This thesis presents analysis and computations of non-isothermal falling films flowing down an inclined, heated plane. We consider two types of wall heat- ing: uniform and non-uniform. We examine the heat transfer of a viscoelastic liquid film with variable viscosity as it flows over a uniformly heated plane. The polymeric viscosity is modeled using the Oldroyd-B model, and, as the solvent viscosity, is temperature-dependent. The determination of the flow involves the numerical solution of the energy equation and Navier-Stokes. We continue with problems regarding Newtonian fluids and non-uniform heating. The flow and heat transport is modeled with a long-wave theory for small Brinkman numbers, and it leads to reduced systems of ODEs. Analytic so- lutions of the velocity, temperature, and shape of the surface for the basic flow and the next order are obtained. We carry out extensive numerical ex- periments and reveal the contribution of each parameter in the velocity and temperature profile, as well as in the deformation of the surface, for various heating conditions. We continue with numerical analysis of non-uniformly weak heated falling film for zero Brinkman number as well as for arbitrary values of it.
The linear stability of a non-isothermal falling film with temperature-dependent viscosity over a uniformly heated, inclined plane is studied. We derive the system of equations: the non-isothermal analogue of the Orr -Sommerfeld equation coupled with the energy equation. We solve analytically the above system for small wavenumber and numerically for arbitrary values. Finally, we verify the model using isothermal and non-isothermal comparisons.