Groundwater is a major source of drinking water and irrigation in many countries in the world. Overexploitation of groundwater has led to aquifer contamination by various point sources (e.g. leakage from storage tanks, spills, septic tanks, leachate from landfills, etc.) as well as nonpoint sources (e.g. fertilizers and pesticides used in agriculture fields, acid rain, etc.). The pollutants can interact with fluid and solid phases of underground system through different processes including diffusion, dispersion, advection, chemical reaction, decay and biodegradation. The contaminant transport phenomena through porous media can be analysed by analytical solution of transport equations. The present study deals with the analysis of a simplified 1-dimensional advective–diffusive transport equation for the instantaneous placement of a long-lasting source of contaminant. An analytical solution of a combined transport equation from advection, diffusion and dispersion in one dimension from available literature has been studied for varying parameters. Effects of spatially varying time, hydrodynamic dispersion and retardation factor on contaminant concentration have been observed for a moving front of contaminant from a constant source. The present study can be helpful in predicting the concentration of contaminants through porous media under varying parameters.