## Data Reduction

The local heat transfer coefficient is calculated from the local net heat transfer rate per unit surface area to the cooling air, the local wall temperature on each copper plate, and the local bulk mean air temperature as:

Local total net heat transfer rate is the electrical power generated from the heater (q=VI) minus the heat loss outside the test duct. The heat loss is determined experimentally by supplying electrical power to the test section until a steady state condition is achieved for a no flow (without any airflow) condition. This is done for several different power inputs to obtain a relation between the total heat loss from each surface and the corresponding surface temperature. The highest heat loss is about 5% of the total power input for non-rotating cases and about 27% for a rotating low Reynolds number (Re=5000) case. To place the results on a common basis, the heat transfer area used in equation (1) was always that of a smooth wall. The local wall temperature is obtained from thermocouple that impeded in each copper plate. The bulk mean air temperatures entering and leaving the test section were measured by thermocouples. The local bulk mean temperature (Tbx) is used in equation (1) was calculated from the linear interpolation between the measured inlet and exit air bulk temperatures. Another way to find the local bulk mean air temperature is determined by marching along the test section and calculating the temperature rise from the local net heat input through each set of four heated surfaces. The differences between the calculated and measured outlet bulk mean temperature are between 1-2 ° C in all of the cases. .

Local Nusselt number was normalized by the Nusselt number for the fully developed turbulent flow in a smooth stationary circular pipe to reduce the influence of the flow Reynolds number on the heat transfer coefficient. The correlation is by Dittus-Boelter/McAdams or (Rohsenow and Choi 1961), as:

Nuo k

The Prandtl number, Pr, for air is 0.71. Air properties are taken based on the mean bulk air temperature.

The uncertainty of the local heat transfer coefficient depends on the uncertainties in the local wall and bulk air temperature difference and the net heat input for each test run. The uncertainty increases with the decrease of the both local wall to bulk air temperature difference and the net heat input. Based on the method described by Kline and McClintock20, the typical uncertainty in the Nusselt number is estimated to be less than 9% for Reynolds number larger than 5000. The maximum uncertainty, however, could be up to 23% for the lowest heat transfer coefficient at the lowest Reynolds number tested (Re=5000).

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