This paper presents the preliminary findings of an optimization study of transversal flow strength in tube cross-sections with arbitrary external contours and an internal inclusion. The eccentric tube contours are generated through a one-to-one mapping of a base circular cross-section. The working fluid obeys the non-linear modified Phan-Thien-Tanner (MPTT) constitutive model. The computation of the total transversal flow rate leads to the determination of effective cross-sections for heat transfer enhancement.

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