MATLAB

BU

Due: 09/01/2015

CE 371

Numerical Methods in Civil Engineering

PROJECT

Fall’14

Page 1 of 1

Find the temperature history ( , )r t in the solid bounded by two infinite

cylindrical surfaces of radii 1r and 2r as shown in figure below. Initially (at

0t  ), 0  everywhere (inner circle is insulated);

and for 0t  , the outer surface 2r r is maintained at 1  . The inner

surface, 1r r behaves as a perfect insulator.

The dimensionless heat conduction equation in radial coordinates is;

2

2

1

r r r t

      

  

To reduce the situation to a characteristic value problem, we must

render the boundary conditions homogenous, that is, of form 0a r

 

  

 .

By changing the variable to 1   , the governing differential equation

becomes;

2

2

1

r r r t

      

  

subject to;

i) the initial condition: 1  at 0t 

ii) the boundary conditions: 0 r

 

 at 1r r

0  at 2r r

a) Simulate the equation using finite difference method explicit scheme

with Δt = 0.25, 0.5, 1.0

b) Simulate the equation using finite difference method implicit scheme

with Δt = 0.25, 0.5, 1.0

c) Plot your findings and compare the results for a and b.

r1 = 1 m

r2 = 10 m

NOTE: Your project reports will be evaluated for both correctness and accuracy of

your results and for clarity and neatness of your report. Be sure to organize your

plots neatly.