Forced Convection Heat Transfer I. Introduction This laboratory deals with forced convection, forced convection can be considered as a staple of heat transfer. That is to say that forced convection can be found in almost any heat transfer problem, and thus understanding its importance and how it affects a given problem is one of the more important learning objectives/outcomes of heat transfer. When dealing with forced convection the most important section, after understanding how convection works, is the convection heat transfer coefficient.
The heat transfer coefficient for convection is denoted by (h) and is measured in w/m^2*K, this lab delves into the application of convection heat transfer and how it correlates to temperature, velocity, ect of the fluid in question. II. Objectives The objectives for this laboratory include; determining the convective heat transfer coefficient and friction factor of the air flowing through a copper pipe, as well as evaluation of the Reynolds analogy and taking measurements of the radial velocity and temp profile in an internal pipe flow. III. Procedure and Apparatus Apparatus A fan forces air through a long pipe with an orifice plate along the way. Before the test section there is a reduction in diametrical area which will cause an increase in velocity and a decrease in pressure. It should also be noted that the test section has a coiled heater around it which travels the length and has proper insulation. There are seven thermocouples placed along the test section as shown in Fig 1. The exit section of the test pipe has a radial temperature and pressure measuring device as shown in figure 2.
Pressures and temperatures are measured along the test section with Pitot tubes (pressure measurement) and thermocouples (temp measurement). The measured values are output on digital displays and the desired temperature is chosen by using a selection dial switch. Orifice plate diameter 1. 625" Pipe Internal Diameter 1. 249" Heating Element Length 72" Thermocouple Output 0. 232 mV/? F Note – cold junctions are located at air temperature thermometer -Procedure
The fan was started and the heater turned on, then the voltage control was adjusted to a maximum of 4 amperes at least an hour before the lab (This was done by the lab TA). The experiment consists of two parts, Axial profile and Radial profile measurements; -Axial profile Values of the set of parameters given in Table 1 are read from the respective displays and the procedure is repeated for 3 more sets after 5 minutes each. The 7 temperatures in Table 1, (T1 to T7) are the surface or the wall temperatures of the test section. - Radial profile
The set of parameters given in Table 2 are read just once. The temperature measured in Table 2, (Te,1 to Te,13) are air temperatures. The apparatus should be allowed to run for 30 minutes to allow the test conditions to become IV. Calculation method Axial profile Calculations Formula 1 Volumetric flow rate of air at orifice plate, Qo=AoCd2? Porifice? air m3/s Where: Cd = 0. 63 discharge coefficient Ao=? do24 area of orifice plate (m^2) ?Porifice pressure drop at orifice ?air density of air And; Ao=? do24 area of the orifce (m2) Formula 2
Mass flow rate of air at oriface plate, mo=? airQo (kgs) Formula 3 Inside area of test section, Ain=? din24m2 Formula 4 Mass flow rate of air in test section, mtest=? airAinVtest=? airAin2? Porifice? air kg/s Formula 5 Heat input as a fraction of total Heat input, Pi=Pow*1-loss*L1+L2+…+LiLtest Formula 6 Mean temp rise of fluid above entrance,? Tmean= Pimcp? =Ti,air=To+? Tmean Formula 7 Heat flux, q''=PiAl= Pi? dinL1-i= Pi? din(L1+L2+…+Li) W/m2 Formula 8 Convective heat transfer coefficent, hi=q''? T=q''Ti-Ti. air Formula 9 Wall shear stresss, ? w=din?
Ptest4LtestPa Formula 10 Bulk temp rise in test section, Tbulk,test=T1,air+T2,air+T3,air+T4,air+T5,air+ T6,air+T7, air 7 Radial profile Calculations Formula 11 Pressure head, =Hi=Hleft-Hright(m) Formula 12 Pressure drop across pipe diameter, ? Pradial=? oilgHi(Pa) Where ? oil=0. 826? Water(Pa) Formula 13 Velocity, Vi=2(? Pradial)i? air ms;Vavg=i=213Vi13 ms Formula 14 Bulk temp rise at exit, T0+i=113Te,iTe,7(C) Reynolds Analogy Formula 15 Nu1=havgdinkair Formula 16 Nu2=0. 023Re0. 8Pr0. 4 Formula 17 Where; Re=? airVtestdin? air,Pr=Cp? kand Vtest=2? Ptest? ir Formula 18 Friction factor, F1=2? Ptestdin? airLtestV2test Formula 19 F2=0. 184Re-0. 2 V. Results and discussion -results (Table 1) Heat input at thermocouple in (W) p1| p2| p3| p4| p5| p6| p7| 145. 77| 310. 79| 420. 8| 475. 81| 530. 82| 585. 83| 640. 83| (Table 2) Temp of air at thermocouple locations (C) T1,air| T2,air| T3,air| T4,air| T5,air| T6,air| T7,air| 37. 56| 42. 16| 45. 22| 46. 76| 48. 29| 49. 83| 51. 36| (Table 3) Convective heat transfer coefficient (W/m^2*k)| | | | | | | | | | | | | | h1| h2| h3| h4| | h5| h6| | h7| | | havg| 3. 04| 2. 82| 2. 4| 2. 12| | 2. 72| 2. 7| | 2. 76| `| | 2. 657143| | | | | | | | | | (Table 4) Pressure in head (m), Pressure drop across diameter of pipe (m), Velocity of air (m/s), Exit temp(C), Bulk temp rise (C), Radial Position (in). Figure 2 Exit velocity and exit temp as a function of radial position Figure 3 Pipe wall temperature as a function of distance along pipe. -Discussion In many ways the importance of certain coefficients has been lost on students. When a problem presents itself we may simply look up certain coefficients or values in order to solve the problem.
The emphasis of importance always falls on method or theory of problem solving. The benefit of laboratories is that, through the experimental knowledge gained, we can see where certain values come from that help us to solve difficult problems. This realization that certain coefficients do have a background shows the students the importance of the values they use without thought. In this lab we have performed an experiment to identify certain properties of convective heat transfer, through looking at the results gained and calculations performed we can inturpitate a variety of information.
Table 1 shows the power input to each of the thermocouple locations, as we can see the power input is in the form of a ramp (increasing) this is caused by the increased exposure of the air to the heating wires. Table 2 is an indication of the accuracy with which we have been able to raise the air flow temperature; this table indicates a confirmation of the expected results from Table 1. It is expected that with a constant heat flux the parameter that affects the convective heat transfer coefficient is the temperature difference, this theory can be proven correct with the examination of Table 3.
Looking at the results from Table 3 we can see a greater coefficient at the first thermocouple location due to the greater temperature difference between the cool air and the hot wall. As the flow moves axially (h) is reduced as the air temp is raised to closer resemble the wall temp, then as the wall temp is raised (h) begins to rise again. Moving on to the results obtained from the radial section of the lab we can first examine Table 4. This table shows a variety of information including Pressure in head(m), Pressure drop across diameter of pipe (m), Velocity of air(m/s), Exit temp(C), Bulk temp rise (C), and Radial Position (in).
Looking at the pressure section we see that the greatest pressure is found in the center of the pipe and as we extend radially outward the pressure is decreased. This is quite an odd result and defies a proven fact of fluid dynamics, boundary layers. The theory of boundary layers states that the fluid in contact with a surface has no velocity as it form a boundary layer on the surface. Little to no velocity should, in theory, result in a greater pressure. The other values obtained from this table are of expected quantities, these trends include; exit temperature and bulk temp rise increasing radially outwards, and velocity nd pressure drop decreasing radially outwards. Upon examining Figure 2(Exit velocity and exit temp as a function of radial position) we can see that the curve for temperature of the fluid is approximately inverse to the velocity of the given fluid. This would indicate that the greater the velocity of the fluid the greater the heat transfer, that is to say that the higher velocity fluid is able to remove heat more effectively then the lower velocity fluid. This experiment proves theoretical knowledge but is slightly biased due to the heating element being places around the pipe.
Greater accuracy could be achieved by placing the heating element in the center of the pips radius. Figure 3 is a representation of the wall temperature of the pipe with respect to the length of the pipe. This graph should show a liner relationship due to the continual heat input as a ramp function, but an outlier is present which prevents a completely linear relationship. The outlier in figure 3 can be attributed to errors and/or uncertainties encountered throughout the laboratory.
As with all experiments errors are encountered, some of the sources of error for this laboratory are; the accuracy with which the thermocouples and pitot tubes measured values and the accuracy to which the digital displays were able to transform the signal of the measuring devices to a digital output. As with most experiments the greatest source of error can be traced back to the human element. During the calculations and when finding properties from various resources many errors may have accumulated. Calculation errors and reliability of references may be the greatest sources of error for this laboratory.
For the reporting section of this laboratory some of the obtained or calculated values were compared, the first of these comparisons was that between the integrated mass flow rate (integrated from fig 3) and the calculated value. From integration we obtain a value of 0. 1440 and from calculation we obtain a value of o. 0339 (kg/s) this is a sizable error and can be attributed to the poor quality of the function generated from excel, as well as the inaccuracy with which a computer can evaluate an integral.
The second of the comparisons is the integrated value of the bulk temperature rise compared to its calculated value. From integration we receive 277. 9K and from calculation 318. 88K again this is a sizable error and can be attributed to the same sources as the previous integration. Another comparison is the Nusselt number (N) and friction factor (F), calculated results show F1=0. 0159 and N1=3. 28, while numbers generated from correlations show F2=0. 0196 and N2=160. 15. Now the difference between friction factors is reasonably small but unfortunately we have encountered a sizable gap between the Nusselt numbers.
This error may be traced back to an unreliable reference when looking up various properties of air, in particular the value of Cp. If we briefly look at a moody diagram we can see from the friction factors that the flow is indeed turbulent. Axial and radial temperature profiles are an important section of this laboratory, because of this importance we will briefly talk about some of the factors that affect these profiles. Axial temperature is controlled by the amount of heat put into the fluid flow through the pipe.
The amount of heat passed on to the fluid flow will be one of the main factors affecting the temperature profile but velocity will also affect the temperature. A greater velocity will remove heat from the heating element more effectively but will also reduce fluid temp as we have less time for fluid to experience heat exposure. Radial temperature profile is controlled by heating element placement, velocity of fluid, and pipe roughness. Because the heating element was placed around our fluid flow it only makes since that the temperature of the fluid will increase as the radial distance increases.
However it is not only the heater element placement, due to the boundary layer formed along the pipes inner diameter we will have stationary fluid. This stationary fluid will have a greater exposure time to the heating element and will thus accumulate a greater temperature. The roughness of the pipe is the determining factor as to, for a constant fluid, the size of the boundary layer. During this lab we have dealt with bulk temperature, like energy, temperature is difficult to define.
In simplest terms temperature can be described as the property that gives a measure of the degree of hotness or coldness of a body, but it should be noted that temperature is not really a property in fact it is a concept. Bulk temperature is in simplest form the average of all the temperatures of fluid flow across the cross-section of the pipe. Temperature is not to be mistaken for heat, as stated previously temperature can be described as the property that gives a measure of the degree of hotness or coldness of a body, well on the other hand heat is a form of energy. VI. Conclusion
This laboratory was based on an interest in the concept of forced heat convection heat transfer. This laboratory was accomplished through the use of a fan forcing a given fluid (air) through a heated section of pipe. From the results obtained many quantities were calculated such as; bulk temperature raise, friction factor, Reynolds number, ect. The main results of the laboratory were the calculation of the convective heat transfer coefficient, and the realization of how it was affected by various portions of the experiment. The laboratory could be deemed a success as it educated the student and completed its objectives.
Some recommendations are; a reduced calculation portion as the length of the calculations portion prevented achieving better focus on the laboratory itself, and it would be more beneficial if all the labs could more closely follow the course. VII. References  ME3435: Heat Transfer Laboratory, Department of Mechanical Engineering, The University of New Brunswick.  ME3415: thermodynamics/ ME3435Heat Transfer Laboratory Format, Department of Mechanical Engineering, The University of New Brunswick.  Archimedes: A Gold Thief and Buoyancy/ Larry "Harris" Taylor, PhD  Engineering tool box/air properties, 156. html. VIII Appendices