Thermal efficiency maximization for H- and X-shaped heat exchangers based on constructal theory

Constructal optimizations of H- and X-shaped heat exchangers are carried out by taking the maximum thermal efficiency (the ratio of the dimensionless heat transfer rate to the dimensionless total pumping power) as optimization objective. The constraints of total tube volumes and spaces occupied by heat exchangers are considered in the optimizations. For the H-shaped heat exchanger, the thermal efficiency decreases when the dimensionless mass flow rate increases. For the higher order of the X-shaped heat exchanger, when the order number is 3, the thermal efficiency of the heat exchanger with Murry law is increased by 68.54% than that with equal flow velocity in the tubes, and by 435.46% than that with equal cross section area of the tubes.