The operation of heat exchangers and other thermal equipment in the face of variable loads is usually controlled by manipulating inlet fluid temperatures or mass flow rates. This is a fundamental study of the basic issues regarding state and output controllability in such systems. A numerical method based on finite-differences is developed to approximate infinite-dimensional equations by finite-dimensional ones for the study of a conduction-convection system. The dynamics of a single-pass cross-flow heat exchanger with simultaneous advection, convection and conduction, in which water and air are the in- and over-tube fluids, respectively, is represented by a coupled set of partial differential equations. The numerical method is used to analyze the behavior of the heat exchanger equations. Using the water or air inlet temperature as the manipulated variable leads to a linear problem, and for the water flow rate it is non-linear. Controllability results for different choices of the manipulated variable are presented. (C) 2003 Elsevier Ltd. All rights reserved.