Improving Accuracy of Heat Flux Measurements
Perhaps because heat flux is an invisible quantity, many people have difficulty making heat flux measurements in a way that will yield correct results. Although heat flux data can be very useful, a heat flux sensor must be applied carefully to ensure correct measurements. This article will illuminate some of the important details of heat flux measurements so that common pitfalls can be avoided.
Some DefinitionsHeat flux often is confused with temperature, and although they are related, heat flux usually is more useful. As in any technical discussion, keeping the terminology straight is important. Refer to this glossary if things start to get confusing.
Heat is the movement of energy across a thermodynamic barrier and is measured in joules (J).
Heat transfer is the rate at which energy moves across the thermodynamic barrier measured in watts (W), that is, joules per second. Heat transfer occurs in three different modes: conduction, convection and radiation.
Heat flux is the rate of energy transfer per unit area, expressed in W/m2 or W/cm2. We will examine this in more detail below.
Temperature is an indication of the amount of thermal energy present in a substance. Any temperature scale (Celsius, Fahrenheit, etc.) may be used as long as the units are kept consistent.
Conduction is a mode of heat transfer through a substance, either solid or fluid, on a molecular level as a result of a temperature gradient being present.
Convection is a mode of heat transfer when there is fluid flow. As in conduction, a temperature gradient must be present, but convection is influenced by fluid flow, which alters the temperature gradient.
Radiation is a mode of heat transfer that occurs via electromagnetic radiation and does not require any transport medium or material.
A thermocouple is used to measure temperature. It consists of a junction between two different metals that will produce a voltage proportional to the temperature difference between the endpoints of the wires due to the Seebeck effect. For a thermocouple to give an accurate reading, there must be a reference temperature at some point along the wires; that is, a point where the temperature for both thermocouple leads is the same. Frequently, this is taken to be room temperature where the leads are connected to a voltmeter or electronic thermometer. For more accurate measurements, both leads are lowered to a known temperature such as the ice point.
A thermopile is essentially an array of thermocouples. By linking many thermocouples in a series, the temperature sensitivity is increased. Like a thermocouple, the thermopile reads the temperature difference between two points. For a heat flux sensor, these two points are the top and bottom layers of the thermopile.
Heat Flux Sensor ConstructionUnderstanding how heat flux sensors work can help a great deal in understanding how to use them. A heat flux sensor typically consists of a thermopile, or sometimes just a pair of thermocouples, in which the elements are separated by a thin layer of thermal resistance material. Under a temperature gradient, the two thermopile junction layers will be at different temperatures and so will register a voltage. The heat flux is proportional to this differential voltage. Notice that a temperature gradient must exist -- otherwise, both thermocouple junction layers will be at the same temperature and hence register no voltage. The thermal resistance layer usually is as thin as possible to improve sensor response time. To help ensure a proper thermal gradient, heat flux sensors should be designed to have a high thermal conductivity.
Most heat flux sensors are calibrated using radiation heat sources because they are the most consistently repeatable sources for heat flux. However, the fraction of the radiation absorbed by the sensor, the emissivity(e), is never 100%, so the absorbed heat flux differs from the incident heat flux. All heat flux sensors can only measure the absorbed heat flux, regardless of the source of heat flux or the mode of heat transfer.
k is the thermal conductivity of the sensor and
ΔT/Δn is the thermal gradient with n as the unit vector perpendicular to the surface through which the heat flux is being measured.
Because the incident and absorbed heat flux are the same, for a purely conductive heat flux, a heat flux sensor will read the actual incident heat flux. For convective heat flux, the heat flux equation is
ΔT is the temperature difference between the sensor and the fluid.
Heat Transfer CoefficientThe heat transfer coefficient is a function of the thermal conductivity of the fluid and the fluid flow characteristics. Unfortunately, fluid flow is extremely complex and difficult to model; consequently, the heat transfer coefficient is usually only determined from the measurement of the surface heat flux. This procedure assumes that the heat transfer coefficient for the heat flux sensor and the surrounding system are the same, so the incident and absorbed heat flux are equal. The accuracy of this assumption will vary with system configurations and materials.
All three modes of heat transfer can be measured as described above. When radiation is mixed with the other modes, however, there is the question of what fraction of the heat flux needs to be corrected for emissivity and what fraction does not. Ideally, the different modes can be isolated -- for example, using a heat flux sensor in a radiometer configuration to view only radiation sources. If the modes cannot be differentiated experimentally, some intelligent estimates of the relative fractions of the heat flux that each mode contributes must be made. In these cases, the emissivity of the heat flux sensor should be as high as possible to minimize error. Some sensors are restricted to the mode of heat transfer for which they can be used. Other sensors can measure heat transfer in any mode.
Mounting ConsiderationsNow that the operation of the heat flux sensor is understood, some potential mounting difficulties can be examined. The presence of a heat flux sensor will invariably alter the heat flux distribution where it is mounted. The idea is to minimize this disruption as much as possible while still achieving good sensor output. The exact mounting will depend on the system geometry, materials and modes of heat transfer.
Heat flux sensors have two basic shapes: a flat, surfaced-attached, layered wafer or a insert-style cylinder. The surface-attached configuration may have greater sensitivity than cylindrical designs because it has greater surface area. However, cylindrical sensors generally can withstand higher temperatures and can be water-cooled more easily.
The first issue to take into account is the thermal gradient across the sensor. If there is no thermal gradient, no heat flux will be measured. This is especially important during long duration tests in which a sensor may heat up to a uniform temperature. In these cases, the sensor probably will need to be actively cooled.
Because of the need for a thermal gradient, heat flux sensors do not function well if they are not mounted: They quickly come to a uniform or near-uniform temperature without some way to dissipate absorbed heat. This also means one must be careful mounting a heat flux sensor in a substrate with a high thermal conductivity such as copper or aluminum. Such materials will have little or no thermal gradient because heat distributes itself so quickly. As a general guideline, the thermal conductivity of the sensor should be the same or larger than the material in which it is mounted for good heat flux measurements. For some sensors, the thermal conductivity of the sensor is so high (equivalent conductivity to aluminum) that it will function in almost any substrate.
The next factor to consider is thermal contact resistance. If a heat flux sensor does not make good thermal contact with the material it is to be measuring, the sensor will cause a local hot spot to form (or a cold spot if the heat flux is negative). This hot spot will alter thermal gradients and change the convective and conductive heat transfer coefficients. For this reason, cylindrical sensors usually are pressed into a substrate or held tightly into place with a mounting nut. Flat, layered sensors usually are mounted with a thermally conductive adhesive to minimize contact resistance. Simply butting a sensor against a surface may still result in a heat flux reading, but the contact resistance will keep the reading from being particularly meaningful. In a similar vein, water-cooling a sensor must be done carefully. Otherwise, a temperature mismatch between the sensor and the substrate will occur that may skew measurements.
Fluid flow, whether gas or liquid, must be examined as well. This convection can be forced (e.g., a jet of gas or liquid in a pipe) or natural (e.g., hot air rising). The heat flux sensor disturbs the convection in a system in two ways: physically and thermally. Physically, the sensor creates a discontinuity in the surface -- even if it is mounted flush. The more the sensor protrudes from the surface, the greater the disruption. Thermally, the sensor alters the local temperature gradient due to its physical protrusion. The impact of the disruption the sensor causes will depend on the speed of the fluid flow. The disruption is greater for a laminar flow than for a turbulent one because of the rapidly changing, chaotic nature of the latter. The system can be considered effectively undisturbed when
Δ is the thickness of the sensor
ksensor is the thermal conductivity of the sensor
ksubstrate is the thermal conductivity of the substrate and
R is the radius of the sensor.
When dealing with a radiation source, two factors in particular must be considered. The first is the emissivity of the sensor, as discussed earlier. The second is the distance of the sensor from the source. Because heat flux drops with the square of the distance from the source, the sensor must be positioned carefully to ensure accurate measurements. That is to say, if the surface of interest is 3.937" (10 cm) away from the radiation source, the sensor should take measurements 3.937" away from the source. If the radiation source does not emit in a spatially uniform pattern, the sensor position relative to the source becomes important. For example, a lit candle does not emit in a spatially uniform pattern because the heat flux is much higher directly over the flame than it is to the side.