Keller–Box simulation for nonzero and zero mass fluxes of nanofluid flow impinging over a bi-directional stretching sheet: An unsteady mathematical model

The countless applications of nanofluids in the improvements of nanotechnology, thermal and physical analogies have attracted our attention to frame an unsteady mathematical model for bi-directional flow of a Newtonian nanofluid over a stretching sheet with the potencies of nonzero and zero mass fluxes. Mathematically, this newly presented analysis is more genuine, where the action of a prescribed heat source at a stretching surface is used to control the distribution of heat. Mathematical formulation is carried out using a novel two-phase nanofluid model. Dimensionless forms of governing equations are obtained with the help of a suitable set of variables. The transformed equations are then solved by using an innovative computational technique, namely, Keller–Box approach. Moreover, the convergence of the numerical solution has been discussed via grid-independence tactic. The results for reduced Nusselt and Sherwood numbers have been arranged in the form of a table with CPU run time. Graphical illustrations have been presented for concentration and temperature distributions. It is inspected that escalating amounts of heat distribution indices reduce the mass concentration and the temperature of the nanomaterial. Rate of heat transference is noticed approximately 228.62% higher, while rate of mass transference is observed approximately 16.79% lower when analysis is shifted to zero mass flux environment from nonzero normal mass flux environment.