Hydraulically and thermally developing laminar flow induced dust deposition on a flat plate is of practical and fundamental interest with isothermal/non-isothermal and heat flux boundary conditions. The paper deals with the analysis of a steady, incompressible, two-dimensional, laminar, Newtonian fluid flow over an inclined flat plate. The reduced forms of momentum and continuity equations using boundary layer approximation are solved using the fourth order Runge-Kutta numerical scheme integrated with the shooting method. Subsequently, the energy equation with boundary layer approximations is solved for the considered flow over a flat plate using a constant heat flux or constant/variable wall temperature boundary conditions along the length. The calculated velocity and temperature profiles are used for analyzing the particle trajectory over the flat plate. Finally, the one-way coupling of Eulerian and Lagrangian approaches is presented and the effects of Stokes number, particle shape/size, and heating condition are analyzed on the transport and deposition of an inelastic isolated particle on the flat plate. The methodology will be helpful in addressing for instance, the dust deposition over a photovoltaic panel or a solar water heater, and a way of mitigating its effect on the same.