  The heat-balance integral method of Goodman is studied with two simple 1-D
heat conduction problems with prescribed temperature and flux boundary
conditions. These classical problems with well known exact solutions enable to
demonstrate the heat-balance integral method performance by a parabolic profile
and the entropy generation minimization concept in definition of the
appropriate profile exponent. The basic assumption generating the additional
constraints needed to perform the solution is based on the requirement to
minimize the difference in the local thermal entropy generation rates
calculated by the approximate and the exact profile, respectively. This concept
is easily applicable since the general concept has simple implementation of the
condition requiring the thermal entropy generations calculated through both
profiles to be the same at the boundary. The entropy minimization generation
approach automatically generates the additional requirement which is deficient
in the set of conditions defined by the heat-balance integral method concept.
