<p>The current study explores an analysis of unsteady thermo-viscous fluid flow around a moving horizontal cylindrical surface. The modeling of partial differential equations pertaining to the flow through cylindrical objects is coupled, complex, and non-linear in nature. These equations have been analyzed for the solutions of velocity and temperature fields. The numerical techniques used so far in literature are very complex; moreover, they are not giving accurate, convergent solutions because of their own disadvantages. These methods also require more time, high computational cost, and processing resources to obtain the required results. The available analytical methods to solve these kinds of equations are not applicable since these are simultaneous, highly non-linear equations. The tool NDsolve, developed in Mathematica software, is utilized to solve these problems in the current study. The code of the algorithm has been developed in this software via. Runge–Kutta finite difference 6th-order method to obtain the results of the modeling equations. The results obtained have been depicted in graphical illustrations and tabular data. The numerous values of the material constraints such as viscosity coefficient, temperature gradient factor, thermo-mechanical interaction factor, strain thermal conductivity factor, pressure gradient factor, and Fourier thermal conductivity constraint effects have been studied as graphical plots and tabular data. Additionally, numerical findings of the governing equations for a fluid’s slow, steady motion have been obtained, and comparison is made with the current available literature results; they show great agreement. The modeled governing equations of the present study have been observed in the studies of flows through the pipeline systems and nuclear reactors.</p>