Numerical simulation for variable thermal properties and heat source/sink in flow of Cross nanofluid over a moving cylinder

A numerical simulation for variable thermal properties and heat source/sink in unsteady Cross nanofluid past expanding/contracting cylinder is completely a new idea of rheological study and the behaviors of such flows are not investigated as yet in the open literature. This innovative investigation of such flows has relevance to several technological and industrial applications. This modern physical problem has mathematical modeling in the form of highly nonlinear PED's. In order to simplify this mathematical formulation, these set of nonlinear PDE's are non-dimensionalised via reasonable transforming variables and then solved numerically by employing RK45 Fehlberg method. In this investigation, interesting results have been achieved, for example, magnitude of skin friction coefficient (surface drag force) enhances for larger estimation of Weissenberg number. The nanoparticle concentration and its associated layer thickness are upgrading functions of solutal Biot number. Fluid temperature enhances when heat source and thermal conductivity parameters are incriminated. The mass transfer rate (Sherwood number) grows when unsteadiness parameter is depressed. Heat transfer rate (Nusselt number) is reduced for larger estimation of thermophoresis parameter, solutal Biot number, thermal conductivity parameter, heat source parameter and Brownian motion variable. Further, unsteadiness effects the fluid velocity, fluid temperature and nanoparticle concentration. Present numerical analysis is validated with existing data and achieved to be in excellent agreement.