- #1

danai_pa

- 29

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I don't understand this problem. I think it is difficult for me. Please anyone

suggestion this problem to me. Thanf you

Let us cosider steady state heat transfer problem in which laplaceT(r)=0

What is the temparature at the center of a thin disc of radius a

whose average boundary temparatue is 70 degree?

Hint:

1) Assume that the temperature distribution is independent of the direction

along the cylinder

2) Use Laplace equation in cylindrical coordinates

3) the temperature at the center is determined from the temperature

distribution for which r=0

4) The functions Sin beta(x) and Cos beta(x) have a periodicity if and only if

the values of beta are integer

5) The average boundary temperature at r=a is given by

T(average) = 1/2*Pi intregrate from 0 to 2*Pi [(T(a,seta)d(seta)]

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suggestion this problem to me. Thanf you

Let us cosider steady state heat transfer problem in which laplaceT(r)=0

What is the temparature at the center of a thin disc of radius a

whose average boundary temparatue is 70 degree?

Hint:

1) Assume that the temperature distribution is independent of the direction

along the cylinder

2) Use Laplace equation in cylindrical coordinates

3) the temperature at the center is determined from the temperature

distribution for which r=0

4) The functions Sin beta(x) and Cos beta(x) have a periodicity if and only if

the values of beta are integer

5) The average boundary temperature at r=a is given by

T(average) = 1/2*Pi intregrate from 0 to 2*Pi [(T(a,seta)d(seta)]

--------------------------------------------------------------------------------

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