4- A long insulated wire was initially at a uniform temperature, then both ends of the...

Transcribed Image Text:

4- A long insulated wire was initially at a uniform temperature, then both ends of the wire were suddenly immersed in a cup of hot fluid and kept there. If the dimensionless temperature 0 in the wire is obtained by the solution of the дө %3D дt a20 subject to the conditions: equation: дх2 0 = 0 for 0<x<1 and t = 0 0 = e-8t at x = 0 & x = 1 for t>0 Employing the Crank-Nichlson method with r= 2 and h = 0.1; find at time t = 0.02 the following: a- Write the finite difference computational molecule at (i, j+1). b- Display the matrix of coefficients in a simplest form. c- Hence solve these equations employing a suitable direct method. d- If you had employed an explicit scheme, what is the minimum number of time steps you could use for this problem. 4- A long insulated wire was initially at a uniform temperature, then both ends of the wire were suddenly immersed in a cup of hot fluid and kept there. If the dimensionless temperature 0 in the wire is obtained by the solution of the дө %3D дt a20 subject to the conditions: equation: дх2 0 = 0 for 0<x<1 and t = 0 0 = e-8t at x = 0 & x = 1 for t>0 Employing the Crank-Nichlson method with r= 2 and h = 0.1; find at time t = 0.02 the following: a- Write the finite difference computational molecule at (i, j+1). b- Display the matrix of coefficients in a simplest form. c- Hence solve these equations employing a suitable direct method. d- If you had employed an explicit scheme, what is the minimum number of time steps you could use for this problem.

Answer rating: 100% (QA)

MATLAB Code CRANK NICOLSON SCHEME clc clear all x1 ... View the full answer