Composite materials offer customizability of properties, good specific strength and corrosion resistance. These make composites reliable for structural and wear-resistant applications. The wear of a material is sensitive to its properties in addition to the environment and operating conditions. The experimental evaluation of the wear of a material requires extensive experiments to determine the effect of all the parameters. Numerical modelling and simulation are effective tools to estimate the wear in the early stages of design decision-making. In the present study, a numerical model was developed using time dependent wear formulation derived from Archard's wear law for sliding contact. The wear depth was expressed as a function of time and spatial position along the contact, considering the non-uniform pressure conditions. Three numerical models were developed. The first model represents baseline wear accumulation governed by Archard’s law. The second model introduces a first-order spatial derivative to account for directional wear transport, while the third model incorporates a second-order diffusion term to capture smoothing of wear gradients.  All three models were discretized by the finite difference method and implemented using MATLAB. The first derivative model produced asymmetric wear profiles showing the influence of directional wear on material removal patterns, while the second derivative model generated smooth and stable wear distribution by reducing sharp gradients.