Analytical Solutions of Unsteady Thin Film Flow with Internal Heating and Thermal Radiation

Abstract

The formation of boundary layer takes place whenever an object is placed in the path of flowing fluid. This phenomenon of formation of hydrodynamic and thermal boundary layer is used in various engineering processes. This type of fluid flow can be expressed mathematically in terms of Navier-Stokes equations. The solution of the Navier-Stokes equations may help in creating better understanding of the said phenomenon and may also help in the creation of better and improved engineering processes. However, the exact solution of the Navier-Stokes equations for all fluid flow types do not exist yet, but the approximate solutions may be obtained using different numerical and analytical techniques. In this research, a system of partial differential equations (PDEs) of an unsteady film flow over a stretching surface with internal source of heat generation and thermal radiation is considered. An algebraic technique, Lie symmetry is used to obtain the Lie point symmetries of system of partial differential equations for constructing invariants and reductions. Multiple reductions are obtained to solve the fluid flow for different physical conditions. Then the deduced reductions are used to transform a system of partial differential equations into various systems of ordinary differential equations in order to apply homotopy analysis method, which solves the system of ordinary differential equations analytically. In this study, all systems of ordinary differential equations are solved analytically to investigate the impact of unsteadiness parameter, Prandtl number, internal heat generation parameter, and thermal radiation parameter on flow velocity, temperature and heat transfer rate. The study then presents the results of this analysis using both graphical and tabular formats. The study of thin film flows under different physical conditions can provide valuable insights into dynamics of fluid flows, and how they can be controlled and optimized for better performance. By understanding the impact of various parameters on the velocity and heat transfer rate, engineers can design and improve various engineering processes.