This study investigates entropy generation due to the unsteady boundary layer flow of an Oldroyd-B nanofluid past a Riga plate. The velocity, temperature and concentration fields are obtained and the flow equations solved numerically using the spectral collocation method with overlapping grids. The local entropy generation distribution is obtained by solving the entropy generation equation numerically. Sensitivity and convergence analysis is performed to demonstrate the accuracy and convergence of the numerical method. The effect of principal flow parameters on entropy generation is investigated and it is established that entropy generation is directly proportional to the width of the Riga plate, Brinkman number, Prantl number and the Brownian motion parameter. It is further shown that the entropy generation is inversely proportional to the Eckert number and Deborah number in relaxation time. The range of parameter values were obtained from the reported literature. The current study may have applications of physics, including in the design of both cooling and heating devices.