The Unsteady Problems

It may be noted that are only spatially dependent functions and the time dependence is reflected only in nodal temperature values. The resulting global matrix equation derived from Eq. (23.2) takes the form:

(23.3)

Eq. (23.3) can be solved using the explicit or semi-implicit schemes,

(23.4)

(23.5)

(23.6)

It is to be noted that Eqn. (23.4) is an explicit formulation, while Eqn. (23.5) and Eqn.(23.6) are implicit and semi-implicit schemes, respectively.

For the implicit scheme, substituting for from Eq. (23.3), we get:

or,

(23.7)

Solving the matrix Eq. (23.7), the temperature vector at the time level can be obtained, knowing the level temperature vector.