Plot of Solution for Problem in Chapter 13, Section 1.1

M.M. Yovanovich

PLOTSOL1P1.MWS

Plot of the solution of the problem discussed in Chapter 13, Section 1.1 of Spiegel's Text.

The initial dimensionless temperature is 1 over the entire length of the bar.

> restart:

Define the nth term of the summation. Use dimensionless form.

> term:= 4/Pi/(2*n-1)*exp(-(2*n-1)^2*Pi^2*tau)*sin((2*n-1)*Pi*xi);

Set the number of terms of the summation and the dimensionless time.

> nmax:= 100: tau:= 0.001:

Obtain a sequence of terms.

> terms:= [seq(term, n=1..nmax)]:

Obtain the summation for the dimensionless temperature.

> phi:= sum(terms[j],j=1..nmax):

Plot the solution.

> plot(phi,xi=0..1);

Calculate the dimensionless temperature near the left boundary.

> evalf(subs(xi=0.05, phi));

Show the number of terms of the summation and the dimensionless time.

> nmax; tau;

Try different times and number terms of the summation to appreciate the dimensionless solution.