5.1 This test method will provide guidance for the measurement of the net heat flux to or from a surface location. To determine the radiant energy component the emissivity or absorptivity of the gage surface coating is required and should be matched with the surrounding surface. The potential physical and thermal disruptions of the surface due to the presence of the gage should be minimized and characterized. For the case of convection and low source temperature radiation to or from the surface it is important to consider how the presence of the gage alters the surface heat flux. The desired quantity is usually the heat flux at the surface location without the presence of the gage.

5.1.1 Temperature limitations are determined by the gage material properties and the method of application to the surface. The range of heat flux that can be measured and the time response are limited by the gage design and construction details. Measurements from 10 W/m² to above 100 kW/m² are easily obtained with current sensors. Time constants as low as 10 ms are possible, while thicker sensors may have response times greater than 1 s. It is important to choose the sensor style and characteristics to match the range and time response of the required application.

5.2 The measured heat flux is based on one-dimensional analysis with a uniform heat flux over the surface of the gage surface. Because of the thermal disruption caused by the placement of the gage on the surface, this may not be true. Wesley (3) and Baba et al. (4) have analyzed the effect of the gage on the thermal field and heat transfer within the surface substrate and determined that the one-dimensional assumption is valid when:

5.3 Measurements of convective heat flux are particularly sensitive to disturbances of the temperature of the surface. Because the heat transfer coefficient is also affected by any non-uniformities of the surface temperature, the effect of a small temperature change with location is further amplified, as explained by Moffat et al. (2) and Diller (5). Moreover, the smaller the gage surface area, the larger is the effect on the heat-transfer coefficient of any surface temperature non-uniformity. Therefore, surface temperature disruptions caused by the gage should be kept much smaller than the surface to environment temperature difference causing the heat flux. This necessitates a good thermal path between the gage and the surface onto which it is mounted.

5.3.1 Fig. 2 shows a heat-flux gage mounted onto a plate with the surface temperature of the gage of T_s and the surface temperature of the surrounding plate of T_p. The goal is to keep the gage surface temperature as close as possible to the plate temperature to minimize the thermal disruption of the gage. This requires the thermal resistance of the gage and adhesive to be minimized along the thermal pathway from T_s and T_p.

FIG. 2 Diagram of an Installed Surface-Mounted Heat-Flux Gage

5.3.2 Another method to avoid the surface temperature disruption problem is to cover the entire surface with the heat-flux gage material. This effectively ensures that the thermal resistance through the gage is matched with that of the surrounding plate. It is important to have independent measures of the substrate surface temperature and the surface temperature of the gage. The gage surface temperature must be used for defining the value of the heat-transfer coefficient. When the gage material does not cover the entire surface, the temperature measurements are needed to ensure that the gage does indeed provide a small thermal disruption.

5.4 The time response of the heat-flux gage can be estimated analytically if the thermal properties of the thermal-resistance layer are well known. The time required for 98 % response to a step input (6) based on a one-dimensional analysis is:

where α is the thermal diffusivity of the TRL. Covering or encapsulation layers must also be included in the analysis. Uncertainties in the gage dimensions and properties require a direct experimental verification of the time response. If the gage is designed to absorb radiation, a pulsed laser or optically switched Bragg cell can be used to give rise times of less than 1 μs (7,8). However, a mechanical wheel with slits can be used with a light to give rise times on the order of 1 ms (9), which is generally sufficient.

5.4.1 Because the response of these sensors is close to an exponential rise, a measure of the time constant τ for the sensor can be obtained by matching the experimental response to step changes in heat flux with exponential curves.

The value of the step change in imposed heat flux is represented by q_ss. The resulting time constant characterizes the first-order sensor response.