ABSTRACT
Using the method of separation of variables, the solution of Eq. (1 1,251) is by (11.255)
or
(11.256)
(11.257)
which gives more than one solution for A. These solutions are called the eigenvalues of the linear boundary value problem (Fig. 1 L 16). As a result, the solution for the time dependent temperature profile [Eq. (11.255)] could be expressed as a linear combination of the solutions corresponding to each A (calculated from Eq. (11.257)],
(11.258)
where en is the integration constant to be calculated corresponding to Aw Using the initial condition expressed by Eq. (11.254),
Figure 11.16 Calculated eigenvalues from the solution of Eq. (1 1.257) corresponding to the heat transfer problem depicted in Fig. 1 1.15.
