Measuring the temperature distribution along an extended surface and comparing the result with a theoretical analysis
- Calculating the heat transfer from an extended surface resulting from combined modes of free convection and radiation heat transfer
THEORY Where it is required to cool a surface by convection, the rate of heat removal can be improved by increasing the area of the surface. This usually achieved by adding extended surfaces called fins. The term extended surface or fin is commonly used to depict a case that involves heat transfer by conduction within a solid and heat transfer by convection (and/or radiation) from the boundaries of the solid (fins enhance heat transfer from a surface by exposing a larger surface area to convection and radiation.. The direction of heat transfer in extended surfaces from the boundaries is perpendicular to the principal direction of heat transfer in the solid. A temperature gradient exists along each fin or pin due to the combination of the conductivity of the material and heat loss to the surroundings A temperature gradient exists along each fin or pin due to the combination of the conductivity of the material and heat loss to the surroundings. The temperature distribution along the fin must be known to determine the heat transfer from the surface to its surroundings. Since radiation and natural convection from the surface occur simultaneously, both of these effects must also be included in the analysis.
EXPERIMENTAL APPARATUS
Figure 1. Turbine Service unit
The experimental setup consists of a cylindrical 1cm diameter brass rod and an electrical heater that is in direct contact with the brass rod. The brass rod is 35cm long rod with eight thermocouples each are located 5cm apart. There is one extra thermocouple to measure the ambient temperature.
1-Brass rod (Diameter "D" = 10mm and Length "L" = 35 cm) 2- Thermostat 3- Insulating housing 4 Power supply lead and plug 5- 240 V electric heater 6- S upport 7- Plate 8- Support for thermocouple 9- Additional thermocouple to measure ambient temperature 10- Mounting 11- Eight thermocouple with 5cm intervals 12Plugs that connect the thermocouple to console. Figure 2. Extended surface heat transfer unit.
Figure 3. Thermocouples location.
For steady state the temperature distribution along the fin can be calculated from
( ) () ( )
… (1)
Note: the magnitude of the temperature gradient decreases with increasing "x". This trend is a consequence of the reduction in the conduction heat transfer with increasing x due to continuous convection and radiation losses from the fin surface and the value for "m" can be found by iteration using a suggested starting value of 7.0. Plot a graph of measured surface temperature "Tx" against position "x" along the extended surface and draw a smooth curve through the points. Plot the theoretical temperature profile which you have calculated using the average value for m and compare the curve with your measured values.
2
The total heat loss from the rod can be calculated as follows: QFin = H As (Ts – Ta)
… (2)
H = hc + hR
… (3)
As = π D L
… (4)
hc = 1.32
[( )]
… (5)
hR = σεF [ ]
… (6)
Ts = (T1 + T2 + T3 + T4 + T5 + T6 + T7 + T8)/8
… (7)
Where "H" is the combined heat transfer coefficient due to natural convection and radiation (W/m2ºC), "hc" is the convection heat transfer coefficient (W/m 2ºC), "hr " is the radiation heat transfer coefficient (W/m 2ºC), "As" is fin heat transfer area (m2). "Ts" is the average surface temperature of the fin (ºC),"Ta" is the ambient temperature = T 9 (ºC), "D" is the fin diameter (= 1 cm), "L" is the fin length (= 35 cm), "σ" is Steven Boltzmann constant (= 5.67 × 10 -8 W/m2 K 4), "ε" is the emissivity of the sur face (= 0.85) and "F" is the shape factor (=1). Fin efficiency can be calculated from
× 100
… (8)
QInput = V × I
… (9)
Where " " is the fin efficiency (%), QInput is the supplied heat (Watt), "V" is the supplied voltage (volt) and "I" is the supplied current (ampere).
PROCEDURES 1- Switch on the front Mains switch (if the panel meters do not illuminate check the RCD and circuit breakers at the rear of the service unit, all switches at the rear should be up). 2- Set the heater voltage to the required volts (adjust the VOLTAGE CONTROL potentiometer to give a reading on the top panel meter with the selector switch set to position V). 3- Allow the temperatures to stabilize (Monitor the temperatures using the lower selector switch/meter). 4- Record the Voltage and Current supplied to the heater. 5- Record the temperature at each position along the rod (T1 to T8). 6- Record the ambient air temperature T9.
