Unsteady nonlinear convective flow of a nanofluid over a vertical plate due to impulsive motion: Optimization and sensitivity analysis

Abstract

The classical Boussinesq approximation (linear density-temperature variation) is valid for small temperature differences in the system. However, density varies with temperature nonlinearly in various applications, such as heat exchangers, solar collectors, and nuclear reactors. Therefore, unsteady nonlinear mixed convection (quadratic density-temperature variation) in a nanofluid on a vertical plate due to impulsive motion is investigated. Modified Nield and Kuznetsov nanofluid model is incorporated that considers physical realistic boundary conditions. Unsteady flow is governed by the conservation of mass, momentum, energy, and the continuity equation of nanoparticles. Williams-Rhyne transformations are used to parameterize and reduce the infinite time domain to a finite time domain. Subsequent nonlinear differential equations system is solved by using the Finite Difference Method (FDM) based routine. Rayleigh and Hiemenz type equations are obtained respectively in an initial-unsteady and final-steady state. The Response Surface Method (RSM) and Central Composite Design (CCD) are used for the simultaneous optimization of the friction factor and the rate of heat transport. It is found that the quadratic density-temperature variation significantly affects the flow fields. The friction factor has the highest and positive sensitivity toward the thermal buoyancy number. The heat transport rate has the highest and negative sensitivity toward the thermo-migration of nanoparticles.