Problem 3 (10 pts.) Consider steady state heat transfer in a cylinder as shown. The ends...

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Problem 3 (10 pts.) Consider steady state heat transfer in a cylinder as shown. The ends of the cylinder are held at two different temperatures and the other surface is held at temperature equal to zera. The radius of the cylinder is taken to be unity and the length, L. The temperature field is governed by Laplace's equation: 82/02 +(1/1){0/9 [3/3]}=0 -T=2. BC1: 2-0. T-1: BC2: 2=L, T=2; BC3: =0, finite; 7=0& 51-2 BC 1,T-0 Solve for Tir,z) using a Fourier-Bessel series. Find the formal solution. By "formal solution" mean you do not have to evaluate any Fourier coefficients, but you de need to give the expressions for them in terms of specific integrals. Problem 3 (10 pts.) Consider steady state heat transfer in a cylinder as shown. The ends of the cylinder are held at two different temperatures and the other surface is held at temperature equal to zera. The radius of the cylinder is taken to be unity and the length, L. The temperature field is governed by Laplace's equation: 82/02 +(1/1){0/9 [3/3]}=0 -T=2. BC1: 2-0. T-1: BC2: 2=L, T=2; BC3: =0, finite; 7=0& 51-2 BC 1,T-0 Solve for Tir,z) using a Fourier-Bessel series. Find the formal solution. By "formal solution" mean you do not have to evaluate any Fourier coefficients, but you de need to give the expressions for them in terms of specific integrals.