Page |1 Kayla Smith 10/27/2024 MMAE 315 Laboratory 10: The Heat Transfer Coefficient in a H350 Cross Flow Heat Exchanger Abstract Within this experiment the forced convective heat transfer coefficients are determined using velocity and the temperatures of the ambient air and the elemental air. Within the investigation lab data was gathered using the H350 Cross Heat Flow Exchanger and this data is then used to analyze these heat transfer coefficients. The rate at which the heat transfer coefficients changed with respect to the velocity was consistent but the experimental and empirical data was not the same. It was noted that the experimental data had a higher heat transfer coefficient than the empirical data. The range for the experimental Reynolds number is found to be 10,348 – 27,163, which is within Hilpert’s range of 4,000-40,000. With this the πΆ and π coefficients that are affected by the Nusselt number are found to be similar with the πΆ coefficient varying from Hilpert’s slightly more. Differences between Hilpert’s experiment and the one in the lab may have led to the discrepancies seen within the data. Another prominent discrepancy may have happened due to the cylindrical rod not coming to thermal equilibrium for each trial. Introduction This experiment utilizes a H350 cross flow heat exchanger model, to investigate and quantify heat transfer from a cylinder subjected to a cross flow. This system uses forced convection heat transfer through using a fan to induce airflow over the heated element. It raises the cylinders temperature to 95 degrees Celsius. The focus of this experiment is observing the change in the mean convective heat transfer coefficient. Through predictions it is anticipated that the coefficient of heat transfer will increase proportionally with the increase of velocity and Reynolds number. To start the airflow velocity through the duct is calculated using the following equation: 2βπ (1) π = √π πππ Where “π” is the flow velocity,” βπ" is the change in pressure,”ππππ ” which is the density of air. Page |2 Through making substitutions using simplified versions of Bernoulli’s equation and the ideal gas law, it gives the following: (2) βπ = ππ€ππ‘ππ ππ» (3) ππππ = ππ π ππ ππ π Where ππ€ππ‘ππ is the density of 1000 π3 water, π is the gravitational constant 9.81 π , π» is the height of the fluid in the manometer in πππ»20, ππ is the ambient pressure in π½ pascals, π is the Ideal Gas constant which is 287 πΎπ∗πΎ,ππ is the ambient temperature in Kelvin. In order to obtain the final velocity equation, the values must be plugged in above and converted to the correct units by dividing by 1000. This will lead the equation as: π=√ (2 ∗ 9.81 ∗ 287 ∗ 1000 ππ π» √ 1000 ππ Through substituting these values, the flow velocity equation gives: (4) π = 75√ ππ π» ππ Where π is the flow velocity, ππ is the ambient temperature, ππ is the ambient pressure and H is the height of the fluid in πππ»20. With the calculated velocity it is possible to then calculate the power from the convection using: (5)πππππ£πππ‘πππ = π = π2 π Where π is the voltage supplied by the instrument console, π is the resistance of the element in Ohms, and πππππ£πππ‘πππ is the heat coefficient of the convicted air over the cylinder. Once Q is found then we use: (6)π = βπ΄π (ππ − ππ ) Where β is the experimental convective heat transfer coefficient, π΄π is the area of the element ππ is the surface temperature of the element, ππ is the ambient temperature. For the empirical heat transfer coefficients, the following equations are needed: Page |3 (7) (8) (9) (10) Where ππΉπππ is the temperature of the film, πΎπ is the thermal conductivity of the fluid, ππ is the viscous forces, ππ is the Prandtl Number. With these relations we can calculate the Reynolds number and the mean Nusselt number: 1 (11)ππ’π· = πΆπ ππ·π ππ 3 = (12)π ππ· = βπ· πΎπ ππ· ππ Where ππ’π· is the Nusselt number. C and m are empirical coefficients they are found from Hilpert correlation, and they are dependent on the Reynolds number. They are C= .193 and m=0.618 (Lienhard,2020). D is the Diameter of the element. Experimental Setup To conduct the experiment, the following materials are needed: o Cross Flow Heat Exchanger H350 o P.A. Hilton LTD Page |4 Figure 1: Schematic of Cross Flow Heat Exchanger To start the experiment, collect the materials that are listed above. This experiment uses the crossflow heat exchanger that is displayed in Figure (1). This system creates forced convection over a cylindrical rod positioned within a duct. This duct intersects the airflow at a right angle. The speed of the airflow within the heat exchanger is regulated using an iris damper. Ensuring the main console switch and fan are off, verify that the inlet duct pressure tap is connected to the low-pressure side of the inclined manometer. Page |5 Cylindrical Rod Figure 2: Cross flow heat exchanger H350 Page |6 Voltmeter Figure 3: P.A. HILTON LTD To start the experiment the cylindrical rod in the cross-flow heat exchanger H350 is heated to 95 degrees Celsius. Once the rod obtains the desired temperature the iris damper is set to a specific value to start (9) this opens the valve the least and introduces the slowest freestream velocity. As the air flows into the duct the rod’s temperature decreases which means that there needs to be voltage to maintain the rod at 95 degrees Celsius. To capture the flow at this iris damper, the system reaches a steady-state temperature, and at this point, the manometer is employed to measure the pressure within the duct. Using the voltmeter display and the digital thermometer it is possible to get the voltage needed for the system to maintain 95 degrees Celsius and the element and ambient temperature. Recording the pressure on the manometer, the elemental and ambient temperature on the digital thermometer, and the voltage from the voltmeter for iris damper levels 0-9. For level 0 the flow will be moving at its highest flow rate over the rod. With all of this information the calculation for the heat transfer coefficients will be able to be made for the cross flow heat exchanger. Results Once the data has been collected, equation (4) is used to calculate the velocity of the air. Once the velocity has been calculated πππππ£πππ‘πππ can be solved for using Page |7 equation (5). With all of this information equation (6) can be used to solve the experimental Heat Transfer Coefficient. In order to calculate the empirical values for the Heat Transfer Coefficient equation (7) must be used to first find the temperature of the film. Then using ππΉπππ to calculate the Prantl number, thermal conductivity and viscous forces using equation (8), (9), and (10). Then Reynolds number is able to be determined using equation (12) and the Nusselt number can be found using equation (11). The relationship that is found in Equation (11) can then be used to solve for the empirical Heat Transfer Coefficient. Table 1: Initial Data Collected Throughout the Experiment Table 2: Processed Data With the results found from the calculations, a graph comparing the heat transfer coefficients of the empirical data and empirical data against the flow velocity can be found. Page |8 Heat Transfer Coefficient Vs. Velocity Heat Transfer Coefficent(Wm^-2K^-1) 250 Experimental 200 Empirical 150 100 50 0 10 15 20 25 30 35 Velocity (m/s) Figure 4: Comparison of Experimental and Empirical Data for Velocity and Heat Transfer Coefficients NuD Vs. Re Graph Experimental 140 y = 0,2357x0,6114 120 NuD 100 80 60 40 20 0 0 5000 10000 15000 20000 25000 30000 Re (J/kg*K) Figure 5: Power law graph displaying πΆ ∗ (ππ )^1/3 and π coefficients for experimental data Discussion of Results Through analyzing Figure (4) it can be seen that there is a distinct pattern between the Heat Transfer Coefficient and the velocity. As the Velocity increases so does the Heat Transfer Coefficient. This trend can be seen in the experimental data and the empirical predictions. However, it can also be noted that they are not the same and Page |9 the experimental Heat Transfer Coefficient is consistently higher than the empirical Heat Transfer Coefficient. Although there are various sources of error that have led to the discrepancy between the empirical coefficient and experimental one monumental source of error may have been due to the calculations. In order to find the empirical and experimental heat coefficient values πΆ and π are used. For Hilpert’s calculations the values of πΆ = 0.193 and π = 0.618(Lienhard,2020). These values are based on the Reynolds number which for Hilpert’s calculation varies from 4,000-40,000. However, for the experimental data the Reynolds number varies from 10,348-27,163 which in turn caused the experimental data to have similar but not exact πΆ and π coefficients for its heat transfer calculation. The experimental π coefficient does not vary much from Hilpert’s as it is π = 0.6114. However the πΆ coefficient vary by a bit more and is found experimentally to be πΆ = 0.265. The differences between the experimental πΆ and π coefficients and Hilpert’s has most likely partly contributed to the discrepancy between the experimental and empirical data points(Connor,2019). These coefficients may be different due to differences between Hilpert’s experiment and this one that were not accounted for. Another likely source of error that contributed to the experimental Heat Transfer Coefficient to be higher could have happened during the data collection process. The elements high time constant for converting electric energy to thermal energy may have introduced delays in the ability for the system to reach thermal equilibrium. Although ample time was waited until measurements were taken it is possible that the system never reached 95 degrees Celsius. Additionally, the experiment only took the surface temperature on the point on the back of the cylinder. This means we assumed the temperature of the total surface area of the cylinder was the same, which may not be true and caused variation in the data. Another source of error that could have happened during the data collection process comes from reading the analog dials and temperature readings. Since the voltage readings are only accurate to the nearest whole number this means that the data is not being collected with complete precision. During the end of the experiment the time allowed for the state to reach thermal equilibrium decreased and this may attribute to the differences between the experimental Heat Transfer Coefficient and the Empirical Transfer coefficient becoming greater than earlier in the experiment. Another source of error in the experiment may have come from the lack of trials. This experiment called for 10 trials, however the group I worked with began to run out of time and was only able to complete 9 trials. This led to some data not being recorded that could have been used to analyze the efficiency of this experiment. Conclusion P a g e | 10 In this lab a relationship between forced convective heat transfer over a cylinder and flow velocity was established. The relationship between the forced convection heat transfer over a cylindrical element and the fluid velocity within the duct is directly proportional. This relationship is explored using figure (4), where it is possible to see that the relationship between the heat transfer coefficient and velocity is linear. However, within this graph the empirical guesses for heat transfer coefficient against the experimentally found heat transfer coefficient were not the same and the experimental data was larger at each velocity point. It is noted that these discrepancies may have arisen due to several potential areas for error. One main specific error noted is the discrepancy in the πΆ and π coefficients between the experimental data and Hilpert’s calculations which is used for the empirical data. These differences which may be attributed to differences between Hilpert’s experiment and the lab, that led to the values for empirical and experimental data to be different. Other sources of error that are noted are attributed to the data collection process stating that the temperature may not have been held at constant through out the experiment and there may have been accuracy error due to the lack of decimal places on the voltmeter. Overall eliminating these sources of error would have most likely led to the experimental and empirical data being more closely related for each velocity point. References Connor, Nick. What is Nusselt Number . 22 05 2019. <https://www.thermal engineering.org/what-is-nusselt-number-definition/>. Lienhard, John H. Heat Transfer. Cambridge Massachusetts: Phlogiston Press, 2020.
