The current study deals with the influence of heat and mass transfer characteristics of viscous fluid near a moving wall with transpiration. The wall and free stream velocities are assumed to be decelerating functions. The calculated solution of unsteady Navier–Stokes equation is an exact solution. In the absence of internal energy change,the analytical solutions of energy and concentration equations are calculated for constant wall temperature near rare stagnation point. The influence of transpiration, unsteadiness parameter, Prandtl number, stretching/shrinking wall parameter and Schmidt number on the fluid, heat and mass transfer features have been shown graphically and elaborated in detail. With the particular values of the governing parameters, two branch solutions are calculated for heat and mass transfer phenomena. These closed-form outcomes are exceptional and can be used as a standard modelling for numerical code justification.