Steady-State, Local Heat Transfer Measurement Technique
This technique can be used to obtain the local temperature distribution on the surface as opposed to the regionally averaged heat transfer distributions. Typically, the test surface is covered with a thin metal foil which itself acts as a heater. By applying a voltage across the foil, heat is generated by the foil proportional to its electrical resistance. The temperature of the foil is measured using thermocouples attached to the underside of the foil heater. The measured temperature corresponds to the wall temperature of the test surface. As the foil heater is thin, lateral heat conduction through its cross section is small due to its small cross-sectional area even though large temperature gradients might exist. Thus, it can be assumed that the temperature distribution measured is local and hence, local heat transfer coefficients can be calculated. Foil heaters are also the most popular choice for heating a surface when used in combination with optical techniques such as liquid crystal thermography, temperature sensitive paint (TSP), and infrared thermography under steady-state conditions.
Thin Foil Heaters with Thermocouples
Along with the copper plate method discussed earlier, this technique is one of the simplest and more inexpensive methods to measure heat transfer coefficients. This technique has been available in literature for several decades with studies performed to measure both heat transfer coefficient and film cooling effectiveness distributions. Typical uncertainty with this technique is approximately 5%-10%. This method has been used extensively by researchers as it can give consistent results. A major disadvantage of this method is the requirement of skilled labor in setting up the foil heaters and thermocouples. This technique demands that the experimentalist is dexterous when attaching the thermocouples to the foil without damaging the foil. Slight damage to the foil can cause hot spots resulting in biased data. Also, in order to have a comprehensive local temperature distribution on the surface, many thermocouples must be used, necessitating a large data acquisition system.
As opposed to the copper plate method where the copper plate separates the fluid and the heater, with this method, the foil acts as a heater and is in direct contact with the fluid. A stainless steel or Inconel thin foil can be used as the heater. The thickness of the foil used is typically about 0.05 mm (0.002"). A thin foil is desired as it reduces lateral heat conduction in the foil. However, thinner foils are difficult to handle and tend to get damaged easily. The foil is cut to the desired shape and mounted on a substrate. The substrate is typically a material with low conductivity such as polystyrene or Plexiglas.
The foil heater can be constructed by the experimentalist by cutting a foil sheet to the desired shape corresponding to the test surface. By applying a voltage across the ends of the foil, heat is generated internally within the foil. The foil heater should be designed such that the resistance across the heater is large. A low heater resistance will require large currents to generate heat. The test surface area can be covered with a single foil or several foil heater strips depending on the electrical resistance of each strip. Each foil strip is relatively small in width compared to its length. A smaller width also ensures a more uniform heat flux from the heater. The resistance of a foil heater can be calculated using
where p is the electrical resistivity and depends on the foil material. As resistance is proportional to the length of the heater and inversely proportional to the cross- section area, by maintaining a small width and a large span, the resistance of each foil strip can be manipulated so that the current requirement is manageable and is lower than the maximum current that can be drawn from the available power supply line. The heat generated by the foil can be given as
where / is the current flowing through the foil. Thus, the foil heater can be cut into an “S” pattern to adjust the length of the heater and hence the resistance to appropriate limits. The “5” pattern can be avoided by using individual foil strips connected to each other in series through copper bus bars. The heater is then connected to a power supply through a variable auto-transformer to obtain the desired heat output. When all the foil strips are connected appropriately, the entire bank of strips provides a uniform heat flux over the surface. Care should be taken when handling the foil due to its delicate nature. Wrinkling the foil can cause a non-uniform heat distribution resulting in hot spots.
As with the copper plate method, thermocouples are used to record the temperature. Thermocouples can be soldered on the underside of the foil strip along its length. A thermally conductive epoxy can also be used to attach the thermocouples. In some cases, using thermally conductive epoxy is advantageous as it acts as an electrical insulator preventing large currents in the foil heater from flowing through the thermocouples and into the data acquisition system which may damage it. As these heaters can provide local data too, the chosen spatial resolution of the thermocouples should provide a sufficiently detailed temperature distribution on the surface.
The foil strips can be attached to the substrate using double-sided tape or some sprayable adhesive. Manual application of glue may cause bumps in the foil surface due to inconsistency of the glue thickness when it is being applied. Using a doublesided tape or sprayable adhesive ensures that the test surface is smooth. The nonconducting substrate helps to reduce extraneous heat losses. Additional insulation such as fiberglass, wood, etc. can be used to further reduce the heat loss. The foil heaters should be designed such that the requisite heat input for the highest Reynolds number to be investigated can be achieved.
After starting the experiment, the test section will attain steady-state after some time has elapsed. The heater power input should be set so that the wall temperature is about 20°C higher than the fluid temperature. The power input and the temperatures must be recorded along with the other flow measurements. Heat loss information can also be obtained for the test section under no flow conditions. By knowing these parameters, the heat transfer coefficients can be calculated.
