Heat Transfer F12-ENG Lab #4 Forced convection School of Engineering, UC Merced.

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1 1 Heat Transfer F12-ENG Lab #4 Forced convection School of Engineering, UC Merced. October 23, General purpose of the Laboratory To gain a physical understanding of the behavior of the average heat transfer coefficient (h) for forced convection over a cylinder as a function of free-stream velocity. More specifically, the objectives are: (a) determination of the heat transfer coefficient for transverse flow around a single cylinder, (b) determination of the heat transfer coefficient for a single tube in a tube bank array, (c) determination of pressure and velocity distribution across the wind tunnel duct. 2 Laboratory Theory The ability to transfer heat from a wall to a medium or vice versa is described by the coefficients of heat transfer h. Q = h A T (1) where Q is the heat transfer rate, A the wall area, and T the temperature difference between the temperature of the medium and wall. In a flowing medium the heat transfer is essentially determined by the conduction processes in the boundary layer near the wall. Outside the boundary layer the heat is transported by the mass flows rates. Here good turbulence improves the heat transfer. The heat transfer from the wall to the medium depends on the conductivity (k) and the thickness of the boundary layer. Due to the large number of heat exchanger shapes and conditions, the thickness of the thermal boundary layer would need to be determined in each case. However, by means of the application of the similitude theory a dimensionless number, the Nusselt number, can be developed that takes into account the thermodynamic and fluid mechanics related conditions, Nu D = hd k, (2) where, for a cylinder or pipe in a transverse flow, the characteristic length on which dimensionless parameters are based on is outside diameter D. Based on experimental measurements and correlation of data the Nusselt number can be calculated from the Reynolds and Prandtl number. The Reynolds number represents the flow state (laminar/turbulent) Re D = VD ν, (3)

2 2 where V is the flow velocity and ν the kinematic viscosity. relationship between flow and thermal boundary layer. The Prandtl number defines the Pr = ν α, (4) where α is the thermal diffusivity of the medium. For cylinder banks the Nu correlations may be taken from the text book (Incropera and DeWitt, 2007). Other books use descriptions based on crossflow over a single cylinder with correction factors for tube banks, e.g. Mills (1995). We will follow this approach here, because it allows us to calculate the Nusselt number for a tube in the first row independently from the average Nusselt number for a tube bank. For the cylinder in a transverse flow, the Nusselt number can be given as follows (from Churchill and Bernstein, 1977): Laminar (Re < 10 4 ): Nu lam = Re Pr 1/3 [ 1 + (0.4/Pr) 2/3 ] 1/4 (5) Transition (10 4 < Re < ): Turbulent ( < Re < ): Nu tr = Re Pr 1/3 Re [ 1 + (0.4/Pr) 2/3 ] 1/ (6) Nu tur = Re Pr 1/3 [ ( ) [ 1 + (0.4/Pr) 2/3 ] Re 5/8 ] 4/5 1 + (7) 1/ Figure 1: Tube bank configurations: (a) aligned, (b) staggered If the cylinder in a flow is in a pipe bundle, then the Reynolds number necessary for the calculation of the Nusselt number must be determined using the mean velocity in the cavity portion of the pipe bundle. The average velocity in the space between two adjacent tubes is defined by the relation V max V = S T S T D (8) where V is the velocity of the fluid external to the tube bank, S T and S L are transverse and longitudinal pitches (see Fig. 1). Now we define the dimensionless transverse pitch as P T = S T /D,

3 the dimensionless longitudinal pitch as P L = S L /D, and a factor ψ as Then the arrangement factors (Φ) are ψ = 1 π, i f P L 1 4P T (9) π ψ = 1, i f P L 1 4P T P L (10) Φ ali ned = ψ 1.5 S L /S T 0.3 (S L /S T + 0.7) 2 (11) For tube banks fewer than 10 rows (as the case for this experiment) Φ sta ered = P L (12) Nu D = 1 + (N 1)Φ Nu N 1 D, (13) where Nu 1 D is the Nusselt number for the first row, which can be obtained from Eqs. (6) to (8), and Nu D is the Nusselt number averaged over all row. To determine the flow velocity, the dynamic pressure needs to be calculated from the difference between the total pressure and the static pressure. p dyn = p es p stat = p. (14) The velocity can then be determined with the aid of the density ρ V = ρ = k /m 3 can be taken for the density of air. 2 p ρ. (15) 3 Laboratory equipments - Apparatus An air duct (1) with a square cross-section (150x150 mm) is used as the measurement section. The air is drawn through the duct by a fan (2). A model of a pipe bundle heat exchanger (3) is inserted in the duct. Here an individually electrically heated heater element (4) can be used in the positions for various pipes. A thermocouple is integrated into the rod heater; this thermocouple can measure the heater surface temperature directly. Using the adjustable flap (6) the air mass flow rate can be adjusted. The air flow rate can be measured at the air inlet with the aid of a flow nozzle (14) and an inclined tube manometer (5). The air temperature can be determined using a temperature measuring unit. A moving Pitot tube (7) can be inserted in the duct before and after the heat exchanger. In this way the dynamic pressure across the cross-section of the air duct can be measured. At the same point there are measuring glands (13) for the measurement of the static pressure. A pressure station with inclined tube and dial manometer (5) is used to indicate the pressure. In this way a velocity distribution can be measured.

4 Transparent windows (12) enable the Pitot tube to be observed and thus precisely positioning, e.g., for the measurement of a wake. The system is switched on at the main switch (9). The fan is switched on at the switch (10). Figure 2: General setup of the apparatus 4 Laboratory procedure 4.1 Pressure and Velocity Distribution in the Duct In this experiment the pressure distribution and the resulting velocity profile after the heat exchanger insert are determined. Connect the manometer tubes properly to the pressure tapping points of the duct Turn on the flow and let it stabilize for at least 2-3 minutes

5 5 Measure the static pressure first. For this purpose connect the inclined tube manometer to the bottom measuring connection on the duct. Measure the total pressure with the aid of the Pitot tube. For this purpose connect the inclined tube manometer to the measuring connection for the Pitot tube. To obtain a pressure profile, the move the Pitot tube across the entire cross-section. Take pressure readings at various depths (from mm in steps of 10 mm) using the Pitot tube (At 0 mm and 150 mm non slip condition). Depth [mm] P 1 [Pa] P 2 [Pa] p [Pa] Velocity [m/s] Heat Transfer Coefficient for a Single Tube In this experiment, the heat transfer coefficient is measured for transverse flow around a single tube. The measured heat transfer coefficient is compared with the heat transfer coefficient obtained using Nusselt number correlations. The individual heater (diameter 12.5 mm) is inserted in the duct above the fan. The temperature of the air is measured at bottom of the duct below the fan. It is assumed that the temperature of the air is only changed slightly by the fan. Switch on the fan. Set the power for the heat on the control and display unit. Once the heater is switched on, the temperature at the heater will increase. Measure the temperature of the air and temperature of the rod element when steady state is achieved i.e. temperature does not change any more. Get the flow velocity measurement from the previous part; find the average bulk velocity of air flow for heat transfer calculations. Repeat for six different values of heater input power, keeping the air flow velocity constant No. Power [W] T air [C] T rod [C] Air vel. [m/s] Re Nu theory h theory h measured

6 6 4.3 Heat Transfer Coefficient for a Tube in a Tube Bank Array In this experiment, the heat transfer coefficient is measured for flow across a tube bank array in which one of the tubes is heated electrically. The measured heat transfer coefficient is compared with the heat transfer coefficient obtained using Nusselt number correlations. 24 positions are provided in the heat element. Here it is possible to perform measurements in various layers of the air flow. Measurements are possible starting from the flow at the centre to the boundary layer. The heater (diameter 10 mm) is inserted in the air flow in the required position and the remaining positions filled with empty rods. Perform the experiment with two different positions of the heater within the tube array (consult the lab instructor). For each heater position perform the steps as described for the single tube experiment to obtain values of air and rod temperatures, and rod power input. No. Power [W] T air [C] T rod [C] Air vel. [m/s] Re Nu theory h theory h measured Front rod Back rod Lab report The report should include the following: Brief introduction Description of the problem. Experimental methodology including list of measurements taken. Results and physical interpretation of results. Conclusions. Any references used. References [1] Frank P. Incropera and David P. DeWitt, Fundamentals of Heat and Mass Transfer, Wiley (2007). [2] Anthony F. Mills, Basic Heat and Mass Transfer, IRWIN (1995). [3] GUNT Geratebau GmbH Barsbuttel, Instruction Manual WL 314 Heat Transfer Bench, (June, 2002).