Research Note on a Parabolic Heat-Balance Integral Method with Unspecified Exponent: An Entropy Generation Approach in Optimal Profile Determination

摘要

The heat-balance integral method of Goodman is studied with two simple 1-Dheat conduction problems with prescribed temperature and flux boundaryconditions. These classical problems with well known exact solutions enable todemonstrate the heat-balance integral method performance by a parabolic profileand the entropy generation minimization concept in definition of theappropriate profile exponent. The basic assumption generating the additionalconstraints needed to perform the solution is based on the requirement tominimize the difference in the local thermal entropy generation ratescalculated by the approximate and the exact profile, respectively. This conceptis easily applicable since the general concept has simple implementation of thecondition requiring the thermal entropy generations calculated through bothprofiles to be the same at the boundary. The entropy minimization generationapproach automatically generates the additional requirement which is deficientin the set of conditions defined by the heat-balance integral method concept.