<p>This paper yields analytical and numerical solutions of the one-dimensional Burgers’ equation occurring in longitudinal dispersion phenomenon via porous media. The phenomenon, which can be either miscible or immiscible fluid flow, leads to nonlinear partial differential equations, which are difficult to solve. To overcome this, the work here uses the Homotopy Analysis Method (HAM), a powerful analytical method, to obtain approximate solutions. Moreover, the numerical techniques like Crank–Nicolson Scheme and the B-Spline Collocation Method are used for comparison purposes. Results from all the techniques are in good agreement with each other, and the patterns of convergence are similar. Sufficient boundary conditions are assigned, and graphical plots of the concentration profiles are obtained using Mathematica software (version 12.0). The graphical plots are very effective and accurately represent the reliability and accuracy of the solutions achieved.</p>