Double diffusive convection in an unsteady flow of nanofluid over a vertical and non‐flat sheet with nonlinear kinematics

Double diffusive convection flow is required for many applications, including cooling structures, energy‐efficient concepts, and nanofluid‐based heat transfer systems. It also has a significant impact on geophysical processes such as the flow of magma and ocean circulation. The analysis of this flow aids in the optimization of thermal systems and the improvement of energy utilization. Double diffusive convection flow of nanofluid from/into a vertical, heated/cold, rough, and porous sheet/fluid has been discussed, whereas the sheet is moving with nonuniform and nonlinear speed. The temperature/concentration of the sheet is assumed variable. Unsteadiness in the three field variables has been induced by the transient nature of these quantities, prescribed at the surface of non‐flat sheet. In this simulation, the Buongiorno model of nanofluid has been used for the diffusion of nanomaterials and thermal energy in base fluid. The simulation includes the particular cases of uniform and linear (polynomial and algebraic functions) kinematic properties of the sheet. The governing PDEs are reduced into a new system of ODEs by using transformations. After this treatment many, dimensionless parameters have emerged in the final system, and it is solved by for different values of these parameters. Moreover, the effects of the unsteadiness parameter, the two Grashof numbers, Thermophoretic and Brownian motion parameters, the Prandtl and Schmidt numbers, wall roughness, injection/suction, and stretching/shrinking are noted on the field properties and some other characteristics. Furthermore, the asymptotic nature of all these entities has been noted and presented in different figures. Assisting/opposing flow cases and the overshooting nature of the profiles, along with the rise and decrease in the profiles of fields variables, have been observed and demonstrated in different figures.