The effect of melting and solute dispersion on heat and mass transfer in non-Darcy fluid flow over a vertical surface has been studied numerically in the present article. The flow is assumed to be laminar and steady state. Using similarity transformations, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved by using boundary value problem solver. A comparison with the numerical results made for different 𝑅𝑎/𝑃𝑒 values in the absence of some particular parameters. The velocity and concentration inside the boundary layer are observed to be influenced by the parameters like 𝑅𝑎/𝑃𝑒, 𝐿, 𝐵, 𝑀. The flow heat and mass transfer coefficients are discussed through the plots.