In the heat exchanger considered here, the particulate phase may consist of solid particles, liquid droplets or gas bubbles, while the continuous phase may be a liquid or a gas. The operation takes place in a vertical column of uniform diameter extended to inlet and outlet zones of geometry determined by the character of the two phases. The variable design parameters are classified as operation and geometry variables. The analysis is restricted to two elemental geometry variables: the diameter and the length of the column proper. The use of the method is illustrated by a numerical example of a liquid-liquid heat exchanger. Flow rates, temperatures, particle size and physical properties are included in the analysis.