This paper presents a simple, efficient, robust, optimum design methodology for the design of a high heat transfer and low pressure drop cross-flow shell and tube heat exchanger with integral low fin tubes. This type of heat exchanger has the potential for application in the design of coolers in hypersonic wind tunnels to cool the air that emerges from the diffuser section of the wind tunnel. The methodology described here allows for the design and optimization of any type of heat exchanger that has constraints on pressure drop, as well as the design of an exchanger for very low pressure drop on the shell side fluid.