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Step 1: Pre-Analysis
With the current problem setup, we know that the temperature will increase as the air passing through the heated section. Depending on whether the pipe is long enough, we might see uniform temperature at the end of the pipe.
Since the pipe cross-section is circular, we'll assume that the flow is axisymmetric. In cylindrical polar coordinates, this means that the flow variables depend only on the axial coordinate x and radial coordinate r, and are independent of the azimuthal coordinate θ. Hence we can model the pipe problem with a rectangular domain.
Figure above shows the simplified geometry of our problem where R = radius of the pipe, and L = length of the pipe.