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In the recent years, nanotechnology has been widely used in several fields regarding its rapid developments which create a lot of prospects for researchers and engineers. More specifically, replacement of conventional liquid with nanofluid is considered as an innovative solution to heat transfer problems. Keeping aforesaid pragmatism of nanofluid in view, we considered a time-dependent mathematical model to formulate the heat sink-source based Sutterby nanofluid model under thermophoretic and Brownian movements. New mass flux and melting boundary conditions are used for heat/ mass transfer analyses. Moreover, Prandtl’s boundary-layer idea is employed for mathematical formulation. The leading nonlinear set of partial differential equations is transformed to nonlinear set of ordinary differential equations. Numeric outcomes are acquired through bvp4c algorithm, graphical results are found via MATLAB technique. Acquired numerical data shows that temperature of nanofluid boosts for greater thermophoretic and unsteady parameters. Intensification is measured in concentration distribution.