Analysis of a chaotic system of equations for ethanol-based graphene pulsating heat pipe

When cooling electronic components, pulsating heat pipes, an effective heat exchanger, are frequently paired with fins. Common fluid-solid coupling approaches, however, are unable to completely characterize its internal features due to the complexity and variety of its internal forces, which are often chaotic systems heavily influenced by the initial value. In this study, we build a three-dimensional system of differential equations with a significant amount of dynamical information by starting with the conjugate complex roots of the three main conservation equations of the pulsating heat pipe, converting the partial differentiation into ordinary differentiation, and truncating the superposition solution of its eigen-solutions. This approach is inspired by the lorenz atmospheric model. Additionally, various concentrations of graphene nanofluids based on ethanol are added to the pulsating heat pipe. The coefficient matrix in the differential equation set is then determined using the experimental data and fundamental physical parameters, and it is discovered that as the concentration increases, the center of gravity of the singular attractor seems to shift to the right. The reconstructed attractor is differentially homogeneous with the singular attractor and topologically equivalent to the singular attractor after the phase space reconstruction of each sequence individually with the aid of the mutual information method, G-P algorithm, Takens embedding theorem, etc. This research offers fresh perspectives on elucidating the behavior of nanofluids inside pulsing heat pipes.