The study defines the conditions and constraints that must be obeyed to obtain the maximum benefit from using a heat exchanger with a T-shaped tree flow configuration and rectangular shape of the channels. The flow is laminar and fully developed with constant physical properties. The boundary condition is the fixed temperature of the channel wall. The variation of the heat flow ratio and augmentation entropy generation number Nsa with the dimensionless mass flow rate, shape factor ratio, and complexity have been investigated. Comparisons of the thermal performance with other heat exchanger configurations like serpentine for two cases have been made. The requirement for Nsa <=1 has been implemented as a constraint instead of one of fixed pumping power. The performance evaluation criterion has been introduced as a general criterion to define the most beneficial complexity and working parameters.
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