This paper shows the development of a design approach for plate and fin heat exchangers to meet fixed dimensions. This approach adopts the concept of volume design region that establishes the limits within which the physical dimensions (length, width and height) of a specific design problem can be set. The design region is determined by minimum and maximum dimensions. The heat exchanger volume is dictated by the problem specifications and the type of secondary surface used on each of the fluids. High density surfaces tend to produce small volumes, while the opposite applies to low density surfaces. In principle, if the heat transfer and friction factor correlations for secondary surfaces are expressed as a function of the geometrical parameters that define the fin density, then it possible to fix the surface density boundaries that give the smallest and largest exchanger volume. The design methodology presented in this work enables to include exchanger dimensions as a design objective along with the heat load and the pressure drop. To achieve these objectives, surface design is a central strategy. In this work, triangular, louvered, rectangular and offset surfaces are used to demonstrate the methodology.