# 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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