The chief aim of this research is to explore the various rotation patterns of hot cylinders in four non-linear structures in laminar flow regime with different rotational speed(ω). For this purpose, using the finite volume method, the thermo-hydraulic parameters such as Nusselt number (Nu), friction factor, and thermo-hydraulic performance parameter (THP) of the cooling fluid, water, were investigated. This is a three-dimensional numerical study on a compact heat exchanger in which all possible rotation patterns of hot cylinders in non-linear structures were analyzed based on energy and exergy approaches. The results showed that in each non-linear structure of the cylinders, with increasing the rotational speed, at least one of the rotation patterns had a better thermo-hydraulic performance. In this regard, 22 possible patterns are investigated in a way that one of which provides a better performance based on first and second law of thermodynamic. In the seventh rotation pattern, which is known as C27 and belongs to the second non-linear structure, the thermo- hydraulic parameter (THP) is improved by 38% compared to the linear structure of rotating hot cylinder.