Heat Transfer by Free and Forced. Convection

Transcription

1 Heat Transfer by Free and Forced Convection Steven Manole ME 406 Prof. Koplik March 27, 2013

2 Abstract The flow of heat through a condenser tube wall differs depending on whether or not the condenser experiences free or forced convection. By measuring the temperature difference across the tube wall for both of these cases, the overall heat transfer coefficient can be be determined. In addition to the heat lost through the condenser wall, the entire system loses heat due to the combined effect of convection and radiation. These losses are estimated using the overall heat transfer coefficient.

3 Table of Contents Introduction... 1 Procedure... 2 Theory... 5 Sample Calculations... 6 Results... 7 Analysis... 9 Conclusion References Appendix...13

4 Manole 1 Introduction Dealing with heat transfer in a condenser is made all the more difficult due to the fact that the cooled vapor forms a film of droplets on the surface of the condenser. This film serves to cover the cooler surface of the condenser wall, preventing further vapor from forming a condensate. Condensers are built to be vertical, so that the droplets of film are able to drain from the surface more rapidly. This creates an interesting effect, as the thickness of the film on the lower surface is much greater than the thickness on the higher surface due to gravity. Therefore, the upper portion is much more effective at transferring heat. Since it can be difficult to calculate the heat transfer of such a complicated problem, it is advantageous to find an overall heat transfer coefficient.

5 Manole 2 Procedure Figure 1 Experimental System of Boiler and Condenser The system used in this experiment is diagrammed in Figure 1. The boiler (B) is fed by a water supply tank (A). After being heated into steam by the boiler, the vapor enters the condenser (C). Here, it condenses into droplets on the surface and is received through the exit at the bottom. Simultaneously, cooling water is fed into the head control tank (D). This tank is connected to the cooling tube, which passes the cool water through the center of the condenser. This cooling water, which has increased in temperature considerably, exits the condenser and is received by a tank (E). Each aspect of this system serves a purpose. The boiler supply tank limits the level of water

6 Manole 3 inside the boiler, ensuring that the mass of the system remains constant. The condenser works through the use of cooling water that passes upward through the condenser tube, causing the steam to condense on the outside surface of the cooling tube. The steam also condenses on the inside surface of the condenser jacket due to heat escaping from the system into the room. The head control tank manages the level of the cooling water, allowing for forced or free convection depending on the height of the water. The experiment is performed at both forced and free convection levels for twenty minutes each. During the experiment, the condensate is collected and its volume measured from the exit of the condenser. The weight of cooling water collected in the tank is also measured. At certain points throughout the system, thermocouples are attached to provide temperature readings. The locations of these thermocouples are shown in Figure 1, and compiled in Table 1. These temperatures are recorded four times for each run, and averaged for a final result.

7 Manole 4 Table 1: Location of Thermocouples Designation Location T1 T2 Steam in Cooling Water Out T3 Cup Condensate Out T4 T5 T6 T7 T8 T9 T10 T11 T12 Tube Wall Condensate Out Condenser Surface Outside Boiler Surface Outside Cooling Water Bottom Cooling Tube Surface Upper Cooling Tube Surface Lower Condenser Steam Inside Room Cooling Water Supply Tank

8 Manole 5 relationship: Theory The rate of change of heat in a cooling fluid can be calculated from a simple thermodynamic Δ q=ṁc Δ T (1) Where ṁ represents the rate of change of mass, c the heat capacity of the fluid, and Δ T the change in temperature. In addition, the rate of change of heat in a condensing gas can be found through: Δ q=h v ṁ (2) Since the condensing steam first cools, then undergoes a phase change to water, and cools further, the total heat loss for this process can be found by summing all three of these losses. In order to perform these calculations, however, the initial and final temperatures must be found. Using Figure 1 in the previous section, the designations for the required temperatures can be located. Of note is the final value of the condensate, which is the average of T3 and T4. The condensate is collected both on the wall of the condenser and the wall of the cooling tube, so both values must be averaged. Equation (1) is used once again to determine the rate of change of heat in the cooling water. It will be assumed that all heat not lost to the cooling water is lost through the wall of the condenser. This means that the rate of change of heat through the condenser wall is the difference between the magnitude of heat lost by the condensing steam, and the heat lost to the cooling water. Finally, in order to find the overall heat transfer coefficient: U 0 = Δ q A surface Δ T (3)

9 Manole 6 Sample Calculations The properties are taken at temperature of exiting condensate = 199 F ṁ= ρ V t 0.963g/mL 515 ml = 20 min 1/60 hr/min =1487.8g/hr Δ q condensate = ṁ c water (T 10 (T +T ) 3 4 ) 2 Δ q condensate = g/hr 1Btu/lb F (205 ( ) ) F lb/g= Btu/hr 2 Δ q phase =H v ṁ=2.26 kj/g 0.948Btu/kJ g/hr= Btu/hr The properties are taken at average steam temperature = 210 F Δ q steam = ṁ c steam (T 1 T 10 )= g/hr Btu/lb F ( ) F lb/g= 15.14Btu/hr Δ q total =Δ q condensate +Δ q phase +Δ q steam = = Btu/hr The properties are taken at room temperature = 77.2 F 117oz Δ q cooling =ṁ c water (T 2 T 7 )= 16oz/lb 20min Btu/lb F (191 74) F= Btu/hr 60 min/hr Δ q outerwall =Δ q total +Δ q cooling = = 674.3Btu/hr A surface =π d h=π =250.3in^2 Δ q U 0 = outerwall A surface (T 3 T 4 ) = 674.3Btu/hr 144 in^2/ft=38.4 Btu/hr ft^2 F in^2 ( ) F

10 Manole 7 Results Time (min) Bolier Feed (ml) Water Quantity Cooling Water (oz) Steam In Free Convection Cooling Water Out Thermocouple (F) Cup Condensate Out T1 T2 T3 T4 T5 T Total Average Cooling Water Bottom Thermocouple (F) Cooling Tube Surface Cooling Tube Surface Tube Wall Condenser Out Condenser Surface Outside Boiler Surface Outside Thermometer (F) Condenser Cooling Water Steam Inside Supply Tank Room Watts Upper Lower T7 T8 T9 T10 T12 T Take at T (F) Take at T (F) Take at T (F) del_q Cylinder Area Mass/Time del_q phase del_q steam del_q total del_q cooling condensate (in^2) (g/hr) (Btu/hr) (Btu/hr) (Btu/hr) water (Btu/hr) (Btu/hr) Tube Area (in^2) del_q U_0 (Btu/hr U_0 (Btu/hr h2 (Btu/ hr condenser in^2 F) ft^2 F) ft^2 F) wall (Btu/hr) U_cool (Btu/hr ft^2 F)

11 Manole 8 Time (min) Bolier Feed (ml) Water Quantity Cooling Water (oz) Steam In Forced Convection Cooling Water Out Thermocouple (F) Cup Condensate Out T1 T2 T3 T4 T5 T Total Average Cooling Water Bottom Thermocouple (F) Cooling Tube Surface Cooling Tube Surface Tube Wall Condenser Out Condenser Surface Outside Boiler Surface Outside Thermometer (F) Condenser Cooling Water Steam Inside Supply Tank Room Watts Upper Lower T7 T8 T9 T10 T12 T Take at T (F) Take at T (F) Take at T (F) del_q Cylinder Area Mass/Time del_q phase del_q steam del_q total del_q cooling condensate (in^2) (g/hr) (Btu/hr) (Btu/hr) (Btu/hr) water (Btu/hr) (Btu/hr) Tube Area (in^2) del_q U_0 (Btu/hr U_0 (Btu/hr h2 (Btu/ hr condenser in^2 F) ft^2 F) ft^2 F) wall (Btu/hr) U_cool (Btu/hr ft^2 F)

12 Manole 9 Analysis From the results, it has been determined that the coefficient of overall heat transfer, U_0, is 38.4 Btu / (hr-in^2-f) for free convection and 57.8 Btu/ (hr-in^2-f) for forced convection. This makes sense, as it would be expected that more heat be transferred through forced convection versus free convection. Through the equation: r 1 ln( r 2 ) 1 r =R= U 0 k A 1 h 1 A 1 r 1 h 2 r 2 A 1 (4) one can estimate the expected value for U_0. However, since there is no film on the outside of the condenser, the convection coefficient h_2 does not come from the values for film coefficients. The other heat transfer coefficients, however, can be estimated. The conduction coefficient through the condenser wall, k, is about 25 Btu / (hr-ft-f) for steel. For the purpose of this analysis, let it be assumed at first that the heat transfer coefficient h_1 is much larger than h_2. Therefore, it is simple to assume the U_0 to be known as estimated in the results, and calculate h_2: h 2 = r 1 r 2 A 1 U U r 1 ln( r 2 r 1 ) k (5) The resulting values for h_2 are 18.9 Btu / (hr-ft^2-f) for free convection and 28.1 Btu / (hr-ft^2-f) for forced convection. Solving now for h_1: h 1 = 1 A 1 R r 1 ln(r 2 /r 1 ) r 1 k r 2 h 2 (6) yields h_1 = Btu/(hr-ft^2-F) for both free and forced convection. Since h_1 >> h_2, the assumption made when calculating h_2 holds.

13 Manole 10 The convection coefficient for free convection of air should vary between 0.88 and 4.41 Btu/ (hr-ft^2-f). Since h_2 for free convection was 18.9 Btu/(hr-ft^2-F), this value is much higher than would be expected. The reasons for such a differing value are discussed in the conclusion. For forced convection, the value for h_2 was within the range of expected values. The convection coefficient should be between 1.76 and Btu/(hr-ft^2-F), so 28.1 Btu/(hr-ft^2-F) is a reasonable result. Using empirical values for U_0 is another method that can be used to validate these results. The expected value for U_0 in a steam-water condenser is between 350 and 750 Btu/(hr-ft^2-F). The results of 38.4 and 57.8 Btu/(hr-ft^2-F) are far below these expected values. However, the heat transfer through the condenser tube wall is not the only source of heat loss. In addition, there is also the heat transfer to the cooling water, which is much larger than the heat transfer through the condenser tube wall. The values for the overall heat transfer coefficient to the cooling water are and Btu/ (hr-ft^2-f) for free and forced convection respectively. In addition, it is likely that there are other sources of heat loss, as the system was not perfectly insulated. It is reasonable to assume that these combined sources of heat loss will result in an overall heat transfer coefficient for the system that is within the expected range. The total rate of heat loss from the equipment can be estimated using thermodynamics analysis on the condensing steam. The heat lost from the system must be equivalent to the sum of the heat lost from the temperature changes of the steam and water, and the phase change from steam to water. This total rate of heat loss has been estimated to be 3223 Btu/hr for free convection and 3503 Btu/hr for forced convection. To check if this estimate is reasonable, consider that 1100W of power entered the system. Therefore, the same amount of heat should be leaving the system, as long as the overall temperature of the system is not increasing W is equal to 3753 Btu/hr, so this estimate is very reasonable.

14 Manole 11 Conclusion The results of the experiment had strong correlations with empirical observations. This both confirms the empirical results and validates the experimental results. However, there were still some disparities between the empirical and experimental values. The value furthest from the expected value was the convective heat transfer coefficient for air for free convection. At a value of 18.9 Btu/ (hr-ft^2-f), it was far from the expected interval of 0.88 to 4.41 Btu/(hr-ft^2-F). One reason for this error could be that the free convection was not perfect, and at times, the heat transfer problem resembled that of forced convection. Since there was human error in determining the level of the cooling water, it is reasonable to assume that the water level may have been too high during this portion of the experiment. Another explanation could be that there were minor air currents in the room, causing a mild forced convection phenomenon. Another result that warrants explanation is the difference between the power input into the system of 3753 Btu and the resulting heat losses of only 3223 and 3503 Btu. Since the temperature of the system remained constant, the heat into the system should equal the heat leaving the system. However, only the heat lost inside the condenser was accounted for. The difference in heat can be explained by the heat lost between the boiler and the condenser. Since that portion of the system was not perfectly insulated, some of the power that entered the system left as heat before even entering the condenser.

15 Manole 12 References "Convective Heat Transfer." Engineering Toolbox. Web. 16 Apr "Heat of Fusion." Kent Chemistry. N.p., n.d. Web. 16 Apr "Heat Transfer Coefficients Typical Values." H & C Heat Transfer. N.p., n.d. Web. 16 Apr ME 406 Lab Manual. Heat Transfer by Free and Forced Convction. Sept "Water - Thermal Properties." Engineering Toolbox. N.p., n.d. Web. 16 Apr "Water Vapor - Specific Heat." Engineering Toolbox. N.p., n.d. Web. 16 Apr