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A heat transfer problem involving a transient solution

Assume you are at the center of the South Pole of Mars. In this area directly around the South Pole, the Martian surface can be assumed to initially be uniform. Since you are at the ice caps of Mars, the physical constants of the ground are similar to ice.

See attached file for equation.

Suppose the atmospheric gas directly above the surface drops to -260 °F. This will affect the ground below. How deep below the surface would you find the temperature of Mars to be -254 °F after a) 1 hour b) 3 hours.

Additional Martian data resources:
http://mars.jpl.nasa.gov/mgs//sci/msss27Sept04/press-rel1.html
http://mars.jpl.nasa.gov/mgs//

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The problem with solution is contained in the attachments in .pdf and word formats.

Mars Global Surveyor spacecraft orbits Mars collecting data. It has collected more Martian images than all the past Mars missions combined. This graph contains information about the surface temperature of Mars collected by the Mars Global Surveyor using a thermal emission spectrometer.

http://www.windows.ucar.edu/tour/link=/mars/exploring/MGS_surfaceT.html
This image from NASA/JPL shows surface temperatures for the south pole of Mars.

Assume you are at the center of the South Pole of Mars. In this area directly around the South Pole, the ...

Solution Summary

This problem includes actual temperature data collected from the Mars Global Surveyor. This was collected from the Thermal Emission Spectrometer. The problem involves using the properties of Mars, the collected temperature data, and dimensionless parameter formula to determine the time involved with a transient solution and corresponding temperature below the Martian surface. Fun way to practice key heat transfer problem fundamentals!

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