenser. Substituting all of these equations into the relevant
preceding equations yields the equation that describes the energy out of the system, given in
Equation 27.
𝑄𝑐 = 𝑚̇ 𝑐 𝑝 ∗ ( 𝑇2 − 𝑇3′ ) + 𝑚̇ 𝑐 𝑝 ∗ ( 𝑇3′ − 𝑇3) + 𝑚̇ �ℎ3,𝑣 − ℎ3,𝑙� (27)
A third constraint equation could be created to accommodate the fourth variable, x1, in the
objective function could be created, however due to the nature of the process, where x1 is
selected prior to the optimization, a third constraint equation is unnecessary.
6. Appendix B: Optimization Procedure
The method of Lagrange multipliers is a constrained optimization algorithm that takes a function
to be minimized (or maximized), the objective function, and, along with a set of constraints,
finds the values within the system that minimize the objective function. The method of Lagrange
multipliers states that the optimum occurs when the Equations 28, 29 and 30 are satisfied.
𝛻𝐹( 𝑥1, 𝑥2, … , 𝑥 𝑛) − � 𝜆𝑖∇𝜙𝑖
𝑚
𝑖=1
= 0
(28)
𝜙1( 𝑥1, 𝑥2, … , 𝑥 𝑛) = 0 (29)
..................................
𝜙 𝑚( 𝑥1, 𝑥2, … , 𝑥 𝑛) = 0 (30)
In this set of equations, F is the objective function, λi is the set of Lagrange multipliers and φi is
the set of constraint equations. The set of Lagrange multipliers is always the same size as the set
of constraint equations, but the number of constraint equations is always less than the number of
variables, n, in the objective function. If the set of equations resulting from Equations 38, 39 and
40 are linear then linear algebra can be used to solve that respective set. The set of resulting
equations is non-linear so the Newton-Raphson method must be implemented on the set of
Lagrange multiplier equations. Regardless of the process, the solution to the system of equations
given in Equations 38, 39 and 40 produce the values x1, x2,…,xn and λ1, λ2,…,λm that result in the
minimum (or maximum) output of the objective function. The resulting set of Lagrange
multipliers shed light on how the minimum (or maximum) changes with a perturbation in the
control parameters (the constants in the system).

27
7. Appendix C: Lagrange Multiplier Code
function [f,err] = LagrangeComplete(objf,conf,mx,ml,xt,step)
F = objf - ml*conf;
hF = hessian(F,[mx(1:numel(mx)-1) ml]);
A = eval(subs(hF,[mx(1:numel(mx)-1) ml],xt));
jF = jacobian(F,[mx(1:numel(mx)-1) ml]);
B = eval(subs(jF,[mx(1:numel(mx)-1) ml],xt));
Sol = [xt eval(subs(objf,mx(1:numel(mx)-1),xt(1:numel(mx)-1)))];
xc = xt' - AB';
err = step;
while err>1E-6;
xt = xc';
A = eval(subs(hF,[mx(1:numel(mx)-1) ml],xt));
B = eval(subs(jF,[mx(1:numel(mx)-1) ml],xt));
SolL = [xt eval(subs(objf,mx(1:numel(mx)-1),xt(1:numel(mx)-1)))];
Sol = [Sol;SolL];
xc = xt' - AB';
err = [err;max(abs((AB')./xt'))];
end
si = size(Sol);
f = [xc;double(vpa(subs(objf,mx(1:numel(mx)-1),xc(1:numel(mx)-1)')))];
tab(f',mx,ml)
check = eval(subs(conf,[mx(1:numel(mx)-1) ml],f(1:numel(f)-1)'));
display(check)
hold on
for i = 1:numel(xt)+1
plot(1:si(1),Sol(:,i),'Color',rand(1,3))
end
m = [mx(1:numel(mx)-1) ml mx(numel(mx))];
legend([mx(1:numel(mx)-1) ml mx(numel(mx))],'Location','SouthEastOutside');

28
for i = 1:numel(m)
text(si(1),Sol(si(1),i),[char(m(i)) ' converges to ' num2str(Sol(si(1),i))],...
'FontSize',5);
end
xlabel('No of Iterations')
ylabel('Variable')
title('Convergence Chart')
hold off
Nam = cellstr(num2str([1:si(1)]'))' ;
array2table(Sol,...
'VariableName',[mx(1:numel(mx)-1) ml mx(numel(mx))],...
'RowNames',Nam)
Published with MATLAB® R2014b
The purpose of the Lagrange Multiplier code is to take any set of objective function, constraint
equations, system variables and Lagrange multipliers, as well as an initial guess and error, and
solve for the minimum value of the given objective function subject to the given constraints. The
output of the code is an iteration table showing how much iteration the function took to
converge, a convergence chart, the optimized values for the set of x and λ and the final error
output of the code.
8. Appendix D: Refrigerant Justification
The selections of the refrigerants to use in the binary mixture were made such that the resultant
refrigerant mixture was actually usable as a replacement to R134A according to ASHRAE and
EPA standards [28]. That is, any refrigerant with flammability class A2 or higher cannot be used
as a replacement to a refrigerant with an A1 flammability class. The properties for the four best,
and available, refrigerants that were up for selection are in Table 3.
TABLE 5. LIST OF REFRIGERANT PROPERTIES AT 140 KPA [5],[22],[24],[25]
Refrigerant Hfg
(kJ/kg)
Cp(L,V)
(kJ/kg)
Density(L,V)
(kg/m^3)
Tsat@Pe=140
(C)
GWP/ODP Flammability
Class
R-32 374.6057 1.5978;0.91044 1194.6;4.0502 -45.093 675;0 A2
R-125 160.3147 1.1294;0.71763 1488.7;9.2095 -41.267 3500;0 A1
R-134A 212.08 1.2957;0.82037 1354.5;7.1353 -18.760 1100;0 A1
R-152A 323.061 1.6454;1.0104 995.22;4.5770 -16.464 124;0 A2
Of the best performing refrigerants in this table, R125 and R134A are the only two refrigerants
that meet the criteria set by ASHRAE standard 15 [28]. Thusly these were the two refrigerants
that have been selected regardless of harm to the environment. For the scope of this project,
which must abide by the standards that it purports to follow, this refrigerant mixture is acceptable

29
to be used based off of that standard. However a conundrum arises from ASHRAE standard 34
and the Kyoto Protocol which require that the GWP from hydrofluorocarbons (which includes
refrigerants), be reduced. With the mixture of R125/R134A it appears that the GWP actually
increases for these mixtures, which are both HFCs. The contradiction could only be annulled by
creating an entirely new refrigerant with a low GWP, however this is beyond the scope of this
project. The conundrum is only rectified by the fact that complying with ASHRAE standard 15
guarantees immediate safety (i.e. the refrigerator won’t explode), and of the four refrigerants in
Table 3 only R125 and R134A are easily available.

30
9. Appendix E: Daewoo Compressor HFL5Y-1 Datasheet
Table 6. SPECIFICATION OF DAEWOO COMPRESSOR
Model HFL5Y-1 Date of Approval 2002-07-22
Voltage 110-115V Frequency 60Hz
APPLICATION
Evaporating temp. range
-35¡É~-10¡É
Refrigerant control
Capillary tube
-31¢µ~14¢µ Compressor cooling Static cooling
Refrigerant R134a Voltage range 94~132 V
PERFORMANCE kcal/h 43 (50W)
Test condition (ASHRAE L.B.P)
Cooling capacity Btu/h 171 Evaporating temp. ¡É -23.3 (-10 ¢µ)
Power input W 65 Condensing temp. ¡É 54.4 (130 ¢µ)
Current A 0.9 Liquid subcooled to ¡É 32.2 (90 ¢µ)
Efficiency : COP W/W 0.77 Gas superheated to ¡É 32.2 (90 ¢µ)
Efficiency : EER Btu/Wh 2.63 Ambient temp. ¡É 32.2 (90 ¢µ)
Test power source : 115V 60Hz
Test equipment : DAEWOO Calorimeter
COMPRESSOR DATA MOTOR DATA
Design Recipro. ball joint Motor type RSIR, 1¥Õ 2-pole
Displacement cc/rev 2.3 Voltage range V 94~132
Bore size (¥Õ) mm 18.0 High potential test V/sec 1800
Speed r.p.m. 3520 Rated current A 0.9
Oil charge cc 230 Starting current (LRA) A 4.3
Weight (incl. oil) kg 6.3 Running capacitor VAC/§Þ NONE
Residual moisture mg ¡é 70 Starting capacitor VAC/§Þ NONE
Impurities mg ¡é 25 LRA : IEC Standard method (335-2-34)
OVERLOAD PROTECTOR (OLP) STARTER
Type 4TM 174SHBYY-52
Type :
PTC
Opening temp. ¡É 135 (275 ¢µ) RSIR
Closing temp. ¡É 69 (156 ¢µ) Resistance at 25¡É §Ù 6.8
Trip current at 70¡É A 1.4 Recovery time sec ¡é 80
Trip current at 25¡É A
5.0 [5~15sec]

31
10. Appendix F: Exhaustive Solution
Due to the size of the equations that are produced from the reduction of equations the
optimization problem was turned into a deterministic problem by assuming that a variable in the
equation set is known. In this case the mass fraction of R125 is assumed to be known, thus
leaving a total of 8 equations and 8 unknowns. The unknown variables are listed below:
1. 𝑚̇ (Mass flow rate of the binary refrigerant)
2. T1 (Temperature at state 1)
4. T3a (Temperature at state 3a)
5. T3b (Temperature at state 3b)
The equations themselves are too large to put into this Appendix. They will be attached in the
second appendix.

32
11. Appendix G: Exhaustive Solution Equations
The 8 equations are shown in Equations 31 through 38.
𝑥
1.4135−0.4135∗𝑥
∗exp�14.861−
2498.3
𝑇3𝑎+273
�
exp�15.407−
2993.2
𝑇3𝑎+273
�−
𝑥
1.4135−0.4135∗𝑥
∗�exp�15.407−
2993.2
𝑇3𝑎+273
�−exp�14.861−
2498.3
𝑇3𝑎+273
��
∗ exp �15.407 −
2993.2
𝑇3𝑎+273
� +
�1 −
𝑥
1.4135−0.4135∗𝑥
∗exp�14.861−
2498.3
𝑇3𝑎+273
�
exp�15.407−
2993.2
𝑇3𝑎+273
�−
𝑥
1.4135−0.4135∗𝑥
∗�exp�15.407−
2993.2
𝑇3𝑎+273
�−exp�14.861−
2498.3
𝑇3𝑎+273
��
� ∗ exp �14.861 −
2498.3
𝑇3𝑎+273
� =
𝑥
1.4135−0.4135∗𝑥
∗ exp �15.407 −
2993.2
𝑇3𝑏+273
� + �1 −
𝑥
1.4135−0.4135∗𝑥
� ∗ exp �14.861 −
2498.3
𝑇3𝑏+273
�
(31)
𝑋𝑙,5( 𝑇1, 𝑇5) ∗ (200 + 0.954 ∗ 𝑇5 + 0.00116 ∗ 𝑇5
2) + �1 − 𝑋𝑙,5( 𝑇1, 𝑇5)� ∗ (200 + 0.925 ∗ 𝑇5 + 0.00081 ∗ 𝑇5
2) + 𝑋 𝑣,5( 𝑇1, 𝑇5) ∗ ( 337.4 +
0.623 ∗ 𝑇5 − 0.000086 ∗ 𝑇5
2) ∗ �1 − 𝑋 𝑣,5( 𝑇1, 𝑇5)� ∗ (351.5 + 0.428 ∗ 𝑇5 − 0.00071 ∗ 𝑇5
2) = 0.1 ∗ (200 + 0.954 ∗ 𝑇5 + 0.00116 ∗ 𝑇5
2) +
(1 − 0.1) ∗ (200 + 0.925 ∗ 𝑇5 + 0.00081 ∗ 𝑇5
2)
(32)
20 = 5 ∗
10−𝑇6−𝑇5
log
−15−𝑇6
−25−𝑇5 (33)
5 ∗ 𝑓𝑆 𝐻 ∗
𝑇2−𝑇𝑐𝑜−𝑇3𝑎+𝑇 𝑚
log�
𝑇2−𝑇 𝑐𝑜
𝑇3𝑎−𝑇 𝑚
�
+ 5 ∗ (1 − 𝑓𝑆 𝐻) ∗
𝑇3𝑎−𝑇 𝑚−𝑇3𝑏+25
ln
𝑇3𝑏−25
=
20 + 𝑚̇ ∗ �0.1 ∗ 158 ∗ �1 −
15.407−ln�𝑃3𝑎(𝑇3𝑎)�
15.407−ln�𝑃𝑡,6(𝑇1,𝑇6)�
� + 0.9 ∗ 188 ∗ �1 −
14.861−ln�𝑃3𝑏(𝑇3𝑏)�
14.861−ln�𝑃𝑡,5(𝑇1,𝑇5)�
��
(34)
20 = 𝑚̇ ∗ �𝐹𝑟𝑙6( 𝑇1, 𝑇6) ∗ �𝑋𝑙,6( 𝑇1, 𝑇6) ∗ (200 + 0.954 ∗ 𝑇6 + 0.00116 ∗ 𝑇6
2) + �1 − 𝑋𝑙,6( 𝑇1, 𝑇6)� ∗ (200 + 0.925 ∗ 𝑇6 + 0.00081 ∗ 𝑇6
2)� +
�1 − 𝐹𝑟𝑙6( 𝑇1, 𝑇6)� ∗ �𝑋 𝑣,6( 𝑇1, 𝑇6) ∗ ( 337.4 + 0.623 ∗ 𝑇6 − 0.000086 ∗ 𝑇6
2) ∗ �1 − 𝑋 𝑣,6( 𝑇1, 𝑇6)� ∗ (351.5 + 0.428 ∗ 𝑇6 − 0.00071 ∗ 𝑇6
2)� −
�𝐹𝑟𝑙5( 𝑇1, 𝑇5) ∗ �𝑋𝑙,5( 𝑇1, 𝑇5) ∗ (200 + 0.954 ∗ 𝑇5 + 0.00116 ∗ 𝑇5
2) + �1 − 𝑋𝑙,5( 𝑇1, 𝑇5)� ∗ (200 + 0.925 ∗ 𝑇5 + 0.00081 ∗ 𝑇5
2)� +
(35)

33
�1 − 𝐹𝑟𝑙5( 𝑇1, 𝑇5)� ∗ �𝑋 𝑣,5( 𝑇1, 𝑇5) ∗ ( 337.4 + 0.623 ∗ 𝑇5 − 0.000086 ∗ 𝑇5
2) ∗ �1 − 𝑋 𝑣,5( 𝑇1, 𝑇5)� ∗ (351.5 + 0.428 ∗ 𝑇5 − 0.00071 ∗ 𝑇5
2)��
𝑚̇ ∗ �0.1 ∗ (337.4 + 0.623 ∗ 𝑇1 + 0.000086 ∗ 𝑇1
2
) + 0.9 ∗ (351.5 + 0.428 ∗ 𝑇1 − 0.00071 ∗ 𝑇1
2
) − �𝐹𝑟𝑙6( 𝑇1, 𝑇6) ∗ �𝑋𝑙,6( 𝑇1, 𝑇6) ∗ (200 + 0.954 ∗
𝑇6 + 0.00116 ∗ 𝑇6
2) + �1 − 𝑋𝑙,6( 𝑇1, 𝑇6)� ∗ (200 + 0.925 ∗ 𝑇6 + 0.00081 ∗ 𝑇6
2)� + �1 − 𝐹𝑟𝑙6( 𝑇1, 𝑇6)� ∗ �𝑋 𝑣,6( 𝑇1, 𝑇6) ∗ ( 337.4 + 0.623 ∗
𝑇6 − 0.000086 ∗ 𝑇6
2) ∗ �1 − 𝑋 𝑣,6( 𝑇1, 𝑇6)� ∗ (351.5 + 0.428 ∗ 𝑇6 − 0.00071 ∗ 𝑇6
2)�� = 0.3 ∗
𝑇3𝑏−𝑇1−𝑇4+𝑇6
ln
𝑇3𝑏−𝑇1
𝑇4−𝑇6
(36)
𝑚̇ ∗ �0.1 ∗ (337.4 + 0.623 ∗ 𝑇1 + 0.000086 ∗ 𝑇1
2
) + 0.9 ∗ (351.5 + 0.428 ∗ 𝑇1 − 0.00071 ∗ 𝑇1
2
) − �𝐹𝑟𝑙6( 𝑇1, 𝑇6) ∗ �𝑋𝑙,6( 𝑇1, 𝑇6) ∗ (200 + 0.954 ∗
𝑇6 + 0.00116 ∗ 𝑇6
2) + �1 − 𝑋𝑙,6( 𝑇1, 𝑇6)� ∗ (200 + 0.925 ∗ 𝑇6 + 0.00081 ∗ 𝑇6
2)� + �1 − 𝐹𝑟𝑙6( 𝑇1, 𝑇6)� ∗ �𝑋 𝑣,6( 𝑇1, 𝑇6) ∗ ( 337.4 + 0.623 ∗
𝑇6 − 0.000086 ∗ 𝑇6
2) ∗ �1 − 𝑋 𝑣,6( 𝑇1, 𝑇6)� ∗ (351.5 + 0.428 ∗ 𝑇6 − 0.00071 ∗ 𝑇6
2)�� = 0.1 ∗ (200 + 0.954 ∗ 𝑇3𝑏 + 0.00116 ∗ 𝑇3𝑏
2
) + 0.9 ∗
(200 + 0.925 ∗ 𝑇3𝑏 + 0.00081 ∗ 𝑇3𝑏
2
) − �0.1 ∗ (200 + 0.954 ∗ 𝑇4 + 0.00116 ∗ 𝑇4
2) + 0.9 ∗ (200 + 0.925 ∗ 𝑇4 + 0.00081 ∗ 𝑇4
2)�
(37)
5 ∗ 𝑓𝑆𝐻 ∗
𝑇2−𝑇𝑐𝑜−𝑇3𝑎+𝑇 𝑚
log�
𝑇2−𝑇 𝑐𝑜
�
+ 5 ∗ (1 − 𝑓𝑆𝐻) ∗
𝑇3𝑎−𝑇 𝑚−𝑇3𝑏+25
ln
𝑇3𝑏−25
= 3.352 ∗ ( 𝑇𝑐𝑜 − 25)
(38)
Where Tm and Tco are shown in equations 39 and 40.
𝑇 𝑚 =
𝑇3𝑎−𝑇2∗�
1−exp�5∗𝑓𝑠ℎ∗�
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
+exp�5∗𝑓𝑠ℎ∗�
1
𝑚̇ ∗0.99
−
1
3.352
��
�
1−
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
1
𝑚̇ ∗0.99
−
1
3.352
��
(39)

34
𝑇𝑐𝑜 =
𝑇3𝑎−𝑇2∗�
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
1
𝑚̇ ∗0.99
−
1
3.352
��
�
1−
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
1
𝑚̇ ∗0.99
−
1
3.352
��
+
⎝
⎜⎜
⎛
𝑇3𝑎 −
𝑇3𝑎−𝑇2∗�
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
1
𝑚̇ ∗0.99
−
1
3.352
��
�
1−
1
𝑚̇ ∗0.99
−
1
3.352
��
𝑚̇ ∗0.99
3.352
1
𝑚̇ ∗0.99
−
1
3.352
��
⎠
⎟⎟
⎞
∗
1
3.352
−
1
𝑚̇ ∗0.99
��
3.352
𝑚̇ ∗0.99
1
3.352
−
1
𝑚̇ ∗0.99
��
(40)
In order to turn this into an optimization problem, the concentration is set between 0 and 1 and the concentration value that produces the highest COP
is the optimal value for the system.

35
12. Appendix H: Water Calorimeter Test
The process of acquiring a crude approximation of the COP of the Magic Chef 2.6 cu ft refrigerator involved
setting a heated bowl of water inside the refrigerator and taking the change in the temperature of the water over
a period of time using a K-type thermocouple. By using a thin and shallow aluminum pan the heat load of the
pan and heat transfer due to vertical components were neglected. The volume of the water, time, temperature of
the water, and the power used by the refrigerator were recorded. Figure 11 shows the graph of the temperature
of the water with respect to time.
FIGURE 111. TEMPERATURE OF HOT WATER WITH RESPECT TO TIME
The pan was filled with 500 mL of water, corresponding to 0.5 kg of water. The water exchanges heat with the
air inside the refrigerator and in turn the air exchanges heat with the evaporator. This relationship is symbolized
in Equation 41.
𝑄 𝑒 = 𝑄 𝑎𝑖𝑟 = 𝑄 𝑤 (41)
Where Qe is the evaporator heat load, Qair is the air heat load and Qw is the water heat load. Since the heat load
of interest is the water heat load Qw, and the temperature-time response is inherently nonlinear an exponential
function is fitted to the data, given in Equation 42.
𝑇 = 48.11 ∗ exp �−8 ∗ 10−
2
5
∗𝑡
�
(42)
Evaluating the function at the 0 and 2460 second marks, multiplying by the mass and specific heat of the water,
and then dividing by the total time gives the heat load of the water, and subsequently the evaporator load, the
entire process is shown in Equation 43.
y = 48.11e-8E-04x
R² = 0.9901
0
10
20
30
40
50
60
0 500 1000 1500 2000 2500 3000
AxisTitle
Axis Title
Thermocouple in Water Temperature vs. Time Data
Thermocouple
Data
Expon.
(Thermocouple
Data)

36
𝑄 𝑒 = 𝑄 𝑤 = 0.5 ∗ 4.19 ∗ 48.11 ∗
�exp(−8 ∗ 10−4
∗ 𝑡0) − exp�−8 ∗ 10−4
∗ 𝑡𝑓��
2460
(43)
With the evaporator load approximated, from this equation Qe is 0.0351 kW, the compressor power is needed in order
to calculate the COP, which is the ratio of the evaporator load to the work of compression. The compressor power graph
is shown in Figure 11.
FIGURE 11. COMPRESSOR POWER VS. TIME
The compressor power varies with time, and as the heat from the water is experienced inside the refrigerator the
compressor power increases. However as the heat load dissipates and is cooled the compressor power decreases
to match the effect. Thus the average compressor power of 68.04 W is used to calculate the COP. From the
calculated total heat load and the average work of compression the COP was found to be 0.52 W/W. Attached
at the end of this report is the Daewoo data sheet for the Magic Chef 2.6 cu ft refrigerator, shown in Table 1,
where the COP for an ambient temperature of 32.2 °C is given as 0.77 W/W. (in the case of the group’s testing
the ambient temperature is approx. 27-28 °C)
65
66
67
68
69
70
71
72
73
0 500 1000 1500 2000 2500 3000
CompressorPower(W)
Time (s)
Compressor Power vs. Time
Compressor Power

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