Summary: The growing interest in emerging nanotechnologies has led the scientists towards to investigate the interaction of nanoparticles with fluids. Current continuation endeavors the rheological analysis for the Oldroyd-B nanomaterial across periodically accelerated and heated surface. The interesting features of thermophoresis and Brownian motions are presented by following famous Buongiorno nanofluid model. Further, Cattaneo-Christov heat and mass flux expressions are exploited to determine the characteristics of thermal and mass diffusions. As a novelty, the variable thermal conductivity and heat absorption/generation consequences are also utilizing the energy equation. The flow model has been developed by using concerning boundary layer equations which are converted into dimensionless forms by using appropriate variables. The analytical solution of such transmuted equations is computed by using homotopy analytic method. Various physical parameters of interest are scrutinized through various graphs. The observations from analysis convey a declining change in nanofluid concentration and temperature with variation of thermal and solutal relaxation parameters, respectively. Moreover, thermophoresis parameter causes an enhancement of concentration profile while a retarded concentration profile results with increment of Schmidt number. The obtained theoretical results reflect significant applications in cooling and heating systems, thermal sciences, manufacturing processes, extrusion systems, enhancement of transport of energy and heat resources.