Consider a flat plate or a plane wall with a thickness L and long cylinder of radius r0. Both of these are made of materials such that they can be treated as lumped capacitances (Bi<0.1). Show that in each case, the characteristic length ? c, defined as ? c=(V/As), can be approximated as (L/2) and (r0/2) respectively.
GIVEN
• Plane wall with a thickness L
• Long cylinder of radius r0
• Both cylinder and plane wall can be treated as lumped capacitances (Bi<0.1)
SHOW
• Characteristic length can be approximated as (L/2) and (r0/2) respectively.
ASSUMPTIONS
• Both plane wall and cylinder can be treated as lumped capacitances
We have,
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