Optimal design of an air-to-liquid finned plate heat exchanger is considered theoretically in this study. Based on existing correlations for the pressure loss and the heat transfer in channel flows, the optimal configuration of the plate heat exchanger including the optimal plate pitch and the optimal fin pitch is obtained to maximize the heat transfer within the limit of the pressure drop for a given flow depth of the plate heat exchanger. It is found that the optimal fin pitch is about one ninth of the optimal plate pitch. In the optimal configuration, the flow and thermal condition in the channels is just at the boundary between the laminar developing and laminar fully developed states. It is also found when reducing the flow depth of plate heat exchangers for compactness, the heat transfer performance can be maintained exactly the same if the geometric parameters such as the plate thickness, plate pitch, fin thickness, and fin pitch are reduced proportional to the square root of the flow depth as long as the flow keeps laminar within the heat exchangers.