Thermal Fluids Design Project

Final Report - Spring 2013

Group F1/F2

Elle Allen, Justin Barsano, Andrew Willig

Alex Munoz, Jennifer Elkin, Rachel Chow

1. Summary

The objective of this project was to design an optimized automated cooling unit for shipping sensitive material in a variety of different environmental conditions. Our group came up with four possible solutions: an ice water cooling system with coolant flow, a device using Peltier cells, a magnetic cooler, and a cooler that works by circulating water. After considering the pros and cons of each design, we decided that the ice water cooling mechanism was the best option. It would be the best at maintaining the set temperature (4°C), the most resistant to environmental conditions, and require a low amount of power for operation comparatively. For this design, we added a water hammer, changed the coolant to acetone, had the coolant flowing through the system continuously, and used a dry-ice bath. The pump we included was the Micropump GA/GAH Series External Gear Pump, the motor chosen was the EagleDrive MSE DC Drive Motor with electromagnetic drive, and the water hammer arrestor was the Sioux Chief Mini-rester. Other specific features included dry ice, a resistive heating wire, self-adhesive thermocouples, an Arduino electronic prototyping platform and motor shield, a serial enabled 16x2 LCD, a styrofoam container box, and different tubing (see the appendix for more details). Based on the specific datasheets for these components, some analysis was completed to estimate the performance of this device. We predicted that we needed about 7.447 W to maintain steady state temperature conditions, we lost 56.36 W of energy during storage in lower storage chambers, and we needed about 10.5 lbs of dry ice for a 12-hour operation cycle. All of these different components are expected to cost a total of about $483.73, and the amount of time it would take to machine this cooling system would probably be a minimum of two full days (48 hours). For the performance expectancy, our cooling system yields a reasonable price and a reasonable amount of time required in the machine shop.

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2. Detailed Design - See next couple of pages for Assembly Drawings of the entire system and Mechanical

Drawings of the parts that will be manufactured in-house.

Assembly Instructions:

1) Cut out a small portion of the Styrofoam Box to allow for the electronics assembly. a. Electronics Assembly – See Appendix A for Arduino installation and LCD.

2) Glue in Styrofoam Divider to have separate compartments. a. Should be ~127mm from right wall

3) Next, insert all of the tubing, the motor and pump assembly and bio-specimen compartment and connect all of these tubes using the Tygon plastic tubing and adapters.

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4) After all of the tubing is installed, connect all of the electronics. 5) Add the acetone to the pipe system through the water hammer arrestor’s top cap.

6) Add the Dry Ice and the Bio-specimen container to the compartment and the electronic system.

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ITEM NO. PART NUMBER DESCRIPTION QTY.1 styrofoam box Box 12 HolderAssembly Biospecimen Holder Assembly 13 series GA-GAH

pump Pump 14 Eagledrive Motor 15 WaterHammer.375 Water Hammer Arrestor 16 styrofoam box lid Lid 17 5117K96 Tube Adapter 68 SquareCopperCoil Copper Coil 19 biospecimen_conta

iner Biospecimen 110 ThemalCouple Thermocouple 111 styrofoam divider Divider 112 electronics_assemb Electronics Assembly 1

Cooling System Assembly

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ITEM NO. PART NUMBER DESCRIPTION QTY.1 arduinoWshield Arduino Assembly 12 3 Way 3-Pin Connector 13 boxFront Laser Cut Acrylic 14 boxSide Laser Cut Acrylic 15 boxSide_switchhole

s Laser Cut Acrylic 16 boxBack Laser Cut Acrylic 17 boxBottom Laser Cut Acrylic 18 boxTop Laser Cut Acrylic 19 LCD_09394 LCD Board 110 battery_pack Battery Pack 1

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3. Detailed Analysis Steady-State Hand Analysis For the simplified steady-state hand analysis, the design was divided into two subsystems: the cooling coil and the coil surrounding the biospecimen container. Using these two subsystems, the temperature of the acetone coolant at the inlets and outlets of both subsystems could be found.

Figure 1: Schematic illustration of the two subsystems using the constant surface temperature

assumption for the biospecimen container subsystem

Figure 2: Schematic illustration of the two subsystems using the annulus assumption for the

biospecimen container subsystem

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Cooling Coil Subsystem The cooling coil (right) was modeled as a copper pipe with an acetone coolant submerged in dry ice. The bulk of this analysis came from the assumption of a constant surface temperature. This assumption was used because the temperature of the dry ice surrounding the copper pipe was assumed to be at a constant -78.5°C, the temperature at which dry ice freezes. In addition, the assumption that the polystyrene container holding the cooling system was thick enough such that outside effects could be neglected was made. This allowed for the cooling coil subsystem to be isolated. For this subsystem analysis, the following assumptions were made:

1. Steady-state conditions 2. Constant properties 3. Incompressible flow 4. Negligible viscous dissipation 5. Fully developed flow 6. Constant wall temperature 7. Negligible tube wall resistance 8. Thin walled tube

Given an inlet temperature, the following equations were used to determine the outlet temperature of the acetone:

𝑅𝑒𝐷 =4𝜋𝐷𝜇

(1)

𝑁𝑢 = 3.66 𝑓𝑜𝑟 𝑅𝑒𝐷 < 2300

0.023𝑅𝑒𝐷45𝑃𝑟0.3 𝑓𝑜𝑟 𝑅𝑒𝐷 > 2300

(2)

ℎ =𝑁𝑢 · 𝑘𝐷

(3)

𝑇𝑜𝑢𝑡 = 𝑇𝑠 − (𝑇𝑠 − 𝑇𝑖𝑛)𝑒−ℎ𝑃𝐿𝑐𝑝 (4)

Equation (1) is the equation for the Reynolds number of the flow, where ṁ is the mass flow rate of the acetone going through the pipe, which was found using the lower bound of the mass flow rate range of the chosen pump, D is the diameter of the pipe, and μ is the dynamic viscosity of the acetone. This dimensionless number determines whether or not a flow is laminar or turbulent. For internal flow, Reynolds numbers below 2300 are considered to be laminar and those above 2300 are generally considered to be turbulent. The Reynolds number is helpful for determining which Nusselt number correlation to use.

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Equation (2) is the equation for the Nusselt number, where ReD is the Reynolds number and Pr is the Prandlt number of the acetone. The Nusselt number is the ratio of convective heat transfer to conductive heat transfer across a boundary. This number is an intermediate step to calculating the convective heat transfer coefficient. Depending on the Reynolds number, different correlations are used. In this case, the Reynolds number of the system is below 2300 allowing for the use of the first Nusselt number correlation. Once the Nusselt number is known, the convective heat transfer coefficient can be found. Equation (3), where Nu is the Nusselt number, k is the thermal conductivity of the acetone, and D is the diameter of the copper pipe, is used to calculate the convective heat transfer coefficient. Finally, once all of the above parameters are known, the outlet temperature of the acetone of the cooling coil subsystem can be found using equation (3), where Ts is the surface temperature of the copper pipe, in this case it is the temperature of the dry ice, Tin in the inlet temperature of the acetone, which is equal to the outlet temperature of the biospecimen container subsystem, h is the convective heat transfer coefficient, P is the perimeter of the cooper pipe, L is the length of the copper pipe, ṁ is the mass flow rate of the acetone, and cp is the specific heat capacity of acetone. Biospecimen Container Subsystem The biospecimen container subsystem (left) was simplified in two different ways. The first simplification is the same simplification used above for the cooling coil where the temperature of the surface of the biospecimen container is at a constant 4°C, the desired temperature. The second simplification made was to model the biospecimen container and copper tube as a concentric tube annulus where the acetone flowed around the biospecimen container. Constant Surface Temperature Assumption For this subsystem analysis, the following assumptions were made:

1. Steady-state conditions 2. Constant properties 3. Incompressible flow 4. Negligible viscous dissipation 5. Fully developed flow 6. Constant wall temperature 7. Negligible tube wall resistance 8. Thin walled tube

The same equations used to calculate the outlet temperature of the cooling coil, were used to calculate the outlet temperature of the biospecimen subsystem. The only differences were that Ts was the temperature of the surface of the biospecimen container and Tin was the outlet temperature of the cooling coil subsystem.

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Annulus Assumption In this subsystem analysis the biospecimen continer was modeled as a concentric tube annulus (Figure 2, left) with the acetone flowing in the annulus. To make the two assumptions comparable, an assumption used for this model was that the outer surface was insulated and the other was at a constant temperature of 4°C. For this subsystem analysis, the following assumptions were used:

1. Steady-state conditions 2. Constant properties 3. Incompressible flow 4. Negligible viscous dissipation 5. Fully developed flow 6. Laminar flow 7. Inner surface is at a constant temperature 8. Outer surface is insulated

To calculate the outlet temperature of the biospecimen container subsystem, the following equations were used:

𝐷ℎ = 𝐷𝑜 − 𝐷𝑖 (5)

𝑞′′ =𝑞𝐴𝑠

(6)

𝑁𝑢 = 𝑣𝑎𝑙𝑢𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑢𝑠𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑎 𝑡𝑎𝑏𝑙𝑒

ℎ =𝑁𝑢 · 𝑘𝐷ℎ

(7)

𝑇𝑚 = 𝑇𝑠 −𝑞′′

ℎ (8)

𝑇𝑜𝑢𝑡 = 2𝑇𝑚 − 𝑇𝑖𝑛 (9)

Because the cross-section that the acetone is flowing in is not circular, the hydraulic diameter must be used. Equation (5) calculates the hydraulic diameter where Do is the outer diameter and Di is the inner diameter. To calculate the heat flux through the inner surface, the heat transfer through the inner surface was divided by the area of heat transfer. In this case, the area of heat transfer is the surface area of the biospecimen container. The heat transfer was calculated using specifications of the heater that was chosen for the design. In addition, it was multiplied by an efficiency value because an assumption of an imperfect heater was used.

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To calculate the Nusselt number, Table 8.2 in Fundamentals of Heat and Mass Transfer (7th edition) was used. In this table, the Nusselt number of the inner surface is calculated using a ratio of the inner diameter to the outer diameter and interpolation. Once the Nusselt number is found, the convective coefficient is calculated using Nu as the Nusselt number, k as the thermal conductivity of acetone, and Dh as the hydraulic diameter as seen in equation (7). Equation (8) is the equation to calculate the mean temperature of the acetone. In this equation, Ts is the surface temperature of the biospecimen containter (4°C), q’’ is the heat flux through the inner surface, and h is the convective heat transfer coefficient. Finally, the outlet temperature of the biospecimen container subsystem can be calculated using the relationship that the mean temperature is the average of the inlet and outlet temperatures. In equation (9), Tm is the mean temperature and Tin is the inlet temperature of the biospecimen container subsystem which is equal to the outlet temperature of the cooling coil subsystem. Iterative Approach Using MATLAB To calculate the inlet and outlet temperatures at the four points, an iterative solution in MATLAB was used. The basic process of how the MATLAB script calculates these values goes as follows:

1. Initialize the inlet temperature to the biospecimen container to the freezing temperature of dry ice (-78.5°C)

2. Plug the parameters into equation (4) or (8 and 9) using the biospecimen container parameters and get the outlet temperature of the biospecimen container subsystem

3. Equate the inlet temperature of the cooling coil to the outlet temperature of the biospecimen container subsystem

4. Plug the parameters into equation (4) using the cooling coil parameters to get the outlet temperature of the cooler

5. Check to see if the outlet temperature of the cooling system is equal to the inlet temperature of the biospecimen container subsystem

6. If the two values match, end the simulation, if not, run it again The MATLAB script is in the Appendix. Results The MATLAB simulation outputs the inlet and outlet temperatures of the acetone at the connection points of the two subsystems. This gives an approximated required acetone temperature in order for this system to work given the conditions of the problem. When running the simulation, the following results were found:

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Table 1: Results to the MATLAB Simulation

Assumption Tin,biospecimen = Tout,cooling coil °C

Tin,cooling coil = Tout,biospecimen °C

Constant Ts -78.499 3.805

Annulus -78.482 -18.591 The main difference in these two approximations comes from the inlet temperature of the cooling coil and the inlet temperature of the biospecimen container. This probably stems from the geometric differences between the two problems. What these results show is that it takes a colder temperature to cool down the biospecimen container for the annulus approximation than it does for the constant surface temperature approximation.

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Computer aided simulation

In order to reduce the complexity and improve the meshing accuracy of our model, we reduced our specimen holder and storage container to a simplified box containing a simple copper container with a silicon sample container. In initial simulation attempts, our coiled heat sink design with a copper tube wrapped around a hollow cylinder produced meshing errors that caused repeated crashes. By simplifying our coil and shell design into a thicker shell, we were able to achieve approximate results for our system while avoiding the repeated crashes associated with our tight geometry. Additionally, for our simulation, we reduced our container down to the sample chamber made of polystyrene foam and used the most extreme external conditions to show the effectiveness of our cooling and heating system. The simplified model in its final state can be seen in the figure below.

Figure 3: Box simplified model with heat sink and sample

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For the final simulation, we used a set external temperature and a set heat sink temperature to simulate the effects of placing a room temperature sample within the system and closing the box. Additionally, since one of the walls in our design borders the dry ice storage box, once of the walls was placed at a dry ice temperature of -70 degrees Celsius to simulate bordering the storage box. Additionally, the internal wall was placed at room temperature. All together the system was simulated for 10 seconds, showing a rapid transition of temperature of the sample. This indicates that given our dry ice and coolant approach is so far in temperature from our target temperature of 4 degrees Celsius we are very rapidly able to approach the desired temperature and can use the heating coil wrapped around our sample holder to better control this temperature. The results of our simulation can be seen in the figure below

Figure 4: Thermal simulation of our simplified model using a cut away via to show the effects after only ten seconds of placing the sample in the central heat sink cylinder and

sealing it in the polystyrene box

One unusual part of the simulation was an unusual simulation result in the polystyrene wall. The large blue region between the outer wall temperatures of 60 and -70 degrees Celsius indicate a temperature at our below the commonly accepted value of -273.15 Celsius. This unusual error in simulation is most likely the result of some unknown meshing or initial condition error, but appears to not affect the results of the simulation.

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4. Cost Estimation

Component Quantity Price per unit Cost per assemblyMicropump GA/GAH Series External Gear Pump 1 $1,299.00 $1,299.00Eagle Drive MSE DC Drive Motor 1 $780.00 $780.00Sioux Chief Mini-rester 660-TR1 1 $12.55 $12.55Dry Ice (in lbs) 10 $1.50 $15.00Resistive Heating Wire (NIC60) 1 $72.00 $72.00Surface-mount Thermocouple Probe, Type K 1 $57.99 $57.99Arduino MicroController 1 $31.08 $31.08Arduino Motor Shield 1 $31.08 $31.08Serial LCD Monitor 1 $24.95 $24.95Styrofoam Container Box 1 $12.51 $12.51Motor Battery 1 $43.33 $43.33Chemical-Resistant Clear Tygon Tubing 3 $1.86 $5.58Clear Polycarb Barbed Tube Fitting Straight (packs of 10) 1 $10.91 $10.91Stainless Steel Barbed Tube Fitting 2 $4.47 $8.94Electrical Wire 1 $8.00 $8.00Plug-In vehicle Charger 1 $24.81 $24.81

Manufactured Styrofoam Divider 1 $20.00 $20.00(Includes Stock and Machining) Custom Copper Piping 1 $40.00 $40.00

Custom Biospecimen Containment 1 $60.00 $60.00Total Production Cost per piece: $2,437.73

Purchased

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5. Appendix A

1) Micropump© GA/GAH Series External Gear Pump

- Flow Rate (min, max): 8.5 𝑚𝐿𝑚𝑖𝑛

, 552 𝑚𝐿𝑚𝑖𝑛

- Differential Pressure: 75 psi (max)

- System Pressure: 300 psi (max)

- Temperature Range: -45.56°C to 176.7°C

- Viscosity Range: 0.2 to 1500 cP

- Datasheet: http://www.micropump.com/support_documents/Series_GA_GAH.pdf

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2) EagleDrive MSE DC Drive Motor

- Electromagnetic Drive

- Speed (min, max): 250 RPM, 2750 RPM (@12V)

- Power Source: 10 to 38 VDC

- Max Torque: 10 oz-in

- Nominal Power: 48 W

- Weight: 0.6 lbs

- Max Ambient Temperature: 120°C

- Datasheet: http://www.micropump.com/support_documents/EagleDrive_Rev.pdf

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3) Sioux Chief Mini-rester 660-TR1 (Water Hammer Arrestor)

- ⅜" O.D. comp. × ⅜" O.D. female comp., clamshell (fits our pipe)

- Max working Temp: 121.1°C

- Max working Pressure: 350 PSIG

- Burst Tested @ 2,900 PSIG

- Meets all 2006 Plumbing Codes

- Product Brochure: http://www.siouxchief.com/Resource_/ProductMedia/155/Mini-Rester%20brochure%20WEB%204-10.pdf

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4) Resistive Heating Wire (NIC60-010-125)

- Nickel-Chromium Alloy 30 AWG

- Specific Resistance: ~675 Ω

- Density: 8.25 𝑔𝑐𝑚3 P

- Melting Point: ~1350°C

- Tensile Strength: ~690 Mpa

- Datasheet: http://www.omega.com/Temperature/pdf/NIC60_NIC80.pdf

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5) Self-Adhesive Thermocouples (SA2C-K)

- Molded Silicone Design for Curved and Flat Surfaces

- Temperature Range: -270°C to 1,260°C

- Extension Wire Temperature Range: 0°C to 200°C

- Standard Accuracy: ±2.2°C

- Reference: http://www.thermometricscorp.com/thertypk.html

- Datasheet: http://www.omega.com/Temperature/pdf/SA2.pdf

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6) Arduino Uno Rev3

- Microcontroller: ATmega328 - Operating Voltage: 5V - Input Voltage (recommended): 7-12V - Input Voltage (limits): 6-20V - Product Info: http://arduino.cc/en/Main/arduinoBoardUno

- Datasheet: http://www.atmel.com/Images/doc8161.pdf

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7) Arduino Motor Shield Rev3

- Operating Voltage: 5V to 12V

- Motor Controller: L298P, Drives 2 DC motors or 1 stepper motor

- Max Current: 2A per channel or 4A max

- Current Sensing: 1.65V/A

- Product info: http://arduino.cc/en/Main/ArduinoMotorShieldR3

- Assembly instructions with Arduino Uno Rev3 (Instructables.com):

http://www.instructables.com/id/Arduino-Motor-Shield-Tutorial/?ALLSTEPS

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8) Serial Enabled 16x2 LCD – White on Black 3.3V (LCD-09067)

- Processing Speed: 10MHz

- Buffer stores up to 80 characters

- Backlight transistor handles up to 1A

- Surface Mount

- Fast Boot-up time

- Dimensions: 36mm x 80mm and 25.4mm thick

- Schematic:

https://www.sparkfun.com/datasheets/LCD/Serial%20LCD%20Backpack%20v28.pdf

- Datasheet: https://www.sparkfun.com/datasheets/LCD/SerLCD_V2_5.PDF

- Quick Start Guide: https://www.sparkfun.com/tutorials/246

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9) Dry Ice

- ~4.5kg lasts 24 hours

- Density ~ 1.4 g/cm3

- Equates to ~3.3 Liters per Day

- Resource: http://dryicenetwork.com/

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10) Styrofoam Container Box

- Inner Dimensions: 390.5mm x 241mm x 266.7mm

- Outer Dimension: 482.6mm x 355.6mm x 381mm

- Wall thickness: 38.1mm

- Kit Includes: 2-Piece Foam Cooler with white cardboard shipping box

- “Plug-style lid” to assure superior temperature protection

- Reusable, recyclable, and CFC-less foam

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11) Chemical-Resistant Clear Tygon Tubing (McMaster 5103K34)

- ID: 6.35mm

- OD: 9.525mm

- Wall Thickness: 1.588mm

- Bend Radius: 19.05mm

- Available in numerous lengths

- McMaster Page: http://www.mcmaster.com/#catalog/119/124/=mmwqe3

- Material: Tygon

12) Tube to Threaded Male Pipe Adapter (McMaster 5117K96)

- For Tube ID: 6.35mm

- Pipe/Thread Size: 3.175mm

- Material: Clear Polycarbonate, Singe Barbed

- McMaster Page: http://www.mcmaster.com/#catalog/119/167/=mmws4v

13) Tube to Male Threaded Pipe Adapter (McMaster 5670K82)

- For Tube ID: 6.35mm

- Pipe Size: 9.525mm

- Material: 303 Stainless Steel Multi-Barbed

- McMaster Page: http://www.mcmaster.com/#catalog/119/169/=mmwweq

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14) Battery Pack

- 8 x Energizer EN91 (Alkaline)

- 12V total, ~4Ah

- Shelf Life: 10 years

- Datasheet:

media.digikey.com/pdf/Data%20Sheets/Energizer%20Battery%20PDFs/EN91.pdf

15) Electrical Wires (Typical 20AWG Wires)

16) Plug-In Vehicle Charger

- Will be modified to work with either (a) charging the batteries or (b) powering the

electronics (while the car is on).

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Thermal Analysis MATLAB Code % Steady-State Thermal Analysis clear all close all clc % Copper Tube D = 0.009525; % in meters L_heatSink = 0.792; % in meters L_cooler = 1.499; % in meters P = pi*D; T_wall = 4; % in Celsius % Acetone m_dot = 1.1206 *10^-4; % in kg/s, lower bound of chosen pump mass flow rate cp = 2150; % in J/kgK mu = 0.4013*10^-3; % at 0 Celsius Pr = 4.3; k = 0.16; % in W/mK % Dry Ice T_dryIce = -78.5; % in Celsius, freezing temperature of dry ice % Initial parameters T_out_cooler_old = 0; T_in_heatSink = T_dryIce; count = 0; % Basic Process % 1. Initialize T_in_heatSink = -78.5 % 2. Plug into heat sink equation and get T_out_heatSink % 3. T_out_heatSink = T_in_cooler % 4. Plug into cooler equation and get T_out_cooler % 5. Check to see if T_out_cooler = T_in_heatSink % 6. If yes, stop simulation, if no, run again while abs(T_out_cooler_old - T_in_heatSink) >= 0.01 % % Heat sink equation (constant wall temperature assumption) % Re = 4*m_dot/(pi*D*mu); % Reynolds number, Re = 37.3 (laminar flow) % Nu = 3.66; % Nusselt number % h = Nu*k/D; % Convective heat transfer coefficient % % T_out_heatSink = T_wall - (T_wall - T_in_heatSink)*exp(-h*P*L_heatSink/(m_dot*cp)); % T_in_cooler = T_out_heatSink; % Heat sink equation alternative (assume sample and copper tube is an annulus) D_inner = 5*10^-2; % in meters, diameter of the sample container D_outer = 5*10^-2 + 2*D; % in meters D_ratio = D_inner/D_outer; % ratio used to calculate Nusselt number

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D_h = D_outer - D_inner; % hydraulic diameter L_sample = 10*10^-2; % in meters efficiency = 0.50; q = 72; % in Watts, calculated from the heater chosen for our design q_flux = 72/(pi*D_inner*L_sample)*efficiency; % heat flux, q divided by area of heat transfer multiplied by an efficiency value due to an imperfect heater % Calculate Nusselt number (inner) % based on above equation, Nu = 0.7241 Nu = interpolate(0.6,5.74,0.8,4.86,D_ratio); % values taken from "Fundamentals of Heat and Mass Transfer" 7th ed. (pg. 554) h = Nu*k/D_h; T_mean = T_wall - q_flux/h; T_out_heatSink = 2*T_mean - T_in_heatSink; T_in_cooler = T_out_heatSink; % Cooler equation (same equation for both assumptions) T_out_cooler = T_dryIce - (T_dryIce - T_in_cooler)*exp(-h*P*L_cooler/(m_dot*cp)); % Redefine parameters T_out_cooler_old = T_in_heatSink; T_in_heatSink = T_out_cooler; if (mod(count,2) == 0) T_in_heatSink T_out_cooler end count = count + 1; end % Final Values T_in_heatSink T_out_cooler T_in_cooler T_out_heatSink

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