The Calculation Of Heat Transfer Coefficient In The Non-Isothermal Flow Around A Finite Flat Plate In the Whole Range Of Laminar Flow

The non-isothermal viscous flow around a finite flat plate is studied as a numerical experiement, by solving the Navier Stokes equations augmented by the energy equation with Galerkin finite elements in the whole range of laminar flow (Reynolds number up to 10⁶). The flat plate or part of it is at a different temperature than the temperature of the environment. In addition, it is studied if the heat transfer coefficient differs in case the temperature of the flat plate is either higher or lower than the temperature of the environment. Sophisticated mesh design is required to avoid oscillations in the solution of the Navier Stokes equations in the neighbourhood of the leading edge of the plate. A proposed mesh which consists of transition elements that separates the dense region close to the flate plate from the sparse region far away from it accomplishes the requirement of a solution free from oscillations and possible inaccuracies. The size of the computational domain is big enough to ensure that the flow of the Newtonian fluid is undisturbed upstream of the leading edge of the flat plate and far away in the transverse direction. The numerical results are compared with exact analysis based on biundary layer theory and integral techiques based on simplified analysis of boundary layers both proposed by Prandtl's school and elaborated further by others. In view of the fact that the real flow around a finite flat plate possesses a negative tranverse velocity close to the trailing edge is the main reason why our results are more realistic than previous analyses which failed to predict this phenomenon.