Heat Transfer Coefficients using a Cylindrical Fin Array

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timer Asked: Mar 7th, 2019
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Question Description

i need:

1. an abstract section. more info attached in file named abstract.

2. results and discussion: just follow the objective statement and run tests required.

3. Conclusion.

all info is in the report, use Tbase of 20 w on varied air velocity part. power is always 20w for varied air velocity.

image 1&2 for important data: measurement and Tbase.

let me know if you have questions.

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Establishing Heat Transfer Coefficients using a Cylindrical Fin Array Last Name, Group R6 Abstract: (Final Report) Introduction/Background: Often in processes, substances need to be cooled to maintain a desired temperature using heat transfer, usually as a form of convection or conduction with the difference being convection has bulk movement of heat in the fluid. Convection is a very useful method for heat transfer because it relocates heat through bulk movement of fluid as opposed to conduction which is heat transferred by molecular collision. With convection as the form of heat transfer, using an array of fins is a common method used in industry. This is due to the additional surface area the fins provide. Fins are often simple and consist of heat conducting rods, most commonly made of metal. Fins are often more efficient with fluids that have a low boiling point and high heat capacity. Incorporating the fin arrays on the equipment allows for greater heat transfer because the additional surface area provides more space for convective heat transfer to occur. Fins are most commonly found in industries that involve air conditioning, refrigeration, chemical processing equipment or electrical chips. These industries consist of food production plants, chemical processing plants, and the technology industry. In food production fins are used in air conditioning units to provide heat transfer producing a refrigeration affect to perverse food and slow bacterial growth (“Air Conditioner Fins: Everything You Need to Know For Your Avon AC System”). The chemical processing industry utilizes fins for various applications such as the production of gases and heat exchangers to separate and purify gases such as oxygen, nitrogen, and other rare gases (“Plate Fin Heat Exchangers”). The technology industry is another recent industry that relies on fins for efficient heat transfer. Fins are used frequently in the heat protection of microchips, a product abundantly used in a plethora of manufactured goods. Goods such as computers, cell phones, controllers, and thousands of other electrical devices are taking advantage of the ability to change the shape of a microchip for heat protection, allowing them to avoid adjusting the material of construction which may have to meet predetermined specifications. The use of fins has become a very effective way to transfer heat and take advantage of convection using increased surface areas. By understanding these concepts, it becomes possible to use fin arrays to manipulate the heat transfer coefficient of a unit operation, as well as gain understanding of alternate approaches that can be taken to optimize the heat transfer of a process. The heat transfer coefficient of the system can be impacted in various ways: the number of fins in the array, the length and diameter of the fins, the pattern in which the fins are arranged. Additional ways to influence the heat transfer coefficient include adjusting the flow of heat in the system and the airflow passing through the fins. This lab focuses on adjusting the power, or heat supplied, in the system, in order to explore the impact power has on the heat transfer and determine their relationship for future optimization. Objective: The experimental objective of the lab is to determine the relationship of the heat transfer coefficient of the cylindrical fin array to the power supplied to the array, through the base. An additional experimental objective will be to compare the results collected to the heat transfer coefficient of a single fin, using previously published correlations which allow for the coefficient to be calculated. The statistical objective of the lab will be to run a two-sample t-test to compare the heat transfer coefficient calculated from the published findings to the heat transfer coefficient calculated from the data collected, to determine if they are statistically the same. If the comparison provides insufficient evidence that they are statistically the same, then an additional experimental objective will be to Last Name, Group R6 establish a new relationship between the calculated heat transfer coefficients to resemble the actual correlation between the fin and fin array. Theory: Fins are surfaces that extend from the surface of an object to help increase the rate of heat transfer from the object by increasing the surface area and therefore increasing convective heat transfer. Usually there is not just one fin, but an array of fins on an object that is desired to have more efficient heat transfer. Air flow around the fin array creates more turbulent mixing and therefore increase the heat transfer coefficient for the system. A diagram of the fin array setup and air flow through the fins is shown below in Figure 1. Figure 1: Cylindrical Fin array depicting turbulent air flow through the fins. Heat transferred from the fins through air convection is calculated by Newton’s law of cooling, which is shown as: 𝑸̇𝒄𝒐𝒏𝒗 = 𝒉𝑨𝒔 (𝑻𝒔 − 𝑻∞ ) (1) Where  is the heat transfer coefficient and Ts-T∞ is the difference between the temperature at the surface of the fin and the ambient air temperature. The area in this case for the total convection must include the surface of the base of the array plus the total surface area of the fins minus the bottom of the fin connected to the base. Since the fins are cylindrical and equal radius along the length, the total surface area is: 𝑨𝒔 = 𝑨𝒔,𝒃𝒂𝒔𝒆 + 𝒏𝑨𝒔,𝒇𝒊𝒏𝒔 = 𝑨𝒔,𝒃𝒂𝒔𝒆 + 𝒏(𝟐𝝅𝒓𝑳) (2) Where n=17 fins for the array. The surface temperature 𝑇𝑠 can also be represented as an average temperature across the fin, 𝑇𝑚 , for which there are three points measured at equal distances along the fin (T1, T2, T3) and the temperature of the base (Tbase). The mean temperature 𝑇𝑚 is simply: Last Name, Group R6 𝑻𝒎 = 𝑻𝒃𝒂𝒔𝒆 + 𝑻𝟏 + 𝑻𝟐 + 𝑻𝟑 𝟒 (3) Since there are no known heat transfer coefficients for the system and the goal of the experiment is to estimate ℎ, it becomes necessary to relate power setting of the fin array apparatus to the total heat transfer from the fins. This can be done by producing a graph of the power supplied (𝑄̇ ) vs the temperature difference (Tm-T∞) which should provide a linear correlation and the resulting slope will be the value of the heat transfer coefficient multiplied by the surface area (As). The relationship proves that there is no dependence of the heat transfer coefficient on the power added to the system, but rather, is a constant which is a property of the bulk fluid preforming the heat transfer. A known dimensionless relationship called the Nusselt number (Nu) is often used to calculate the heat transfer coefficient for a system. The Nusselt number is as shown below: 𝟏 𝑵𝒖 = 𝒄𝑹𝒆 𝒎 𝟏 𝐏𝐫 (𝟑) 𝝆𝒗𝑳𝒄 𝒎 𝝁𝑪𝒑 (𝟑) = 𝒄( ) ( ) 𝝁 𝒌 (4) Where c and m are constant values specific to the bulk fluid preforming the heat transfer, Re is the Reynolds number, Pr is the Prandlt number, 𝜌 is the density of the bulk fluid, 𝑣 is velocity of the bulk fluid, 𝜇 is the dynamic viscosity of the bulk fluid, 𝐿𝑐 is the characteristic length, 𝐶𝑝 is the specific heat of the bulk fluid, and 𝑘 is the thermal conductivity of the bulk fluid. The Nusselt number can be manipulated to resemble the equation of a line in order to determine the value for the constants c and m. The manipulated equation is shown below: 𝑵𝒖 𝐥𝐨𝐠 ( ) = 𝐥𝐨𝐠(𝒄) + 𝒎 𝐥𝐨𝐠(𝑹𝒆) 𝟏 ( ) 𝟑 𝑷𝒓 (5) Where the variables are consistent with equation 4 describing the Nu. This helps determine the constants c and m because the slope of the line is the constant m and log (c) is the y-intercept of the line. Knowing c and m the Nu can be calculated. The Nusselt number is then related to the heat transfer coefficient by the equation shown below: 𝑵𝒖 = 𝒉𝑳𝒄 𝒌 (6) Where ℎ is the heat transfer coefficient, 𝐿𝑐 is the characteristic length (in this case, the diameter of the fin), and 𝑘 is the thermal conductivity of the bulk fluid. Using equation 6 and calculating the Nusselt number for a bulk fluid, the heat transfer coefficient can be determined. Calculations (Final Report) Methods: Experimental Design: Last Name, Group R6 A 5339 Armfield convection heat transfer apparatus was used to determine the relationship between power and the heat transfer coefficient. The apparatus consists of an air duct with a section of seventeen aluminum pins. Air is drawn up through the duct by a variable-speed fan; the velocity of the speed fan can be adjusted by a dial on the apparatus. The air velocity must be set higher than zero cubic meters per second to avoid overheating the apparatus, causing a forced shut down. Air velocity was measured through a sensitive anemometer. Power below 10 Watts does not produce a noticeable temperature difference, causing limited heat transfer due to a small temperature gradient. Power above 50 Watts can cause the apparatus to overheat and shutdown. Several thermocouples measure the air temperature of the inlet air, outlet air, the surface of the pinned area, and tip of the pin. Power supplied to the apparatus was adjusted by the red dial on the apparatus. While the current temperatures can be read off the apparatus, data was recorded using the Arduino application on a connected PC. The system can be seen in Figure 1. Figure 2: Arduino and Armfield Convection Heat Transfer Apparatus To assess the relationship between the heat transfer coefficient and power, the Arduino apparatus was operated at a constant air velocity with varying amounts of power supplied to the system. The air velocity was set to 0.5 m3/s and clarified through Anemometer. The power supply was measured at 20, 30, 35 and 40 Watts, allowing the system to calibrate with each variation of power. Every power setting was measured for 2 min, 3 times. Temperature measurements were recorded every 15 seconds automatically by the Arduino application on the PC. This was done to ensure steady-state of the system. Steady-state could be determined by observing the change in temperature over a time span. When the change in temperature was negligible, or zero, for an extended time period it could be assumed the system had reached steady state. Additional temperature measurements of the base plate were manually recorded by a probe every 30 seconds. Where it is determined that the system has reached steady-state, these values were used in calculating 𝑇𝑚 . The recorded temperatures, air velocity, and power were used to calculate the heat transfer coefficient for each trial. Additionally, the air Last Name, Group R6 velocity will also be varied at four flow rates to solve the heat transfer coefficient related by the Nusselt number. Method of Analysis: Using the recorded temperatures, air velocity and power supply, the heat transfer coefficient was calculated at for each set of data. It was assumed that heat transfer caused by conduction through the pins was negligible. The heat transfer coefficient was then compared to power to distinguish a relationship. Measured values will be compared using regression analysis. Additionally, a regression was run to determine the linearity of the relationship between power and the temperature difference in the system. Using the varied flow rates the heat transfer coefficient will be calculated using the Nusselt number correlation relating the flow rate to the heat transfer coefficient. Safety: Safety glasses must be worn all the time in the lab. Pants and close-toed shoes also must be worn. For safety reasons, at least two people should be present all the time during the experiment. During the experiment, to avoid shutdown of the Arduino due to overheating, air velocity must be greater than zero. Additionally, power should not be set over 50-60 Watts to avoid overheating. If anything goes wrong unexpectedly, the supervisor will be contacted. If an accident happened the nearest authority will be alerted. Results and Discussion: (Final Report) Conclusion: (Final Report) References: “Air Conditioner Fins: Everything You Need To Know For Your Avon AC System.” Westland Heating & Air, 16 Aug. 2012, www.westlandhvac.com/blog/air-conditioning-service/air-conditioner-finseverything-you-need-to-know-for-your-avon-ac-system/. “Plate Fin Heat Exchangers.” Chart Industries, CryoGas International, Jan. 2016, files.chartindustries.com/0116_Plate%20Fin%20Heat%20Exchangers_Chart.pdf. FREE AND FORCED CONVECTION EXPERIMENT. Retrieved from https://www.tecquipment.com/freeand-forced-convection-exp Appendix: Experimental plan 1. Plug in Arduino to power supply found on the power strip underneath the desk. Last Name, Group R6 2. Ensure thermocouples are in contact with the fin; if thermocouples are not in contact, data may become skewed or show error “nan”. 3. Turn on Anemometer and press button zero. 4. On PC, open Arduino application. Select “File” tab and then “Sketchbook”. 5. Hover mouse over “DataCollection” to load code for Arduino. 6. Under “Tools” tab, select “Port”. Ensure program is using “COM4(Arduino/Genuino Uno)”. 7. Verify and upload code to microprocessor by check marking them on the home ribbon. 8. Launch ‘CoolTerm’. Verify serial port is open by clicking the “Connection” tab and selecting “Options”. Select “COM4” as serial port option. 9. Check air flow meter for calibration. Ensure air velocity is greater than zero. 10. Set power 20 Watts. Allow system to equilibrate. 11. To collect data, go back to the “Connection” tab and select “Capture to text file” and then “Start…”. This will record the serial monitor output to a text file. The base plate temperature must be measured manually via probe every 30 seconds. 12. Run 3 total tests at 20 Watts. Repeat for 30 and 40 Watts. 13. Exit Arduino application on PC. 14. Unplug Arduino from power supply. Last Name, Group R6 Data Tables Table 1: Various Temperatures for power setting of 20W t (s) Tbase T1 T2 T3 Tm v air 0 15 30 45 60 75 90 Table 2: Various Temperatures for power setting of 30W t (s) Tbase T1 T2 T3 Tm v air 0 15 30 45 60 75 90 Table 3: Various Temperatures for power setting of 35W t (s) Tbase 0 15 30 45 60 75 90 T1 T2 T3 Tm v air Last Name, Group R6 Table 4: Various Temperatures for power setting of 40W t (s) Tbase 0 15 30 45 60 75 90 Trial 1 T1 T2 T3 Tm v air temp 24 75 24 25 24 50 24 50 24 75 24 50 24 50 24 75 24 75 24 50 24 50 24 50 24 75 24 75 24 50 24 50 24 50 24 75 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 25 25 25 25 25 25 25 25 25 25 25 25 25 25 50 25 50 50 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 50 36 25 30 75 30 50 29 0 25 36 25 30 75 30 50 29 0 25 36 50 30 75 30 50 29 0 50 36 25 30 75 30 50 29 0 50 36 25 30 75 30 50 29 0 50 36 50 30 75 30 50 29 0 50 36 25 30 75 30 50 29 0 50 384 25 30 75 30 50 29 0 50 36 50 30 75 30 50 29 0 50 36 50 30 50 30 50 29 0 50 36 50 30 75 30 50 29 0 50 36 50 30 75 30 50 29 0 25 36 50 30 75 30 50 29 0 50 36 75 30 75 30 75 29 0 50 36 75 30 75 30 75 29 0 50 40 25 30 75 30 50 29 0 25 39 75 30 75 30 50 28 75 25 37 25 30 75 30 75 29 25 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 50 50 50 75 50 50 50 50 50 75 50 25 25 50 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 0 25 0 0 0 0 0 0 0 25 0 25 0 25 0 0 0 0 0 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 50 68 25 33 0 33 50 31 0 75 43 25 33 0 33 50 31 25 75 43 0 33 0 33 50 31 25 75 nan 32 75 33 50 31 25 75 156 75 32 75 33 50 31 25 50 42 0 33 25 33 75 31 25 50 42 0 33 0 33 75 31 25 75 42 0 33 0 33 75 31 50 75 42 0 33 0 33 75 31 25 75 42 0 33 0 33 50 31 0 75 42 0 33 0 33 75 31 25 75 41 75 33 0 33 75 31 25 75 42 0 33 25 33 75 31 25 75 42 0 33 0 33 75 31 25 75 42 25 33 0 33 75 31 25 75 42 0 33 0 33 75 31 25 75 42 25 33 0 33 50 31 25 75 42 0 33 0 33 75 31 25 75 42 0 33 0 33 75 31 25 24 24 24 24 24 24 24 24 24 50 25 50 50 25 25 50 50 50 48 48 48 48 48 48 48 48 48 0 25 25 25 25 25 25 25 25 46 46 46 46 46 46 46 46 46 50 50 50 50 75 75 75 50 50 44 44 44 44 44 44 44 44 44 50 50 50 50 50 50 50 50 75 34 34 34 34 34 34 34 34 34 25 25 25 25 25 25 25 25 25 35 0 32 25 35 0 32 25 35 0 32 25 35 25 32 25 35 0 32 25 35 0 32 25 35 0 32 25 35 0 32 25 35 0 32 25 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 25 50 50 50 50 25 25 25 25 50 50 75 50 50 25 50 50 50 50 50 50 50 25 50 50 50 50 25 25 50 25 50 50 25 50 50 25 25 50 50 0 25 25 25 25 25 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 50 51 51 51 51 50 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 51 25 50 50 50 50 50 50 50 50 75 75 75 75 50 75 75 75 0 0 0 0 75 0 25 0 25 0 0 25 0 0 0 25 0 25 25 0 25 25 25 25 0 50 25 50 25 48 48 48 48 48 48 48 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 49 50 75 75 75 75 75 75 0 0 0 0 25 0 0 0 25 25 0 25 25 25 25 25 25 25 25 25 25 25 25 25 50 50 50 50 50 25 50 50 50 50 25 25 50 50 50 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 46 47 46 47 46 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 25 25 25 50 50 25 50 50 50 75 50 50 75 75 75 75 75 75 75 75 75 75 75 0 75 0 75 0 0 0 0 0 0 0 0 25 0 0 25 0 0 0 25 0 25 0 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 35 25 25 25 25 25 25 25 25 25 25 50 50 50 50 50 50 50 50 25 50 50 50 75 50 50 50 75 50 50 50 50 50 50 50 75 75 50 75 50 75 75 50 75 50 50 75 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 0 0 0 0 0 0 25 25 0 0 0 25 25 25 25 25 25 25 0 25 25 25 25 25 25 25 25 25 25 25 25 50 25 25 25 25 25 25 25 25 25 25 25 25 50 50 33 32 33 33 32 32 33 33 33 32 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 32 33 33 33 0 75 0 0 75 75 0 0 0 75 0 0 25 0 0 25 0 0 0 0 0 25 0 0 25 0 25 25 0 50 0 25 0 0 0 0 0 0 0 0 0 0 75 0 0 0 24 25 51 25 49 75 47 0 35 75 36 25 33 0 24 25 51 25 49 50 47 25 35 75 36 50 33 25 inlet air t 23 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 24 75 0 25 25 25 50 25 25 25 50 50 50 50 50 50 25 25 25 T1 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 38 75 50 75 50 75 75 75 75 50 50 50 50 75 75 75 50 50 75 T2 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 75 75 75 75 75 75 75 75 75 50 75 75 75 75 75 75 50 75 T3 44 38 38 38 42 43 43 42 42 42 43 41 43 43 43 42 43 43 T3 50 25 50 75 75 0 50 25 50 75 0 75 75 25 0 75 0 25 Outlet 1 29 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Outlet 2 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 25 50 50 50 75 50 50 50 75 75 75 75 75 75 75 50 50 50 Outlet 3 28 28 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 29 75 75 0 0 0 0 0 0 0 0 0 0 25 25 0 0 0 0 Time (s) 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 Inlet air T (°C) 23.75 24.00 24.25 24.25 24.25 24.50 24.25 24.25 24.25 24.50 24.50 24.50 24.50 24.50 24.50 24.25 24.25 24.25 T1 (°C) 38.75 38.50 38.75 38.50 38.75 38.75 38.75 38.75 38.50 38.50 38.50 38.50 38.75 38.75 38.75 38.50 38.50 38.75 T2 (°C) 37.75 37.75 37.75 37.75 37.75 37.50 37.75 37.75 37.75 37.75 37.75 37.75 37.50 37.75 37.00 37.00 37.00 37.00 T3 (°C) 44.50 38.25 38.50 38.75 42.75 43.00 43.50 42.25 42.50 42.75 43.00 41.75 43.75 43.25 43.00 42.75 43.00 43.25 Outlet 1 (°C) 29.75 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.00 30.0 ...
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Thomas574
School: New York University

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Establishing Heat Transfer Coefficients using a Cylindrical Fin Array

Last Name, Group R6

Abstract
The reason for conducting the experiment was to establish Heat Transfer Coefficients using a
Cylindrical Fin Array. Heat transfer coefficients are widely used in cooling substances to the
required temperatures through heat transfer mechanisms such as conduction and convection.
Normally, heat transfer through convection is high compared to conduction. This is because in
convection, we have bulk movement of fluid as compared to conduction whereby heat energy
transfers by molecular collision. The experimental objectives involved:- To determine the
relationship of the heat transfer coefficient of the cylindrical fin array to the power supplied to the
array, to compare the results collected to the heat transfer coefficient of a single fin, using
previously published correlations which allow for the coefficient to be calculated, to run a twosample t-test to compare the heat transfer coefficient calculated from the published findings to
the heat transfer coefficient calculated from the data collected. Among the equipment’s used
during the experiment are: - The Cylindrical Fin Array and fluids and metal solids of different
conductivity. The coefficient of heat transfer is usually expressed as W/(m2K). fluids such as gases
in free convection have a coefficient of heat between 5 -37 W/(m2K) whereas metallic conductors
have a coefficient value of approximately between 500-3000 W/(m2K). Therefore, by the end of
the experiment, we expected to have established different heat transfer coefficients using
cylindrical fin array mechanism. For the case of our experiment, the thermal coefficient values
obtained ranged between 24 to 25 W/(m2K).
Introduction/Background:
Often in processes, substances need to be cooled to maintain a desired temperature using
heat transfer, usually as a form of convection or conduction with the difference being convection
has bulk movement of heat in the fluid. Convection is a very useful method for heat transfer
because it relocates heat through bulk movement of fluid as opposed to conduction which is heat
transferred by molecular collision. With convection as the form of heat transfer, using an array of
fins is a common method used in industry. This is due to the additional surface area the fins
provide. Fins are often simple and consist of heat conducting rods, most commonly made of metal.
Fins are often more efficient with fluids that have a low boiling point and high heat capacity.
Incorporating the fin arrays on the equipment allows for greater heat transfer because the
additional surface area provides more space for convective heat transfer to occur. Fins are most
commonly found in industries that involve air conditioning, refrigeration, chemical processing
equipment or electrical chips. These industries consist of food production plants, chemical
processing plants, and the technology industry. In food production fins are used in air conditioning
units to provide heat transfer producing a refrigeration affect to perverse food and slow bacterial
growth (“Air Conditioner Fins: Everything You Need to Know For Your Avon AC System”). The
chemical processing industry utilizes fins for various applications such as the production of gases
and heat exchangers to separate and purify gases such as oxygen, nitrogen, and other rare gases

Last Name, Group R6

(“Plate Fin Heat Exchangers”). The technology industry is another recent industry that relies on
fins for efficient heat transfer. Fins are used frequently in the heat protection of microchips, a
product abundantly used in a plethora of manufactured goods. Goods such as computers, cell
phones, controllers, and thousands of other electrical devices are taking advantage of the ability
to change the shape of a microchip for heat protection, allowing them to avoid adjusting the
material of construction which may have to meet predetermined specifications.
The use of fins has become a very effective way to transfer heat and take advantage of
convection using increased surface areas. By understanding these concepts, it becomes possible
to use fin arrays to manipulate the heat transfer coefficient of a unit operation, as well as gain
understanding of alternate approaches that can be taken to optimize the heat transfer ...

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