In this paper, we have investigated the heat transfer in a circular cylindrical pipe for Hagen–Poiseuille flow and used MATLAB as a scientific tool to plot the graphs. The calculations for the axial heat conduction and the temperature gradient have been performed for both upstream and downstream flows. In this experiment, the results are plotted graphically for different fluids like air, water, milk, glycerin, and mercury. The physical trends of the plotted curves represent the values of heat transfer that were different in hydrogen and air; on the contrary, the rest of the fluids behaved similarly when temperature was taken as an exponential function. For the sinusoidal function, all the fluids behaved in a similar manner.