Optimization of Polymerase Chain Reaction Machine

Transcription

1 Optimization of Polymerase Chain Reaction Machine by Sepehr Farnaghi A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Department of Mechanical and Industrial Engineering University of Toronto Copyright by Sepehr Farnaghi 2017

2 Optimization of Polymerase Chain Reaction Machine Sepehr Farnaghi Master of Applied Science Department of Mechanical and Industrial Engineering University of Toronto 2017 Abstract In this thesis, a numerical investigation was carried out on Polymerase Chain Reaction (PCR) machine. To duplicate DNA samples with a high quality and precision, the temperature uniformity on DNA samples plays a significant role. To study the temperature field, a three-dimensional Computational Fluid Dynamics (CFD) model of PCR device was developed in ANSYS CFX. It was found that by removing the gap between the heat sink and the air duct and cutting the heat sink in half, the efficiency of the heat sink will increase. Finally, an experimental investigation was carried out to compare the performance of aluminum metal foams with regular aluminum heat sinks in terms of heat removal, temperature uniformity, and the outlet temperature of the heat exchanger. It was observed that metal foams can remove heat at a faster rate which leads to a shorter cycling time and a better temperature uniformity in PCR devices. ii

3 Acknowledgments I would like to extend my appreciation to Prof. Javad Mostaghimi for his invaluable guidance and attention throughout the duration of my masters at the University of Toronto. I had the honor to work in the Center for Advanced Coating Technologies (CACT) under his supervision for the last two years. Without his thoughtful encouragement and careful supervision, I would not be able to finish this path successfully. My special thanks go to Bio-Rad company for their contribution to my project and providing necessary equipment throughout my research. Also, I would like to thank Ontario Student Opportunity Grant (OSOG) for their grant and financial assistance for the last two years. A sincere thank you to Dr. Babak Samareh for his contribution to the direction and richness of my research by providing his continues assistance and advice along the way. Also, my special thanks to Sina Alavi for his unfailing help and insights during the writing process of this thesis. Last but not least, my gratitude is extended to all lovely people in my life who have kept me balanced. Most importantly, I would like to thank my parents, Reza and Azita, whose support and guidance have always played a significant role in every chapter of my life. iii

4 Table of Content 1 Chapter 1: Introduction Introduction PCR Literature Review Objectives Chapter 2: Polymerase Chain Reaction (PCR) Introduction Thermoelectric effect Chapter 3: Numerical Model Numerical Model Governing Equations Mesh Independence Study Chapter 4: Numerical Results and Discussion Results Discussion Chapter 5: Metal Foam Introduction iv

5 5.2 Metal Foam Literature Review Pore Density and Porosity Thermophysical Characterization of Metal Foam Experimental Analysis Conclusion and Future Work References v

6 vi Table of Figures Figure 2.1 Different steps of DNA amplification: (1) Denaturation at 94 96, (2) Annealing at 68, (3) Elongation at Figure 3.1 Schematic of the PCR device modeled in the simulation Figure 3.2 Computational domain of the PCR device modeled in the simulation Figure 3.3 Boundary Conditions of the PCR device modeled in the simulation Figure 3.4 Boundary Conditions of the PCR device modeled in the simulation Figure 3.5 Effect of number of cells on heat removal by heat sink. The lines between the data point are solely for demonstrational purposes Figure 3.6 Schematic of decomposed domain with cells Figure 4.1 Temperature distribution in DNA samples during the denaturation Figure 4.2 Temperature distribution in DNA sample during the post elongation Figure 4.3 Comparison of different geometries studied in the simulation Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Temperature distribution of the full device in the denaturation step. Top: isometric view, Bottom: side view Temperature distribution of the full device without air gap in the denaturation step. Top: isometric view, Bottom: side view Temperature distribution of the half full device with air gap in the denaturation step. Top: isometric view, Bottom: side view Temperature distribution of the half full device without air gap in the denaturation step. Top: isometric view, Bottom: side view Temperature distribution of the full device in the post elongation. Top: isometric view, Bottom: side view Temperature distribution of the full device without air gap in the post elongation step. Top: isometric view, Bottom: side view vi

7 vii Figure 4.10 Figure 4.11 Figure 4.12 Temperature distribution of the half full device with air gap in the post elongation step. Top: isometric view, Bottom: side view Temperature distribution of the half full device without air gap in the post elongation step. Top: isometric view, Bottom: side view Locations used to compare the percentage of air which flows underneath the fins 31 Figure 4.13 Comparison of fin efficiency in different geometries in denaturation Figure 4.14 Heat Sink Mass in different geometries Figure 5.1 a) SEM images of the foam fiber cross-section and pore with defined hydraulic diameters and (b) definition of foam fiber and pore diameter in a cubic model of metal foams [24] Figure 5.2 Variation of metal foams strut s cross section with porosity [23] Figure 5.3 Pictures of typical open-cell metal foams with 40PPI and 10PPI pores sizes [24] Figure 5.4 Schematic of experimental setup geometry Figure 5.5 Figure 5.6 Figure 5.7 Schematic of the locations where temperatures and velocities were measured at the channel outlet a) Outlet velocity profile for metal foam heat exchanger b) Outlet velocity profile for aluminum heat sink a) Outlet temperature profile for metal foam heat exchanger b) Outlet temperature profile for aluminum heat sink vii

8 viii List of Tables Table 2.1 Characteristics of the TEC used in this study Table 3.1 Comparison of heat removal in different number of cells Table 4.1 Comparison of different geometries of the heat sink in the denaturation step Table 4.2 Comparison of different geometries of the heat sink in the post elongation step 31 Table 4.3 Amount of air which flows beneath the fins at three different locations Table 4.4 Pressure drop between inlet and outlet of the heat sink Table 5.1 Comparison between two types of heat sinks used in the experiment viii

9 ix Nomenclature A Area of heat transfer [m 2 ] C p Specific heat capacity [ J kgk ] Da Darcy number d h Hydraulic diameter [m] d p Pore diameter [m] h Convection Coefficient [ W m 2 K ] K Permeability k e Effective thermal conductivity [ W mk ] k Thermal conductivity [ W mk ] m p PPI Q Mass flow rate [ kg s] Pressure Pores Per inch Heat transfer rate [W] P in Input power [W] P out Output power [W] Re Reynolds number ix

10 x T U V Temperature velocity Voltage V total Total volume V void Void volume x

11 Chapter 1: Introduction 1

12 Chapter 1: Introduction 2 1 Chapter 1: Introduction 1.1 Introduction Polymerase chain reaction (PCR) is a technique used in molecular biology to amplify a single or number of DNA sample molecules. This technique is used in various applications; For instance, it is used in paternity test, genetic fingerprinting, analysis of ancient DNA, mutagenesis, detection of hereditary diseases, gene cloning, genotyping a specific mutation, and comparison of gene expression. This method is based on thermal cycling, and consists of repetition of heating and cooling cycles. A PCR cycle consists of three steps: denaturation, annealing, and elongation steps respectively. During the denaturation step, DNA samples are heated up to and they are kept at this temperature for 20 to 30 seconds. This procedure unwinds the DNA double helix in preparation for the next step. In the second step, temperature is decreased to for 20 to 40 seconds to anneal primers to the single stranded DNA templates. During the elongation step, also called the extension step, the temperature of the DNA solution is raised once more to approximately 72 (elongation temperature) to facilitate the synthesis of the new DNA strand complementary to the template strand by DNA polymerase enzyme. The duration of the elongation step varies from few seconds to few minutes since it depends on different parameters such as, the type of DNA polymerase that is used and the length of the DNA sample template [1]. The DNA strands will be doubled after each cycle. In other words, DNA molecules will increase to 2 n similar ones after n cycles. After reaching the desire number of cycles, there is a post elongation step in which DNA molecules are cooled down to 4 15 and may be kept for short storage. 1.2 PCR Literature Review Since the activity of Taq DNA polymerase decreases with time, the PCR process should be complete as fast as possible[2]. Reaching the required temperature rapidly while maintaining a uniform temperature distribution along the DNA molecules is very crucial in all PCR devices.

13 Chapter 1: Introduction 3 Thus, thermal management plays a significant role in this case. The PCR thermal cycling performance is specified by temperature ramp, temperature uniformity along the substrate, and the required power. Khandurina et al.[3] used a compact thermal cycling assembly based on dual Peltier thermoelectric elements coupled with a microchip gel electrophoresis platform for a PCR microchip. They reached temperature ramps of 2 s for heating and 3 4 s for cooling the device. Mahjoob et al. [1] worked on techniques to enhance thermal cycling speed while maintaining the temperature distribution throughout DNA samples uniform. They investigated various parameters that have effect on the thermal cycling time and temperature distribution. For instance, they explored heat exchanger geometry, flow rate, conductive plate, the porous matrix material, and utilization of thermal grease. Their results showed higher heating/cooling temperature ramp, s, than any previous results in literature. Hsieh, Luo et al. [4] worked on microthermal cycler, which is used to increase the temperature uniformity of the reaction area on micro PCR chips. They used a new method for enhancing the thermal uniformity which relies on combining symmetrically distributed micro heaters and active compensation (AC) units. Previously, block-type micro heaters have been used in PCR devices but the temperature uniformity was poor. They used two types of micro heaters to enhance thermal uniformity: Block type micro heaters with AC units, and array-type micro-heaters with AC units. The temperature uniformity improved with array-type micro heaters having AC units. Their experimental data for the array type micro heaters from infrared (IR) images showed that the percentages of the uniformity area with a thermal variation of less than 1 are 63.6%, 96.6% and 79.6% for three PCR operating temperatures, 94,57, and 72 respectively. Yoon, D.S., et al. [2] investigated the effect of groove geometries including width, depth, and position on thermal characteristics of micro-machined PCR devices. Their simulation results showed that with increasing groove depth, the heating rate as well as the temperature around the chamber increases. To obtain a higher heating rate, it was necessary to reduce the distance between the groove and the chamber while increasing the groove width. Furthermore, they discovered that the power consumption decreases as the groove depth is increased. The power consumption of the

14 Chapter 1: Introduction 4 chip with a groove of 280 μm is reduced by 24.0%, 23.3% and 25.6% with annealing, extension and denaturation, respectively. Moreover, they obtained the heating and cooling rates of 36 s and 22 s, respectively. Hu, G., et al. [5] used microchannel PCR chip which is fabricated from polydimethylsiloxane (PDMS) and glass. An electrical current was used to generate joule heating to raise the temperature of the microchannel into two different temperatures. During this approach, a highly uniform axial temperature distribution was achieved in the fluidic channel for the first two steps of PCR cycle, the denaturing and annealing/extension steps. However, there was a sharp drop in temperature close to the two ends of the microchannel in a way that in a 30 mm long microchannel, uniform temperature was achieved for a 25 mm length. To achieve a two-temperature PCR thermal cycling, the direction of the electrical field was changed every 5s. This method made it possible to induce electro kinetic pumping in the PCR solution to obtain heating and cooling rates on the order of 3 and 2 s, respectively. Zhang and Xing [6] worked on a thermal gradient convective PCR for parallel DNA amplifications which had different annealing temperature on DNA samples. They showed that PCR can perform well within the range of 60 to 68 for annealing temperature, but with increasing the annealing temperature the PCR does not yield amplification due to defects that have been made. Singh et al. [7] worked on a PCR chamber that was placed either in the center (symmetry) or in the corner (asymmetry) of a chip. Their simulation was designed to study the significance of effective parameters such as the shape of the chamber, chamber placement with respect to the whole chip, the placement of heaters, and the symmetry of thermal loss paths. They concluded that asymmetries in the PCR chamber leads to a highly non-uniform temperature distribution, around 3. In addition, it was found that the asymmetries in the heater and the thermal recessive s link to the sink have a greater effect on temperature non-uniformity in comparison with asymmetry in the PCR chamber. On the other hand, a temperature uniformity within the range of 0.3 and 0.5 were achieved in the symmetric simulations. PCR devices with porous heat exchanger with various effective parameters on their performance such as heat exchanger geometry (exit and inlet channel thickness, inclination angle,

15 Chapter 1: Introduction 5 exit channel location, and conductive plate thickness), the properties of the plate and porous matrix solid parts, maximum porous matrix thickness, the heating/cooling fluid velocity and flow rate, and utilization of thermal grease was investigated in [1]. They reached to a temperature uniformity of 0.25 and also increased the temperature ramp by changing the temperature from 50 to 93.5 in 0.1s. 1.3 Objectives This thesis studies the PCR device which is used in the biomedical field to amplify a specific DNA region. The objective of this study is to investigate the effect of different parameters on the uniformity of temperature distribution on DNA samples in the PCR device. A numerical model is employed to study the effect of two parameters, fin length and air duct size. These parameters affect the heat sink capacity to remove heat and maintain temperature uniformity on DNA samples. In the first step, a conventional PCR device was simulated to further understand its various aspects. Then, the air duct and heat sink were simulated independently from the rest of the system to study the effect of fin length and air duct size. The second part of this thesis is devoted to employing metal foams instead of conventional heat sinks and investigating their efficiency. Using experimental method, it is predicted that implementing metal foam as a heat sink will increase the efficiency of PCR devices.

16 Chapter 2: Polymerase Chain Reaction 6

17 Chapter 2: Polymerase Chain Reaction (PCR) 7 2 Chapter 2: Polymerase Chain Reaction (PCR) 2.1 Introduction The three stages of a PCR cycle are carried out at different temperatures. During the denaturation step, the temperature of the DNA molecules is raised to The high temperature unwinds the DNA double helix since heat breaks the hydrogen bonds between the DNA bases. This results in two single strands of DNA, which act as templates. It is essential to maintain that temperature long enough so that all the double strands have been separated completely. Next, the temperature is lowered to 68, during the annealing step, to facilitate binding of primers at the 3 prime ends of the single-stranded target sequence. The primers are single-stranded short oligo-nucleotides that are complementary to the target sequence. Subsequently, the DNA polymerase enzyme, called Taq polymerase, binds at the site of the primers and it synthesizes complementary strand from free nucleotides present in the solution. Because the Taq polymerase can only copy molecules that have primer attached to them, only DNA containing the target sequences is copied. Since Taq polymerase is stable at high temperatures, during the final stage of PCR the temperature can be raised up to 72 to speed up the synthesis of the new strand. At the end of each cycle, each target region has been duplicated. For instance, at the end of cycle one, two partially double stranded DNA molecules are formed from a single strand and the number of target sequences continue to grow exponentially. For the first few cycles of PCR, the chromosomal DNA will be predominant template used for replication; however, as the number of cycles escalates, the PCR products themselves will be used for the replication. There is no limitation on the number of cycles that can be done on a sample; however, 30 cycles are usually run that yield more than a billion double strand copies of the target sequence

18 Chapter 2: Polymerase Chain Reaction (PCR) 8 and takes approximately 4 hours. Figure 2.1 shows the schematic of DNA amplification through different steps. Figure 2.1 Different steps of DNA amplification: (1) Denaturation at 94 96, (2) Annealing at 68, (3) Elongation at Thermoelectric effect Direct conversion of electric voltage to temperature differences and vice versa is called the thermoelectric effect. A thermoelectric device creates a temperature difference when voltage is applied to it and conversely, creates voltage when there is a different temperature on each side. Thermoelectric effect consists of three different effects: The Seebeck effect, Peltier effect, and Thomson effect. The first two is representative of the same physical process; thus, it is called the Peltier Seebeck effect as well. Thermoelectric Cooler (TEC) which is used in the PCR device is based on Peltier effect which means by consuming the electrical energy, it creates and transfers a heat flux between the sample block and the heat sink. Peltier device and Peltier heat pump are the other names for the TEC. Although, the thermoelectric cooler is most commonly used for cooling, it can be used for heating

19 Chapter 2: Polymerase Chain Reaction (PCR) 9 as well. The thermoelectric cooler has both pros and cons. TECs are high-priced and have poor efficiency while they have long life, small size and flexible shape. Two different types of semiconductors, p-type and n-type, are used in TECs since they have different electron densities. The semiconductors are placed electrically in series and thermally in parallel to each other. They are joined with a thermally conducting plate on each side. A flow of DC current is created across the junction of semiconductors, when a voltage is applied to the free ends of the two semiconductors. This flow of current triggers a temperature difference. Heat is absorbed by the cooling plate and then it is transferred to the side where the heat sink is located. Two ceramic plates surround the TECs which are connected alongside. The number of TECs in the system specifies the cooling ability of the total unit. TECs have both advantages and disadvantages. Their pros are as follows: They do not need frequent maintenance since they lack any moving parts. They can have very small size as well as flexible shape. Their temperature can be controlled precisely They operate for a long time, usually their mean time between failures (MTBF) exceeds 100,000 hours. They can be controlled by changing the input current/voltage. Their Cons are: They can only dissipate a limited amount of heat. Their efficiency is low; hence, they waste a large amount of input electrical energy. The amount of heat that can be absorbed by TEC is proportional to the current and time, and it is obtained by the following relation: Q = PIt 2.1 where P is the Peltier Coefficient, I is the current, and t is the time. The efficiency of TEC in refrigeration cycle is around 10 15% of the ideal Carnot cycle refrigerator which is much lower in comparison with 40 60% obtained by conventional compression cycle systems. As a result, using thermoelectric cooling is only reasonable where its advantages such as low maintenance and compact size outweigh its low efficiency.

20 Chapter 2: Polymerase Chain Reaction (PCR) 10 A set of six thermoelectric heat pump modules consisting of 50 pairs of n-type and p-type Bismuth Telluride elements soldered between metalized 96% alumina ceramic substrate were used in the studied PCR device. The technical specification of these TECS are as follows: Table 2.1 Characteristics of the TEC used in this study Number of couples 50 Optimum Current (I max ) Nominal Input Voltage (V max ) 15.5A at Q max 6.5V DC at I max Heat Pumping Capacity (Q max ) 57W at T = 0 Maximum Temperature Differential ( T max ) 71 at Q = 0 Ac Electrical Resistance at / 0.05Ω Minimum Continuous Operating Temperature 130 Minimum Short-Term Process Temperature 150

21 Chapter 3: Numerical Model 11

22 Chapter 3: Numerical Model 12 3 Chapter 3: Numerical Model 3.1 Numerical Model For the numerical simulation the ANSYS CFX is used. The ambient air, which has a temperature of 25, flows through the heat sink at one end and exits from the other end. In these calculations, air properties are kept constant at: ρ=1.18 kg/m 3, Cp = 1005 J/kg. K, k = 0.02 W/mK and μ = Pa. s, in a way that the inlet air flow has the ambient air properties. The inlet mass flow rate is 0.05 kg s. Figure 3.1 shows the schematic of the PCR device used in this study. Figure 3.1 Schematic of the PCR device modeled in the simulation

23 Chapter 3: Numerical Model 13 As Figure 3.1 shows, the geometry includes different parts. There are two thermoelectric coolers (TEC) on top of the heat sink which are used to create heat flux between the heat sink and the sample blocks by generating electricity. For simplicity, it is assumed that these two TECs are isolated from each other in a way that no heat flux transfers between these two TECs. One of them acts as a sink and the other one as a source. The COP of this TEC is 0.5 according to the data sheet that manufacturers provided. Based on the denaturation or post elongation step, they switch places. During the denaturation step, the upper TEC generates 3.1W heat and the bottom one absorbs 1.03W heat from the heat sink. However, in the course of post elongation step, the upper TEC absorbs 0.6W from the DNA samples and the bottom one dissipates 1.8W to the heat sink. Subsequently, the heat will be removed by the air flow that goes through the heat sink fins. The electric current is the key to change the direction of heat flux during the denaturation and post elongation steps. The heat flux goes from the bottom to the top in order to heat up the DNA samples. However, during the post elongation step the DNA samples need to get cool down. Therefore, the direction of the heat flux is changed while the heat being removed from the DNA samples through the heat sink. There are also two Grafoils placed on the top of the upper TEC and the bottom of the lower TEC. The thermal conductivity of the Grafoil layer varies in different geometrical directions. It is 140 w (m. k) along length and width and 5 w (m. k) through thickness. The flow regime was assumed to be in a steady state condition. The flow regime was turbulent with Shear Stress Transport (SST) model. Figure 3.2 shows the exploded schematic view of the geometry modeled in the simulation.

24 Chapter 3: Numerical Model 14 Figure 3.2 Computational domain of the PCR device modeled in the simulation Figure 3.3 and Figure 3.4 show boundary conditions of the simulation.

25 Chapter 3: Numerical Model 15 Figure 3.3 Boundary Conditions of the PCR device modeled in the simulation Figure 3.4 Boundary Conditions of the PCR device modeled in the simulation

26 Chapter 3: Numerical Model Governing Equations Assuming the flow to be Newtonian, incompressible, and in a steady state, the governing equations would be as follows: Continuity Equation. U = where U is the velocity vector of the flow. Momentum Equation ρu. (U) = p + μ 2 U + f b 3.2 where f b is a body force in z direction e.g. gravitational force and p is the pressure. Energy Equation. (ρue) =. (k T) + S E 3.3 where S E is the heat source which comes from the TECs, explained and e is internal energy. Viscous dissipation is neglected. Additionally, Fourier s law governs the heat conduction in solid parts which is based on the following relation: q = k T Mesh Independence Study To obtain valid numerical results, mesh independency study is performed. Below is the variation of the heat removal rate with the number of cells in the computational domain. Table 3.1 Comparison of heat removal in different number of cells Number of cells Heat removed (W) 779 W 754 W 741W 736W

27 Heat Removal (W) Chapter 3: Numerical Model Number of meshes Figure 3.5 Effect of number of cells on heat removal by heat sink. The lines between the data point are solely for demonstrational purposes. As shown in Figure 3.5 and Table 3.1, with increasing the number of cells the heat removal rate is converging to a certain value. Since the difference between heat removal rate for the last two grid densities is small (0.67%), for all the simulations throughout the thesis the model with the third mesh size was chosen as the optimal one. Computational time for the complete PCR device with the selected mesh size is about 3 days. Figure 3.6 shows the decomposed domain with cells.

28 Chapter 3: Numerical Model 18 Figure 3.6 Schematic of decomposed domain with cells

29 19 Chapter 4: Numerical Results and Discussion

30 Chapter 4: Numerical Results and Discussion 20 4 Chapter 4: Numerical Results and Discussion 4.1 Results At the beginning, the complete model of the PCR device during the denaturation and postelongation steps was simulated to investigate the temperature distribution on DNA samples, the heat removal rate, and the temperature distribution on the heat sink. The annealing and elongation steps were not simulated. For the denaturation step, temperature distribution in sample block is shown in Figure 4.1. Figure 4.1 Temperature distribution in DNA samples during the denaturation

31 Chapter 4: Numerical Results and Discussion 21 The temperature uniformity of 0.36 was obtained on DNA samples. This temperature uniformity is less than 0.8 which was obtained previously at Bio-Rad laboratories. This difference can be due to the adiabatic boundary condition assigned to the common surface between the two TECs leading to no heat being transferred between the upper and lower part of the model. Additionally, simulation of post-elongation was carried out to study the effective parameters as well. The temperature distribution in the post-elongation step is shown in Figure 4.2. Figure 4.2 Temperature distribution in DNA sample during the post elongation Temperature difference on DNA samples in the post elongation step was obtained to be However, as it was mentioned before, there is no heat transfer between TECs. As a result, the effect of fin length cannot be seen directly on the temperature distribution on DNA samples. In this regard, TECs, Grafoils, and sample block were removed from the geometry to investigate the effect of fin length on the heat removal rate by the heat sink. In this step, the simulation of air duct and heat sink was done with different geometrical parameters in order to understand the effect of fin length and the air gap below the heat sink. Initially, the complete geometry of heat sink and air duct was simulated. Later, the air gap underneath the heatsink was removed to investigate how this gap affects the efficiency of the heat

32 Chapter 4: Numerical Results and Discussion 22 sink. After removing the air gap underneath the heatsink, the fin length was cut by half to understand the effect of it. The same procedure was done for the post-elongation step as well. Figure 4.4 through Figure 4.11 show the results of these simulations. Also, a summary of the results are indicated in Table 4.1 and Table 4.2 for comparison. Temperature A B C D Figure 4.3 Comparison of different geometries studied in the simulation

33 Chapter 4: Numerical Results and Discussion 23 Figure 4.4 Temperature distribution of the full device in the denaturation step. Top: isometric view, Bottom: side view

34 Chapter 4: Numerical Results and Discussion 24 Figure 4.5 Temperature distribution of the full device without air gap in the denaturation step. Top: isometric view, Bottom: side view

35 Chapter 4: Numerical Results and Discussion 25 Figure 4.6 Temperature distribution of the half full device with air gap in the denaturation step. Top: isometric view, Bottom: side view

36 Chapter 4: Numerical Results and Discussion 26 Figure 4.7 Temperature distribution of the half full device without air gap in the denaturation step. Top: isometric view, Bottom: side view

37 Chapter 4: Numerical Results and Discussion 27 Figure 4.8 Temperature distribution of the full device in the post elongation. Top: isometric view, Bottom: side view

38 Chapter 4: Numerical Results and Discussion 28 Figure 4.9 Temperature distribution of the full device without air gap in the post elongation step. Top: isometric view, Bottom: side view

39 Chapter 4: Numerical Results and Discussion 29 Figure 4.10 Temperature distribution of the half full device with air gap in the post elongation step. Top: isometric view, Bottom: side view

40 Chapter 4: Numerical Results and Discussion 30 Figure 4.11 Temperature distribution of the half full device without air gap in the post elongation step. Top: isometric view, Bottom: side view

41 Chapter 4: Numerical Results and Discussion 31 Table 4.1Table 4.2 illustrates air duct height, mass, and heat removal capacity of different heat sink geometries. Table 4.1 Comparison of different geometries of the heat sink in the denaturation step Case A Case B Case C Case D Air Duct Height 51mm 44mm (14% less) 30mm (42% less) 23mm (55% less) Mass of Heat Sink 1.22kg 1.22kg 0.96kg (22% less) 0.96kg (22% less) Heat added 741w 840w 648w 860w Table 4.2 Comparison of different geometries of the heat sink in the post elongation step Case A Case B Case C Case D Air Duct Height 51mm 44mm(14% less) 30mm (42% less) 23mm (55% less) Mass of Heat Sink 1.22kg 1.22kg 0.96kg (22% less) 0.96kg (22% less) Heat removed 240w 270w 212w 274w Table 4.3 shows the percentage of air which flows underneath the fins at three different points of the heat sink. As it is shown in the Figure 4.12, these points are located at the beginning, in the middle and at the end of the heat sink. It is shown that by removing the air gap the air gap (case B and case D), less percentage of air flows underneath the fins which results in increasing the efficiency of the fins as it is explained in more detail in the discussion section. Also, by cutting the fins in half, more percentage of the air flows underneath the fins (Case C compared to Case A and Case D compared to Case A). Figure 4.12 Locations used to compare the percentage of air which flows underneath the fins

42 Chapter 4: Numerical Results and Discussion 32 Table 4.3 Amount of air which flows beneath the fins at three different locations Point 1 Point 2 Point 3 Case A 22.6% 27.8% 28.7% Case B 4.3% 4.6% 4.3% Case C 36.8% 43.1% 45.5% Case D 8.6% 9.3% 8.7% Table 4.4 compares the pressure difference between the inlet and outlet of the heat sink. As it is illustrated in the table, by removing the air gap the pressure difference between the inlet and outlet increases since most of the air flows through the fins. Moreover, by cutting the fins in half, the air should flow through the thinner channel, which again, has the same result. Table 4.4 Pressure drop between inlet and outlet of the heat sink Pressure Gradient (Pa) Case A Case B Case C Case D Discussion Figure 4.13 and Figure 4.14 show the difference between the rates of heat transfer for different heat exchanger geometries. According to the results, the air gap underneath the air duct reduces the efficiency of the system since the air partially flows under the heat sink, which cannot remove the heat from the fins efficiently. In addition, reducing the fin length by half, decreases the surface area, which lowers rate of heat transfer. However, increase in the air velocity by approximately two folds results in Nusselt number and convection coefficient increase. Thus, the heat exchanger with the half-length fins without air gap has shown the highest rate of the heat removal. Another factor attributing in this result is the fact that the temperature difference between the base and tip of the fins is reduced when the fins are shortened, as such the case D design is able to dissipate the heat more efficiently compared to the case A. The following correlations have been utilized o compare the efficiency of the fins [8]: η fin = tanh ml c ml c 4.1 where

43 Chapter 4: Numerical Results and Discussion 33 m = 2h 4.2 kt and L c = L + t where L is the fin length, t is the fin thickness, h is the convection coefficient, and k is the thermal conductivity. As shown in Appendix B, the fin length of two different geometries are 42.5mm and 21.5mm and the fin thickness is 1.5mm. The thermal conductivity of aluminum is 237 W (m. k). To calculate the convective heat transfer coefficient of fins using the Newton s law of cooling, the temperature and the heat flux values were averaged over the whole surface of the fins. The efficiency for the half size obtained 0.74 while for full size is As it was predicted by reducing the fin length by half, the efficiency of the fins increase. This efficiency increase can be interpreted as the result of the temperature difference reduction between the base and tip of fins. However, as expected, the heat transfer rate for the case A is more than the case C due to air flow path which prefers to flow beneath the fins with less resistance rather than the path between the fins. Consequently, cutting the fins by half while the gap still exists under the heat sink has resulted in lower heat removal rate. Furthermore, with removing the gap and shortening the fin length, the weight and size of the PCR device decrease which is very desirable as industry currently aims for more compact PCR devices. Therefore, the optimized geometry of PCR device would be one without an air gap and a shorter fin length.

44 Mass of Heat Sink (Kg) Heat Removed (W) Chapter 4: Numerical Results and Discussion Case A Case B Case C case D Figure 4.13 Comparison of fin efficiency in different geometries in denaturation Case A Case B Case C case D Figure 4.14 Heat Sink Mass in different geometries

45 Chapter 5: Metal Foam 35

46 Chapter 5: Metal Foam 36 5 Chapter 5: Metal Foam 5.1 Introduction Metal foams are a group of porous material which have been widely used in different applications for the past recent years. Their main characteristic that make them useful in heat transfer applications is their large surface area to volume ratio which ranges from 200 m^2 m^3 to 5000 m^2 m^3 [9, 10]. Due to this large specific surface area, metal foams are excellent heat transfer medium. Metal foams are also known for another geometrical characteristic which is their pore density. Pore density is defined as the number of pores per linear inch (PPI). The range of porosity of metal foams is from 5 to 70 PPI for the commercially available ones. Based on their structure, metal foams are divided into two different groups: closed-cell and open-cell foams. Closed-cell foams have been used as an impact absorbing material which remain deformed after the impact. Additionally, they are used as light weight structures in aerospace industry. Open-cell metal foams, on the other hand, are newer and are mostly used in heat transfer applications such as compact heat exchangers, combustors, biphasic cooling systems, energy storage devices, spreaders, and heat sinks. Their vast applications in heat transfer is due to their good thermo-physical properties such as high surface area to volume ratio that increases their thermal conductivity. Open-cell metal foams are often made of copper, nickel, aluminum, nickel alloys and stainless steel. They are very lightweight structures as they are highly porous with porosities usually greater than 0.85 [10, 11]. 5.2 Metal Foam Literature Review Study of heat transfer and fluid flow through porous media dates back to the 19 th century when Darcy first established the fundamentals of flow in porous medium in 1856 [12]. His study was based on water flow in packed beds. His results showed that there is a linear relationship between

47 Chapter 5: Metal Foam 37 the pressure drop in the columns of packed beds and the flow rate and viscosity of the fluid while having an inverse relationship with permeability (K) of the porous material. As metal foams differ from packed beds in terms of geometrical complexity and higher porosity, different flow relations were needed to define flow regimes. In 1892 Lord Rayleigh [13] and years later Maxwell [14], investigated heat transfer in porous media by estimating the effective thermal conductivity of porous media analytically under stagnant flow condition. Recently, there have been a number of experimental and numerical studies on fluid flow and heat transfer in metal foams. Calmidi, Bhattacharya and Mahajan [15, 16] determined analytically and experimentally the permeability (K), effective thermal conductivity (k e ) and inertial coefficient (f) of high porosity metal foams. Their experimental results were obtained in high porosity ranging from 0.89 to 0.97 and indicated that inertial coefficient (f) was dependent only on porosity when permeability (K) increases with pore diameter and porosity of the medium. Their analytical study predicted that the effective thermal conductivity of the foam (k e ) was independent of pore density while it highly depends on porosity and the ratio of the cross sections of the fiber and the intersection. In their analytical simulation, they modeled the complex geometry of metal foams with two-dimensional array of hexagonal cells. A theoretical model was developed by Du Plessis et al. [17] to estimate pressure drop in Newtonian fluid flow in metal foams. This model assumes a Poiseuille flow through a simplistic unit cell model of the foam. After extension of this model to the tetrakaidecahedron unit cell representation, they predicted a pressure drop analytically in both Forchheimer and Darcy regimes. From this discovery, they found out that there is not a linear relationship between the pressure gradient and the flow rate for high Reynold numbers [18]. Bhattacharya et al. [13] revised the value for tortuosity in Du Plessis s model and developed new formula for the permeability and Forchheimer coefficient in metal foams with porosities ranging from 0.85 to Bonnet et al. carried out a number of experiments on different metal foams such as copper, nickel and nickel-chrome alloys for pore sizes (d p ) ranging from 500 to 5000 μm to investigate the pressure drop of working fluids, i.e. air and water, to formulate the flow parameters based on the morphology of metal foams [18-20]. Their results were in agreement with the Forchheimer flow model and they concluded that permeability (k) is proportional to the square of pore size while inertial coefficient (C F ) is inversely proportional to the pore size.

48 Chapter 5: Metal Foam 38 Boomsma et al. [9, 21, 22] ran an experiment on aluminum metal foams as compact heat exchangers. They used aluminum block with the dimensions of 40 mm x 40 mm x 2 mm. Water was used as a coolant which flowed through the aluminum foam. They put a constant heat flux on the top of the aluminum foam. Their aluminum metal foam heat exchanger, while consuming the same pumping power, generated two to three times lower thermal resistance than the best heat exchangers available in the market. They also prepared a 3D numerical model to simulate the fluid flow in metal foams using a tetrakaidecahedron unit cell representation. They obtained 25% lower pressure drop compared with the experiments. One reason for this underestimation is that they neglected wall effects in their simulations. 5.3 Pore Density and Porosity There are two different ways to study transport phenomena in metal foams: micro (pore) level and macro level. When analysis is focused on the micro level, there is a need to have a complete understanding of the structure of metal foams. In this regard, the morphological model of the foam needs to be understood. There are two different ways to obtain a model: a simplistic repetitive unit cell representation of the foam or a real structural model attained by computer tomography (CT) or X-ray radiography. The geometrical models can define structural characteristics such as: pore size, fiber (ligament) size, surface area to volume ratio, porosity, fluid flow and heat transfer properties of the foams (e.g., effective thermal conductivity and permeability) [23]. One of the main characteristics of metal foams is pore density. Pore density is defined as the number of pores per linear inch (PPI). The open cell foam in this study has a pore density of 10 PPI. Since there is no complete control over the size of the bubbles in the foaming process, the size of pores are not exactly equal to each other. However, according to the advances in the manufacturing process, less variation in the pore size and shape of metal foams are expected. The average pore diameter (dp) has an inverse relationship with the nominal pore density (PPI) as shown below: d p = 25.4mm PPI 5.1 Porosity (ε) is another physical property of the foams. It is defined as the volume of void divided by the total volume of the foam,

49 Chapter 5: Metal Foam 39 ε = V void V total 5.2 Metal foams generally have a porosity ranging from 0.80 to The foam that is used in this study has a porosity around Diameter of the solid ligaments or the fiber, d f is another characteristic to describe metal foams. Since polymer templates is used in manufacturing metal foams, the cross section of the ligaments is hollow as it is shown in the scanning electron microscope (SEM) image of a strut of 40 PPI nickel foam. Because its structure is very complex, both d f and d p are used to model hydraulic and heat transfer characteristics in metal foams. According to the porosity of metal foams, their cross section shape varies. It changes from circular shape with the porosity of 0.85 to concave triangle with the porosity of The porosity of the foam has two categories: one is the open porosity which is defined as the void volume of interconnected pores and the other one is the closed porosity which is defined as the porosity due Figure 5.1 a) SEM images of the foam fiber cross-section and pore with defined hydraulic diameters and (b) definition of foam fiber and pore diameter in a cubic model of metal foams [24]

50 Chapter 5: Metal Foam 40 to the hollowness of the solid struts [23]. Open-cell nickel foams of both 10 and 40 PPI cell density are shown in Figure 5.3. Figure 5.2 Variation of metal foams strut s cross section with porosity [23] Figure 5.3 Pictures of typical open-cell metal foams with 40PPI and 10PPI pores sizes [24] 5.4 Thermophysical Characterization of Metal Foam One of the main parameters to describe the heat transfer in porous media is effective thermal conductivity. This parameter is equivalent to the thermal conductivity of solids. Fourier s law for conduction is applied to this material in the same way as solid materials. In metal foams, fluids such as air or water fill the pores. Thus, in calculation of the effective thermal conductivity, the fluid should be stagnant in a way that the convection part of heat transfer gets removed [23]. One of the first correlations that is derived to calculate the effective thermal conductivity (ETC) is as follows [23]:

51 Chapter 5: Metal Foam 41 k e,parallel = εk f + (1 ε)k s 5.3 where K e,parallel represents the parallel effective thermal conductivity. K s represents thermal conductivity of solid phase while K f represents thermal conductivity of fluid phase. ε represents the porosity. This equation usually overestimates the actual effective thermal conductivity of porous materials. Thermal resistance analogy is used to calculate effective thermal conductivity. In this analogy, solid and fluid part of porous material are recognized as two thermal resistors, R, and are defined as: R = L ka 5.4 where L is the length. A is the area of heat transfer that is normal to the direction of the conduction. As it is assumed that resistors are arranged in parallel, the total resistance is as follows: 1 R e,parallel = 1 R f + 1 R s 5.5 where R e,parallel is the equivalent thermal resistance. R f and R s are fluid and solid thermal resistances, respectively. The porosity can be written as the ratio of fluid area to total area, ε = V void = L. A f V total L. A = 1 A s A 5.6 By combining equation 5.3 and 5.6 the following equation is obtained: k e,parallel = A f A k f + A s A k s 5.7 For the series arrangement of fluid and solid phases, the equivalent resistance of the metal foam is obtained by the following relation: R e,series = R f + R s 5.8 Thus, the effective thermal conductivity is obtained as follows:

52 Chapter 5: Metal Foam 42 k e,series = ( L f L 1 + L s k f L 1 1 ) k s 5.9 The porosity in series arrangement can be written as: ε = L f. A L. A = 1 L s L 5.10 As a result, the ETC in a series arrangement is obtained according to the following equation: k e,series = ( ε + 1 ε 1 ) k f k s 5.11 This relation results in maximum resistance or minimum effective thermal conductivity. However, in reality the metal foam material has neither parallel nor series arrangement. Therefore, their ETC is between these two boundaries: the upper boundary which is in parallel arrangement and the lower boundary which is in series. Fluid flow through porous media was developed by Darcy when he started working on water flow through beds of sands. He observed a linear relationship between pressure drop and flow rate [12]. Later on, the fluid flow through metallic foams was characterized similarly. Thus, its pressure gradient varies linearly with velocity and it is obtained from: dp dx = μ K u 5.12 where μ is dynamic viscosity and K is permeability of metal foam. However, at higher velocities deviation from Darcy law occurs as inertial effect becomes important [24]. Thus, the Dupuit Forchheimer modification is employed where a quadratic term in the expression for pressure gradient is introduced [9]. dp dx = μ K u + ρc F K u As stated above, in order to use the Darcy law, first the regime of the flow should be defined by the Reynolds number. Hydraulic diameter of the channel can be used as the length scale for Reynolds number definition. Therefore, Reynolds number is obtained from

53 Chapter 5: Metal Foam 43 Re = ρud h μ 5.14 Where ρ is the density of the fluid flow, u is the velocity of the flow, μ is the dynamic viscosity of the fluid, and d h is the hydraulic diameter of the air duct channel which is obtained from d h = 4A P 5.15 where A is the cross-sectional area, and P is the wetted perimeter of the cross-section 5.5 Experimental Analysis The experimental setup is shown below. There is an air duct which has a fan at the inlet of the duct. Two sets of experiments were done: one with an aluminum heat sink and the other one with a metal foam heat sink. In order to replicate the actual device, the same fan is used. Due to higher pressure drop, the mass flow rate was not constant in both experiments. Three cartridge heater were used to heat the heat sinks. On top of these heaters, a copper block was used to dissipate heat More efficiently. For the metal foam heat sink, a layer of aluminum was brazed at the bottom of the foam. Also, a special paste was used to reduce the thermal contact resistance. Fiber glass insulation was used to reduce the heat loss. Figure 5.4 Schematic of experimental setup geometry

54 Chapter 5: Metal Foam 44 In order to calculate the average outlet velocity, a hot wire anemometer (Omega Engineering Inc., USA) was used to measure the local velocity and temperature at multiple points (as shown in Figure 5.5) of the outlet s cross-section. Figure 5.6 shows the measured velocity values for the metal foam and heat sink. The average velocity for the metal foam was obtained to be 1.31 m s. Considering the dynamic viscosity to be constant at μ = Pa. s and the density at 1.12 kg m^3, the Reynolds number would be This shows that the effect of inertia is significant and the pressure gradient should be obtained from the modified version of the Darcy law. Therefore Equation 5.13 is used to calculate the pressure drop as Pa. Figure 5.5 Schematic of the locations where temperatures and velocities were measured at the channel outlet Also, a digital pressure gauge (Omegadyne, USA) was used to directly measure the pressure drop across the heatsink and/or metal foam. In the metal foam heat exchanger, the pressure gradient between the inlet and outlet of the channel was 61 Pa. This shows about 60% difference with the calculated value using Equation One reason of this difference could be the uncertainty in the velocity measurement. Alternatively, it can be asserted that the Dupuit Forchheimer correlation is over estimating the value of the pressure. Nevertheless, both values are in the same order of magnitude. In another approach, the average outlet velocity can be calculated from Equation 5.13, using the measured pressure drop by the digital pressure gauge. This results in a velocity value of 0.98 m s which has 30% difference with the value obtained directly using the hot wire anemometer.

55 Chapter 5: Metal Foam 45 a Figure 5.6 b a) Outlet velocity profile for metal foam heat exchanger b) Outlet velocity profile for aluminum heat sink To measure the input power, the following relation is used: P in = V. I 5.16 where V is the input voltage and I is the input current. In both experiments, the input voltage is 70V and the input current is 4.9A. To calculate the output power (i.e., the heat removed by the airflow), the following relation is used: P out = Q out = m c p T 5.17 where c p is the specific heat capacity which is assumed to be 1005 J (kg. K) and constant. m is the mass flow rate and it is obtained from: m = ρva 5.18

56 Chapter 5: Metal Foam 46 where ρ is the density of the air flow and varies with the temperature. V is the velocity of the flow. A is the cross section area of the air duct. Outlet air temperature was measured at multiple points by thermocouple probes according to the schematic shown in Figure 5.5. The results are shown in Figure 5.7. a Figure 5.7 b a) Outlet temperature profile for metal foam heat exchanger b) Outlet temperature profile for aluminum heat sink To measure the output power, the average outlet temperature was calculated based on the measured data points above. Average outlet temperature for metal foam and heat sink were 38.6 and 25.96, respectively. Table 5.1 shows the comparison between aluminum and metal foam heat sinks. Table 5.1 Comparison between two types of heat sinks used in the experiment Aluminum Heat Sink Metal Foam Heat Sink Volume Flow Rate ( m3 s)