The present investigation deals with the study of unsteady, MHD, heat absorbing and chemically reacting dusty viscoelastic (Walter's liquid model-B) fluid Couette flow between vertical long wavy wall and a parallel flat wall saturated with porous medium subject to convective cooling and varying mass diffusion. The perturbation method is employed to analyze the coupled equations involving nonlinear problem and solution for the velocity, temperature and concentration distributions are obtained analytically. The graphical results are presented and the physical aspects are discussed in detail to interpret the effect of various significant parameters of the problem. The effect of the skin-friction, rate of heat and mass transfer coefficients at the channel walls are tabulated. (C) 2012 Elsevier Ltd. All rights reserved.