March 26, 2017

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A factory would like to produce plain carbon steel strips with pieces of
polyethylene plastic film bonded on them. The bonding operation will use a
laser that is already available to provide a constant heat flux of q′′0= 85, 000 W/m2for a specified period of time, ∆ton, across the top surface of the thin
adhesive-backed film, to be affixed to the metal strip as shown in the sketch.
The metal strip has a thickness D = 1.25 mm, length L = 600 mm, and width
W = 600 mm. The plastic film is perfectly centered on the metal strip and has
thickness d = 0.1 mm, length l = 44 mm, and width w = 500 mm. The heat
flux is applied over the strip’s complete width of 600 mm. The strip is initially
at the ambient temperature of 25◦C and located on a conveyor belt made of an
insulating open mesh material so that the upper and lower surfaces of the strip(including the plastic film) are exposed to air blowing as shown along the length of the plate at 10 m/s.
In order for the film to be satisfactorily bonded it must be cured above 90◦C for 10 s and the plastic film will degrade if a temperature of 200◦C is exceeded. Determine the minimum period of time ∆ton necessary for proper curing and thus optimize productivity of the metal strips, since each strip will have to remain stationary under the laser during the bonding operation.
All modes of heat transfer must be considered, and any assumption must
be justified. If a computer program is necessary, the accuracy of the program
as well as the results need to checked. For example, it may be possible to
check the program by comparing numerical results using different resolutions
to show grid convergence, and against analytical results, obtained for some
limiting situations (e.g. steady state), to show correctness of the program. Your
report will be graded on the basis of the physical understanding exhibited, the execution of the project, and the clarity of the writing and reasoning presented.

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