Heat Transfer from Extended Surfaces

Introduction -

Convective heat transfer theory relies on the assessment of the convective heat transfer coefficient, h, whose value depends upon both the properties of the fluid it characterizes and the circumstances under which convection is occurring. In this laboratory experiment, the value of the convective heat transfer coefficient for air at room temperature was determined empirically for both free and forced convection over a cylindrical external surface (a fin) constructed of pure Aluminum; estimates for the value of h were generated for (a) the situation where the fin tip is considered adiabatic (no heat loss through the tip), and (b) for the event that significant heat transfer occurs through the fin tip. In order to verify the validity of these results, the obtained values for h must be compared with the accepted literature values given the assumptions and particular circumstance of each trial.

The apparatus used to measure h (indirectly) in this experiment consisted of an electric heater mounted to the end of an 11 millimeter diameter cylindrical shaft constructed from pure Aluminum; the heater was encased within an insulating material to ensure consistent heat transfer to the base of the Aluminum rod (the fin). Thermocouples placed along the length of the fin measured the surface temperature at their respective locations, which was subsequently recorded by a computer data acquisition software package. The temperatures at each location along the fin were recorded at 15 minute time intervals and monitored until the fin reached steady state (the event that measured temperatures remained constant across consecutive time intervals).

The testing apparatus, including the locations of thermocouples 2-7 (measuring fin surface temperature) along the fin measured relative to the base, is shown below in Figure 1. Thermocouples 1 and 9 (measuring base and heater temperature, respectively), are not labeled directly; instead the location of the base and heater is shown. Thermocouple 8 recorded the ambient temperature throughout the experiment, and is not shown in Figure 1. The raw data, as measured by each of the thermocouples, is provided in Appendix B.

Figure 1. Schematic of testing apparatus showing locations of thermocouples 2-7 (fin surface temperature) measured relative to the base. Thermocouples 1 and 9 measured the base and heater temperature, respectively; thermocouple 8 (not shown) measured the ambient temperature. All units are millimeters. Source: Matt McClintock.

To estimate the value of h of air at ambient temperature for both free and forced convection, it was necessary to perform a least squares analysis of the temperatures along the fin. The value of h that minimized the sum of the squares of the differences between the analytically predicted temperature and the measured temperature at each thermocouple along the fin is the desired value; this analysis was performed in Excel using the “Goal Seek” function. Analytical predictions were obtained via the appropriate fin equations (see Appendix C), where the value of h within those expressions was varied to minimize the sum of the squares of the differences of the temperatures at each thermocouple along the length of the fin.

After obtaining estimates for the convective heat transfer coefficient, h, under the various assumptions and circumstances described previously, it was necessary to assess the validity of our results by comparing them with accepted literature values. Published values for h are given in the form of a range of known values, due to the significant error typically encountered when measuring h. Therefore, the comparison of the empirical results of this experiment with literature values was limited to identifying whether or not the results were within the published range. If they were not, the percent error was given for…