5. A solid is bounded by long concentric cylinders. The inner cylinder has a radius p and the outer cylinder has a radius q. Diffusivity is a'. Inner and outer surfaces are kept at zero temperatures and the initial temperature 264 APPLICATIONS OF BVPS is dependent onr alone, given by f(r). Find the temperature u(r, t). The BVP follows: u, = a p0 u(p, t) = u(q, t) = 0, t>0 u(r, 0) = f(r) , p
5. A solid is bounded by long concentric cylinders. The inner cylinder has a radius p and the outer cylinder has a radius q. Diffusivity is a'. Inner and outer surfaces are kept at zero temperatures and the initial temperature 264 APPLICATIONS OF BVPS is dependent onr alone, given by f(r). Find the temperature u(r, t). The BVP follows: u, = a p0 u(p, t) = u(q, t) = 0, t>0 u(r, 0) = f(r) , p
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Transcribed Image Text:5. A solid is bounded by long concentric cylinders. The inner cylinder has a
radius p and the outer cylinder has a radius q. Diffusivity is a'. Inner and
outer surfaces are kept at zero temperatures and the initial temperature
264
APPLICATIONS OF BVPS
is dependent onr alone, given by f(r). Find the temperature u(r, t). The
BVP follows:
4, = a°(4, + ; u,), p<r<q,t>0
u. + -
и,
u( p, t) = u(q, t) = 0, t>0
u(r, 0) = f(r) , p<r<q
Ju(r, t)|< M
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