The effective delivery of pharmaceuticals to the respiratory tract is significantly influenced by the three-dimensional covalent network structure of mucus, as well as the motility of cilia within the airway surface liquid (ASL). This study will examine the dissolution and absorption of respiratory drugs within the ASL, considering the effects of mucociliary clearance. A three-dimensional numerical model that characterizes mucus as a nonlinear viscoelastic fluid has been employed for this analysis. To discretize and solve the time-dependent governing equations of fluid flow, alongside the diffusion-convection equation for mass transfer, a hybrid immersed boundary-finite difference projection method was utilized within the segment of the tracheal ASL on a staggered grid.