Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

► A 2-D dispersion model is shown more genuine than a 1-D model. ► Particularly with variable coefficients being in more general form. ► Solved analytically using a much simpler but more viable LITT. ► Heterogeneity and unsteadiness are causes of variations in dispersion and velocity. ► Solution for different combinations of unsteadiness of the two are illustrated. Transport of solute mass transport, originating from a uniform pulse-type stationary point source through a heterogeneous semi-infinite horizontal medium, is studied. The heterogeneity is described by position dependent linear non-homogeneous expression for the velocity. The exponential unsteady variation in velocity of decreasing/increasing is also considered. The variation in dispersion parameter due to heterogeneity is considered proportional to square of that in the velocity. But the same due to unsteadiness is proportional to a power of the velocity which may take any value between 1 and 2 or outside this range. The variable coefficients of the two-dimensional advection–diffusion equation are put in degenerate form. These are reduced into constant coefficients with the help of new independent variables introduced at different stages, paving the way for using Laplace transformation technique to get the desired solution.