Thermal Sensing and Actuation

1. Thermal Sensing and Actuation EE485A Lecture September 29, 2009

2. Thermal Sensors and Actuators • Thermal Actuators • Make use of thermal expansion • Can be divided into: • Thermal bimorphs • Single material structures • Fluidic devices (ink jet printer heads) • Thermal Sensors • Sensors for measuring thermal quantities • Thermometers, infrared sensors, calorimeters • Sensors based on thermal transfer principles • Flow sensors, acclerometers • Most common thermal sensing mechanisms: • Thermal bimorph sensors (use two or more materials with different thermal properties) • Thermal couples • Thermal resistive sensors

3. Fundamentals of Heat Transfer • Mechanisms for heat transfer • Thermal conduction: transfer of heat through a solid media in the presence of a temperature gradient • Natural (passive) thermal convection: transfer of heat from a surface into a stationary body of fluid. • The temperature gradient in the fluid will induce fluid flow through buoyancy. The movement of the fluid facilitates heat transfer. • Forced thermal convection: transfer of heat to a body of moving fluid. • The bulk fluid movement enhances heat transfer compared to natural convection. • Radiation: loss or gain of heat through electromagnetic radiation propagating in vacuum or air.

4. Equations Governing Heat Transfer q” = heat flux (W/m2) k = thermal conductivity (W/(mK)) Conduction: h = convective heat transfer coefficient (W/(m2K)) TS = surface temperature (K) T∞= fluid temperature (K) Convection: • E = emissive power (W/m2) • TR = absolute temperature of surface (K) • = Stefan-Boltzmann constant (5.67x10-8 W/(m2K4)) e = radiative emissivity (0 < e < 1) Radiation:

5. Conductive Thermal Resistance • Thermal resistance: the ability of an object to transfer heat between two points. • Found through electrical analogy: • Heat flow, q (aka q”A) is like current • DT is like a voltage difference • For longitudinal rod with length, L, and cross-sectional area, A, the heat conduction qcond is related to temperature by: (K/W)

6. Resistive Heater Exercise • A resistive heater is located in the middle of a suspended bridge. The beam is made of silicon nitride and the metal leads are made of aluminum. Find the thermal conduction resistance between the heater and the substrate. Assume the width of the beam is 10 mm, the distance from the resistor edge to the substrate, L, is 100 mm and the thickness of both the aluminum and silicon nitride is 0.2 mm. (Hint, treat this as 4 resistors in parallel.) • If the input voltage to the resistor is 10 V and the current is 100 mA, calculate the power, Q, dissipated by the resistor, and the resulting steady-state temperature at the center of the bridge. Assume that the substrate is constant at 300K and that convection and radiation are negligible. L

7. Heat Capacity • Time for heating and cooling is critical for many devices. • Stored thermal energy (Q) related to temperature change through heat capacity, Cth sh = specific heat (J/(kg K)) m = mass (kg) • Time constant associated with heating and cooling is given by:

8. Thermal Expansion • Volumetric expansion coefficient (TCE), a, the ratio between the relative change in volume and the temperature variation (ppm/K) • Linear expansion coefficient: the change of only one dimension of an object due to temperature variation, • The volumetric and linear expansion coefficients are related by:

9. Thermal Bimetallic Effect t1 t2 w1 w2 L For a1 < a2: The radius of curvature of the arc is given by: The angle (in radians) associated with an arc of length L and radius r is given by:

10. Thermal Bimetallic Effect, cont. • Once the radius of curvature is found, the vertical displacement is found from: q r r cos(q) d = r - r cos(q)

11. Exercise • Calculate the radius of curvature and displacement for a bimorph cantilever made up of aluminum and silicon nitride heated to 20 °C above room temperature. The width of both layers is 20 mm and the length is 100 mm. The silicon nitride is 1 mm thick and the aluminum is 0.5 mm thick. E = 250 GPa for silicon nitride and 70 GPa for aluminum. The thermal expansion coefficients of aluminum and silicon nitride are a2 = 25 ppm/°C and a1 = 3 ppm/°C, respectively.

12. Thermal Actuators • Use thermal expansion, created by ohmic heating. • Out of plane uses layered devices with differing thermal expansion coefficients: • “Cilia array for micromanipulation,” Bohringer, Donald, Kovacs, Suh (U. Washington)

13. Actuators with a Single Material • Using geometry to cause differential heating: Luo, Flewitt and Milne, University of Cambridge Hot arm Cool arm • Using a bent beam http://john.maloney.org/thermal_actuation.htm

14. Multiphase Thermal Actuators • See: http://www.howstuffworks.com/inkjet-printer.htm/printable • Commonly uses bulk micromachining. Diepold et al.,”A micromachined continuous ink jet head for continuous high-resolution prints,” J. Micromech. Microeng., vol. 8, pp. 144-147, 1998.

15. Thermal Sensors • Thermocouples and thermal resistors can be used to translate temperature change into a voltage. • Some sensors combine thermal sensing with heat transfer to sense quantities such as flow rate or acceleration.

16. Thermal Couples • Two wires of dissimilar materials joined at a single point. • Work function difference results in temperature-sensitive voltage difference • Voltage change for temperature change given as Seebeck coefficient. • as = DV/DT (specific to material combination) • Several types (E, J, K, T, R, S) in common use, see p. 172. • Thermal pile • multiple thermal couples connected end to end with hot and cold junctions aligned • More sensitive than single thermal couple • Micromachined thermal couples have been made using Ni and W with a sensitivity of 22 mV/K

17. Thermal Resistors • Electrical resistors where the resistance depends on temperature • aR = temperature coefficient of resistance (TCR) • Quick exercise: A thermal resistor is 2 kW at room temperature and has a TCR of 100 ppm/°C. Predict the resistance at 50 °C above room temperature.

18. Sensing Other Physical Quantities through Temperature Change • Gas flow: • Acceleration Hot-wire anemometer from the University of Illinois (http://www.trecc.org/newslink/0407smartskin.php) Sensor magazine, “A Micromachined Thermal Accelerometer” (http://archives.sensorsmag.com/articles/0601/98/main.shtml)