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An arithmetical methodology is used to study natural convection with properties of pressure work over a semi-infinite vertical oscillating cylinder. The governing partial differential equations are set up and the resulting equations are changed into a non-dimensional form using the proper non-dimensional quantities. The set of non-dimensional partial differential equations is solved arithmetically using a well-organized method known as the Crank-Nicolson method. The velocity, as well as temperature profiles for different values of parameters are studied with the assistance of graphs.