A new kind of symbolic program to aid the heuristic simplification of fluid models is presented. The program, AOM, employs order of magnitude analysis and method of dominant balance to generate simplified models. It has two novel features: (1) it uses heuristic techniques to decide what equations to solve and what algebra to do, and (2) it explains its deduction steps. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i.e., terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels to simplify complicated fluid models such as the triple-deck equations. Three annotated examples are presented to explain the operations of AOM. The implications for the development of computer-aided analysis programs for fluid dynamics and education are discussed.