Variable gap thermal conductivity apparatus and method
An apparatus and a method for determining the thermal conductivity of a fluid specimen are provided. The apparatus and the method include determining thermal conductivity using a quasi-steady state variable gap axial flow technique. The fluid specimen is heated on one side by a heat source with a known power output and cooled on the other side. After reaching steady state, a resulting temperature drop through the fluid specimen exists. This temperature drop, the known fluid specimen thickness (or gap distance), and the known power output are used to calculate the thermal resistance of the fluid specimen. The thermal conductivity of the fluid specimen is then determined using a curve fit of thermal resistance with respect to gap distance.
1. An apparatus for measuring thermal conductivity of a fluid specimen, the apparatus comprising:
a test chamber to be at least partially enclosed in a furnace that is maintained at a predetermined temperature, the test chamber having a solid base and a solid wall arranged to hold the fluid specimen on a flat surface of the base, wherein the base comprises:
cooling channels disposed inside the base at a predetermined distance from the flat surface of the base, the cooling channels configured to cool a first side of the fluid specimen adjacent to the flat surface of the base, and
a first set of temperature sensors disposed inside the base and distributed between the flat surface of the base and the cooling channels, the first set of temperature sensors configured to sense a temperature of the cooled first side of the fluid specimen and configured to sense a temperature through the base;
a moveable head having a flat surface, the head disposed inside the test chamber such that the flat surface of the moveable head is parallel to and spaced apart by a controllable gap from the flat surface of the base such that the fluid specimen fills the gap, the head comprising:
a heater module disposed inside and adjacent to the flat surface of the head, the heater module configured to heat a second side of the fluid specimen, opposite of the first side of the fluid specimen, adjacent to the flat surface of the head, and
a second set of temperature sensors disposed inside the head and distributed along the flat surface of the head, the second set of temperature sensors being configured to sense a temperature of the heated second side of the fluid specimen;
an actuator module mechanically coupled with the movable head to cause, during operation of the apparatus, the head to move relative to the flat surface of the base to modify the gap between the flat surface of the head and the flat surface of the base;
a distance sensor configured to measure a size of the gap between the flat surface of the head and the flat surface of the base; and
a controller module communicatively coupled with the actuator module, the distance sensor, the heater module, and the first and second set of temperature sensors, the controller module configured to:
a) determine a heater power (Q) based on a configuration of the heater module,
b) instruct the actuator module to translate the movable head to set the gap between the flat surface of the head and the flat surface of the base to a sequence of different gap sizes,
c) for each gap size from among the different gap sizes, obtain the gap size from the distance sensor and determine a temperature difference (dT) between the heated-side temperature obtained from the second set of temperature sensors, and the cooled-side temperature obtained from the first set of temperature sensors, and
d) determine the thermal conductivity of the fluid specimen based on the determined temperature differences for the corresponding gap sizes and based on the determined heater power.
2. The apparatus of claim 1 , wherein the actuator module is configured to modify the size of the gap over a range of 0.01 mm-25 mm.
3. The apparatus of claim 1 , wherein the actuator module is configured to modify the size of the gap in increments of 5 μm to 10 μm.
4. The apparatus of claim 1 , wherein the temperature sensors comprise one or more of thermocouples, fiber optic-based temperature sensors, RTDs, or pyrometers.
5. The apparatus of claim 1 , wherein the heater module comprises one or more of:
one or more loops of sheathed resistance wire; or
one or more ceramic heaters.
6. The apparatus of claim 1 , wherein the moveable head includes a radial guard heater contained therein.
7. The apparatus of claim 1 , wherein the fluid specimen comprises molten salt, molten glass, molten ceramic, molten metal, or a molten metal alloy.
8. The apparatus of claim 1 , wherein the test chamber is sealed from an ambient environment, wherein the fluid specimen is reactive with gas from the ambient environment.
9. The apparatus of claim 1 , wherein, to determine the thermal conductivity of the fluid specimen, the controller module is configured to:
determine thermal resistances (R) as the respective temperature differences multiplied by an area of the heater module (A) and divided by the heater power (R=(dT·A)/Q),
fit the determined thermal resistances for the corresponding gap sizes using a least square fit, and
determine the thermal conductivity of the fluid specimen from the fit.
10. A system comprising:
an apparatus for measuring thermal conductivity of a fluid specimen, the apparatus comprising:
a test chamber to be at least partially enclosed in a furnace that is maintained at a predetermined temperature, the test chamber having a solid base and a solid wall arranged to hold the fluid specimen on a flat surface of the base, wherein the base comprises:
cooling channels disposed inside the base at a predetermined distance from the flat surface of the base, the cooling channels configured to cool a first side of the fluid specimen adjacent to the flat surface of the base, and
a first set of temperature sensors disposed inside the base and distributed between the flat surface of the base and the cooling channels, the first set of temperature sensors configured to sense a temperature of the cooled first side of the fluid specimen and configured to sense a temperature through the base;
a moveable head having a flat surface, the head disposed inside the test chamber such that the flat surface of the moveable head is parallel to and spaced apart by a controllable gap from the flat surface of the base, such that the fluid specimen fills the gap, the head comprising:
a heater module disposed inside and adjacent to the flat surface of the head, the heater module configured to heat a second side of the fluid specimen, opposite of the first side of the fluid specimen, adjacent to the flat surface of the head, and
a second set of temperature sensors disposed inside the head and distributed along the flat surface of the head, the second set of temperature sensors being configured to sense a temperature of the heated second side of the fluid specimen;
an actuator module mechanically coupled with the movable head to cause, during operation of the apparatus, the head to move relative to the flat surface of the base to modify the gap between the flat surface of the head and the flat surface of the base;
a distance sensor configured to measure a size of the gap between the flat surface of the head and the flat surface of the base; and
a controller module communicatively coupled with the actuator module, the distance sensor, the heater module, and the first and second set of temperature sensors, the controller module configured to:
a) determine a heater power (Q) based on a configuration of the heater module,
b) instruct the actuator module to translate the movable head to set the gap between the flat surface of the head and the flat surface of the base to a sequence of different gap sizes,
c) for each gap size from among the different gap sizes, obtain the gap size from the distance sensor and determine a temperature difference (dT) between the heated-side temperature obtained from the second set of temperature sensors, and the cooled-side temperature obtained from the first set of temperature sensors, and
d) determine the thermal conductivity of the fluid specimen based on the determined temperature differences for the corresponding gap sizes and based on the determined heater power; and
a furnace at least partially enclosing the apparatus, the furnace being maintained at the predetermined temperature.
11. The system of claim 10 , wherein the controller module is configured to:
set the predetermined temperature of the furnace to a sequence of different furnace temperatures; and
determine a steady-state thermal conductivity of the fluid specimen as a function of the furnace temperature by iterating operations a) through d) for each furnace temperature from among the different furnace temperatures.
12. The system of claim 10 , wherein the controller module is configured to:
cause a temperature transient to the furnace, and
determine a transient-mode thermal conductivity of the fluid specimen by iterating operations a) through d) during the furnace temperature transient.