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Two-degree-of-freedom vortex-induced vibration (VIV) of a finned cylinder with heat transfer is studied numerically at the Reynolds number Re = 150. The governing equations in the Arbitrary Lagrangian-Eulerian frame are solved by the finite volume method. The dynamics of the oscillating cylinder (with or without fins) in the fluid flow was approximated as a mass-spring system. The effects of the number and arrangement of the fins (14 different cases) on the vortex shedding pattern, vibration amplitude, and frequency and heat transfer of the cylinder are investigated and discussed. The results indicate that in comparison with the stationary state, the effects of the number and arrangement of the fins on the wake pattern and the heat transfer enhancement in the VIV state are significant. Different vortex shedding pattern like 2S, P, 2P, S + P and combination of them with stable or unstable interactions between vortices and cylinders are observed in an oscillating cylinder. In the vibration state of finned cylinders, the heat transfer enhances up to 50.4% with respect to the stationary state and increases up to 64% with respect to the stationary smooth cylinder.