The top of a 30 cm I-beam is maintained at a temperature of 260°C, while the bottom is at 93°C. The thickness of the web is 1.25 cm. Air at 260°C is blowing along the side of the beam so that h= 40 W/(m2 K). The thermal conductivity of the steel may be assumed constant and equal to 43 W/(m K). Find the temperature distribution along the web from top to bottom and plot the results.
GIVEN
FIND
The temperature distribution along the web and the plot the results
ASSUMPTIONS
The thermal conductivity of the steel is uniform
The beam has reached steady state conditions
One dimensional through the web
The beam is very long compared to the web thickness
SKETCH
The web of the I beam can be thought of as a fin with a uniform rectangular cross section and a fixed tip
temperature the temperature distribution along the web is
Substitute these into the temperature distribution
This temperature distribution is plotted below
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