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Significant impact of unsteady Cattaneo-Christov double diffusion, random motion and thermo-migration of tiny particles on thermal storage and in heat exchangers devices has attracted us to investigate the role of these thermal engineering terms in the existence of convectively heating and zero-mass flux at the bidirectionally stretchable wall. Combination of similarity expressions is adopted to transform the prevailing partial differential equations into ordinary differential equations and then solved, numerically, by using Keller-Box simulation technique. Temperature and concentration phases are discussed under the influences of involved parameters, graphically. It is detected that thermal relaxation dependent on heat flux maximizes the temperature gradient, whereas thermal relaxation dependent on mass flux minimizes the concentration gradient. It is also scrutinized that escalating choice of random motion of tiny particles provides constant temperature gradient because of Nield’s expression. Moreover, augmenting choice of thermo-migration of tiny particles enhances the concentration gradient. Furthermore, intensifying choice of unsteady factor abridges the temperature plus concentration distributions and also it condenses all the three boundary layer thicknesses.