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Increasing application of supercritical phase fluids also leads to increased use of numerical simulations to guide designs. However, the impact of Equations of State (EoS) selection on computational cost and accuracy is not well understood. Laminar flow around a heated cylinder, a canonical flow, is used as a test case. A robust matrix of 99-simulations analyzes carbon dioxide just above the critical point at the isobaric condition of 8 MPa and temperatures between 305-390K. Four established EoS were studied: Ideal Gas Law, cubic EoS’s Peng-Robinson and Soave-Redlich-Kwong, and the Span-Wagner EoS. Results were identical for isothermal cases, but for heated or cooled cases, the high-fidelity Span-Wagner EoS simulations presented drastically different wake structures. Additionally, compared to the high-fidelity SW EoS, cEoS’s underestimated Nu values by up to 38% and cEoS’s underestimated CD values by 18-42%. Finally, the Span-Wagner EoS required only 17% more computation time then the cubic EoS simulations, making the Span-Wagner EoS recommended for engineering design.