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The mathematical models for both numerical and analytical studies are formulated from Navier Stoke equation along with energy equation. CFD technique is utilized for getting the solutions of both developing flow and developed flow regimes. Variations of temperature, velocity and pressure fields have been represented under different values of flow parameters. The overall CFD simulation procedure involves grid generation, setting up boundary conditions and problem specific inputs such as Pr, Re, Ri, etc.In analytical study, a closed form solution as a function of distance and time is obtained by solving the momentum equation and the equation of motion using Separation of Variable method. To obtain the velocity expression, average value of the temperature distribution is considered. Based on those results the temperature field and the velocity field have been plotted. The numerical analysis is the validation of the analytical analysis since the nature of the plots found almost similar.