Determination of convective heat flux on steady-state heat transfer surfaces with arbitrarily specified boundaries

The present study focuses on the high-resolution determination of local heat flux distributions encountered in forced convection heat transfer studies. The specific method results in an uncertainty level less than 4 percent of the heat transfer coefficient on surfaces with arbitrarily defined geometric boundaries. Heat transfer surfaces constructed for use in steady-state techniques typically use rectangular thin foil electric heaters to generate a constant heat flux boundary condition. There are also past studies dealing with geometrically complex heating elements. Past studies have either omitted the nonuniform heat flux regions or applied correctional techniques that are approximate. The current study combines electric field theory and a finite element method to solve directly for a nonun˜orm surface heat flux distribution due to the specific shape of the heater boundary. Heat generation per unit volume of the surface heater element in the Jbrm of local Joule heating is accurately calculated using a finite element technique. The technique is shown to be applicable to many complex convective heat transfer configurations. These configurations often have complex geometric boundaries such as turbine endwall platforms, surfaces disturbed by film cooling holes, blade tip sections, etc. A complete high-resolution steady-state heat transfer technique using liquid crystal thermography is presented for the endwall surface of a 90 deg turning duct. The inlet flow is fully turbulent with an inlet Re number of 360,000. The solution of the surface heat flux distribution is also demonstrated for a heat transfer surface that contains an array of discrete film cooling holes. The current method can easily be extended to any heat transfer surface that has arbitrarily prescribed boundaries.