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The present work analyses the effects of variable porosity and inertial forces on convective flow and heat transfer in porous media. Specific attention is given to forced convection in packed beds in the vicinity of an impermeable boundary. After establishing the governing equations, a thorough investigation of the channelling effect and its influence on flow and heat transfer through variable-porosity media is presented. Based on some analytical considerations, a numerical scheme for the solution of the governing equations is proposed to investigate the variable-porosity effects on the velocity and temperature fields inside the porous medium. The method of matched asymptotic expansions is used to show the qualitative aspects of variable porosity in producing the channelling effect. These qualitative features are also confirmed by the numerical solution. The qualitative effects of the controlling parameters on flow and heat transfer in variable-porosity media are discussed at length. The variable-porosity effects are shown to be significant for most cases. For the same conditions as the perturbation solution, the numerical results are in excellent agreement with the perturbation analysis. The numerical results are also in very good agreement with the available experimental data of previous studies.