# Two rigid circular cylinders, in perfect contact are pressed together by the action of force F….

Two rigid circular cylinders, in perfect contact are pressed
together by the action of force F. Initially, the cylinders are in thermal
equilibrium with the ambient at temperature Tf. At time zero
cylinders begin to rotate at nominal speeds of _1 and _2 as shown in
the figure. The bottom cylinder rotates clockwise and the upper cylinder
rotates counterclockwise. The coefficient of dry friction between the cylinders
is µ. The heat resulting from the friction of the rotating cylinders, raises
their temperature. Heat transfer coefficient for the upper cylinder surface
area is hs1 and for the
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Two rigid circular cylinders, in perfect contact are pressed
together by the action of force F. Initially, the cylinders are in thermal
equilibrium with the ambient at temperature Tf. At time zero
cylinders begin to rotate at nominal speeds of _1 and _2 as shown in
the figure. The bottom cylinder rotates clockwise and the upper cylinder
rotates counterclockwise. The coefficient of dry friction between the cylinders
is µ. The heat resulting from the friction of the rotating cylinders, raises
their temperature. Heat transfer coefficient for the upper cylinder surface
area is hs1 and for the horizontal area is ha1.
Similarly, heat transfer coefficient for the bottom cylinder surface area is hs2
and for the horizontal area is ha2. Use these data and those given
in the figure to a) write the differential equations from which temperature
distribution in each cylinder can be obtained and b) identify the initial and
the boundary conditions.

[Hint: Temperatures are obtained from Equation IVa.2.7 with
_T/__ = 0 due to symmetry in the _ direction. There are 2
initial and 8 boundary conditions].

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