MSE 321 Engineering Thermodynamics and Heat Transfer
LABORATORY MANUAL
EXPERIMENT 3:
Free and Forced Convection
Peyman Taheri
Objective Determination of heat transfer coefficient h , for free and forced convection in different geometries.
Apparatus Figure 1 shows the experimental instrument in details. This unit has the following components:
The vertical air duct (1) with a cross-sectional area of 120 ´120 mm 2 and a length of 1m is used to guide the air flow over a heated surface. The ambient air enters the duct at the bottom and heated air leaves the duct at the top (11)
The air duct has several measuring glands (2) that enable one to record the temperature at various locations by using a type-K thermocouple (3). In addition, a fan with flow sensor (4) blows air into the duct and measures its volumetric inlet flow rate. Two thermistors (5, 6) record the inlet and outlet temperatures of the air flow.
Assemblies of heaters and heated surfaces with different geometries (7-9) can be mounted inside the duct using simple toggle-type fasteners. The different heated surfaces (flat plate, pipe bundle or fins) are each heated by four resistive heaters with maximum heating power of about 170 W. The applied voltage to the heaters is adjustable for achieving variable heat output. There are bimetallic strips to interrupt the supply of power, when certain temperatures are established (also used to ensure that the temperature does not exceed 120°C).
The control and display unit (10) allow controlling the power supply and regulate the fan speed and heaters power. In addition, this unit displays the electrical power supplied to the heaters, the volumetric flow rate of air, the inlet and outlet air temperatures, and the temperatures measured with the type-K thermocouple. A PC is connected to the apparatus for data acquisition.
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Figure 1: Components of experimental apparatus.
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Software The LabView software is used to display the measured data. Figure 2 shows the system diagram in LabView with some sample data values. The system diagram shows temperatures and heat transfer parameters at different locations of the flow path (the blue line). The definitions of the parameters are presented in Table 1. Table 1: Parameters definition Parameter
Definition
Parameter
Definition
T1 w dm / dt dQ / dt P1 T4 T3 p0
Inlet air temperature Air velocity Air mass flow rate Rate of heat transfer Heater input power User defined fin surface temperature Thermocouple (3) temperature Ambient pressure
T0 PHI Fins eta alpha Re Nu T2
Ambient temperature Ambient relative humidity Type of the installed fin Fin efficiency Heat transfer coefficient Reynolds number Nusselt number Outlet air temperature
Figure 2: System diagram in LabView.
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Peyman Taheri Figure 3 shows different geometries for the heated surface;
Flat plate,
Pipe bundle (needle fins),
Rectangular fins.
Air flows past the heating element and absorbs heat in the process. Sensors record the volumetric flow rate of the air, the heating power and the temperatures at all relevant points. The measured values can be read on digital displays. At the same time, the measured values can also be transmitted directly to a PC. Free and forced convective cooling will be investigated on all three surface configurations. Comparison between the flat plate results and the results of finned surfaces can be used to find the effects of fins on the heat transfer coefficient under free and forced convection heat transfer.
(a)
(b) Figure 3: (a) Flat plate, (b) pipe bundle, and (3) rectangular fins
(c)
Theory There are three modes for heat transfer: convection, conduction, and radiation. The convection heat transfer plays an important role in many industrial applications. The convection heat transfer is usually subdivided into free and forced convection. In the forced convection, the fluid is blown or pumped past the heated surface using a pump or a fan, while in the natural (or free) convection, fluid flow is naturally achieved by buoyancy effects, i.e., density variation in the fluid. The heat transfer rate to the fluid Q can be calculated using the fist law of thermodynamics for the heated fluid,
Q = m h
(1)
where h is the enthalpy variation of the fluid before and after the heated surface and m is the mass flow rate which is calculated as,
m = wA
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(2)
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Peyman Taheri here is the air density, w is the averaged velocity and A is the cross-sectional area of the duct which is equal to 0.0144 m2 in this experiment. The air density can be found from thermodynamics tables. Using ideal gas assumption for the air, Eq. (1) becomes,
Q = m cP T
(3)
The temperature difference T is calculated from the difference between the average inlet and outlet temperatures. The specific heat capacity of the air cP also depends on the air temperature and should be found from thermodynamics tables. Since the temperature is varying along the duct, the cP value should be evaluated in the averaged temperature of air in the duct, TM , TM =
T1 + T2 2
(4)
The heat sources on the testbed consist of electrical resistors; thus, the amount of power that is fed to the heaters, P1 , can be calculated. The factor for fin efficiency, , provides information on the losses which occur during heat transfer. This factor indicates the portion of the input energy that is transferred to the fluid. This can be written as,
=
Q P1
(5)
The amount of 1 - shows all losses resulted from convection and radiation to the surroundings and not to
the fluid. The heat transfer from a surface to a fluid can be described mathematically, Q = A Tm
(6)
where is the heat transfer coefficient. The heat transfer rate is the same as the amount calculated from Eq. (3). Determination of Tm is challenging; if one assumes that temperature is varying linearly along the duct, Tm will be identical to TM calculated from Eq. (4). Another important value introduced in the literature is Log Mean Temperature Difference (LMTD). It is calculated using the following formula,
Tm =
(T1 - T fin,in ) - (T2 - T fin,out ) (T1 - T fin, in ) ln (T2 - T fin, out )
(7)
Since the surface temperature, T fin , of the heater remains almost constant across the entire area and only the temperature of the air changes significantly between the inlet and the outlet, one can simplify this equation, Tm = ln
MSE 321 (Fall 2013)
T1 - T2 (T1 - T fin )
(8)
(T2 - T fin )
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Therefore, the heat transfer coefficient, , can be evaluated from Eqs. (3), (6) and (8). The heat transfer depends not only on the temperature difference and the surface material of the heater, but is also influenced by the flow regime, i.e., laminar or turbulent flow. Reynolds number is a criterion for defining whether a flow is turbulent or laminar. For a flow over a flat plate the transition between these two regimes occurs at approximately Recrit = 1- 5´105 . However, there are other
values for pipes and fins. The Reynolds number is defined as, Re =
wl
(9)
where l is a characteristic length scale, which is the plate length for flat surfaces, and = / is the kinematic viscosity of the fluid (air). The kinematic viscosity of the air is temperature dependant and can be taken from thermodynamics tables at TM . The Nusselt number is dimensionless and is used in measuring heat transfer rates,
Nu =
l k
(10)
where k is thermal conductivity. The Nusselt number can be calculated once the heat transfer coefficient , is known. The following correlation (obtained experimentally) offers another way of determining the Nusselt number for a parallel flow over a smooth surface (plate) for laminar flow, Nu = 0.664 Re0.5 Pr 0.33
(11)
Using the values obtained from Eq. (11), it is possible to check the accuracy of experiments for flat plate heater.
Procedure At the beginning of the experiment the heater element with the flat plate is connected to the control and display unit prior to being fixed in the air duct. Once the power supply has been connected, the potentiometer on the control unit is set to 100% and the surface temperature T fin is measured using the thermocouple. Once a steady-state condition has been reached, there is no noticeable temperature change at the surface of the heater element, the temperature is saved. The heater is then placed in the duct. Once again it is necessary to wait until a steady-state condition is established. The following values are measured;
Temperature T1 at the inlet of the air duct,
Volumetric flow rate ( wA ) at the inlet of the air duct,
Temperature T2 at the outlet of the air duct.
This experimental sequence is applicable to all experiments as tabulated in Table 2. In the case of the pipe bundle and the fins, the surface temperature must be measured prior to fitting in the air duct. Turn on the fan and repeat the above-mentioned sequence. Increase the fan power to 100% of its rated capacity with the heater at full power.
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The temperature drop within the heated pipe bundle is measured on the heater insert for the free and forced convection cases. The heater is operated at 100% power output and the thermocouple pushed into the air duct through the measuring gland such that the tip is in the centre of the cylinder bore. The thermocouple is then removed from the first measuring gland and is inserted in the other three holes in the cylinder. Table 1: Measurement data. Flat Plate Natural
Forced
Pipe bundle Natural
Forced
Rectangular fins Natural
Forced
T1 T2 w [m/s] P1
After completing the measurements, find the efficiency of each system at natural and forced convection modes. Determine effects of flow regime on the heat transfer rate. For the flat plate heater calculate the accuracy of the experimental data through comparison of the measured values to the one obtained from Eq. (11).
Discussion 1) What are the differences between laminar and turbulent flows? Which one has the higher heat transfer coefficient? 2) What is the difference in the measured values of heat transfer coefficient if one uses linear average temperature instead of LMTD?
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