Goal programming solutions for heat and mass transfer problems—a feasibility study

Abstract

The feasibility of utilizing goal programming, a multicriteria optimization technique, in solving heat and mass transfer problems is investigated. The heart of the idea is that approximate solutions will in general not be able to satisfy all conditions, such as boundary and initial conditions, at the same time as minimizing the error at the collocation points. This paper describes the formulation of the nonlinear boundary value problem as a preemptive goal programming model via the use of hard and soft constraints (or stiff and weak springs) in linear programming (or mechanics). The technique thus allows controlled weakening and prioritizes the different conditions. The preemptive priority structure of goal programming enables it to reduce the number of trial functions required to yield a satisfactory solution, since it does not need to simultaneously satisfy the interior collocation and boundary points as in the orthogonal collocation method. In addition, the technique enables the number of undetermined parameters to be less than the number of collocation points. Examples are provided to highlight the methodology.