The figure above shows a schematic of the basic electro-thermal actuator.
- (a) Let s denote the length along the centerline (shown dashed), with the left end of the long, slender beam as the starting point, and the left end of the short, narrow beam as the end point. Obtain the Joule heating term as a function of s starting from the governing equation for the electric current distribution.
- (b) Obtain the temperature as a function of s under Joule heating as above. Neglect convective and radiative heat transfer.
A micro-fludic device has a reservoir that is to be heated along with the fluid it contains. A circular 1 um thick, and 3 um wide polysilicon resistive heator is deposited on bottom surface of the reservoir (see figure below). Assume that this surface is well insulated so that negligible heat escapes into the casing from it. There is fluid (not shown in the figure) above the resistor and the purpose of the resistor is to heat the fluid. The radius of the circle is 150 um. The circle is not complete and has two ends going to the on a side for electrical connection (see the figure below). Neglect the straight ends and assume that the two ends of the circle are at the ambient temperature. Assume also that a constant voltage is applied between the two terminals of the circle that forms the resistor. Obtain the steady-state temperature distribution along the resistor without neglecting the TCR effect. Consider only heat transfer via conduction within the resitor and convection to the fluid. Use the following data.
Electrical resistivity = 4.2E-4 omh-m at 300 K (ambient temperature)
TCR = 2000E-6 /K
Thermal condictivity = 146.4 W/(m-K) (assume that it does not change with temperature)
Convective heat transfer coefficient = 30 W/(m^2-K)
