Elham Maghsoudi

Momentum and Heat Transfer in Laminar Slip Flow over a Cylinder

The vorticity transport and energy equations are solved numerically in a laminar gas flow past a circular cylinder. The slip boundary condition and temperature jump are applied at the cylinder wall. The changes in heat transfer and slip velocity at the cylinder wall due to Knudsen and Reynolds number variations are calculated. The velocity at the wall increases as the Knudsen number increases due to the slip condition. The separation point moves downstream as slip increases. As the Knudsen number increases, the slip increases at the wall and the heat flux between the cylinder wall and the flow decreases. These results show that the heat transfer coefficient and the Nusselt number decrease as the slip increases. When hot wires are used for temperature measurements, failure to include a slip boundary condition will also lead to an error in the temperature measurement.

The computation of power requirements and write-time of thermally actuated nano-electro-mechanical memory

An integrated thermal-mechanical simulation of buckling in nano-mechanical memory is performed. The preliminary system is a bridge with a length of 20 microns, a width of 1 micron, and a thickness of 300 nm, in air with a pressure of 5 kPa. Conduction along the bridge as well as convection between the beam and the gas are considered. Simulations are performed for silicon with different dimensions. Longer structures will buckle faster at less temperature and will require less energy to actuate. However, the ideal array would use the smallest beams possible. The current work suggests the length of 20 microns for the unit of the bridge to balance these constraints. As the thickness of the bridge increases, the energy consumption increases due to an increase of moment of inertia. The buckling time increases by increasing the thickness while it decreases by increasing the width. The study of high particle energy collision shows these particles do not cause fast undesired buckling. The heat through collision dissipates in less than 10 nsec which is much smaller than the smallest buckling time.

Unsteady Thermo-Structural Simulation of Nano-Bridge Resonators

This study provides a thermo-structural simulation to investigate the behavior of nano-bridge resonators. A three-dimensional doubly clamped bridge with a length of 10 microns, a width of 1 micron and a thickness of 300 nm vibrating in the air is simulated. A free molecular heat transfer model is used to define the heat transfer coefficient and the damping coefficient. A Finite Difference method is used to solve the transient heat transfer equation coupled with the dynamic structural equation at each time step. The study is performed for silicon. The results show the steady state amplitude variations and vibration amplitude variations by the total heat amplitude correspond to a linear system. The results also show that increasing the total heat amplitude has more significant effects on increasing the vibration amplitude rather than the steady state amplitude by a factor of 1.2. The steady state amplitude and vibration amplitude variation by the surrounding gas pressure is investigated over a range of pressures from 1 kPa to 500 kPa for a total heat amplitude of 5000 MW/m2 (50 mW). The steady state amplitude and the vibration amplitude decrease by increasing the pressure due to an increase in the damping coefficient and the heat transfer coefficient. The rate of decrease is significantly higher for the vibration amplitude. This is due to the combination of increasing heat transfer coefficient, and increased damping, as the pressure increases.Copyright

Thermally Actuated Microswitches: Computation of Power Requirements for Alternate Heating Configurations

Steady state behavior of a thermally actuated RF MEMS switch in the open and closed positions is simulated using the governing thermal and structural equations. The switch is a bridge with a length of 250 microns, a width of 50 microns, and a thickness of 1 micron, in air with a pressure of 5 kPa. Simulations are performed for two different materials: silicon and silicon nitride. Three heating configurations are used: uniformly distributed heat, concentrated heat at the center of the top surface, and concentrated heat at the sides of the top surface. The steady state results show that the displacement at the center of the bridge is a linear function of the heat addition. This can be used to define a switch efficiency coefficient η*. In the uniformly distributed heat configuration, for a specific center displacement, a closed switch needs less heat at the top than an open switch. Adding concentrated heat at the center of the top surface yields a larger center displacement per unit heat addition than adding heat to the sides. When the heating is changed to a concentrated heat load at the center, the required heat is an order of magnitude less than heat added to the sides. Changing the contact length shows that variation in the length of the contact results in negligible changes in required heat to achieve a given displacement.

Simulation of thermally actuated nano-electro-mechanical memory

An integrated thermal-mechanical simulation of buckling in nano-mechanical memory is performed. The preliminary system is a bridge with a length of 20 microns, a width of 1 micron, and a thickness of 300 nm, in air with a pressure of 5 kPa. Conduction along the bridge as well as convection between the beam and the gas are considered. Simulations are performed for silicon with different dimensions. Longer structures will buckle faster at less temperature and will require less energy to actuate. However, the ideal array would use the smallest beams possible because the data storage density is inversely proportional to the area. The current work suggests the length of 20 microns for the unit of the bridge to balance these constraints. As the thickness of the bridge increases, the energy consumption increases due to an increase of moment of inertia. The buckling time increases by increasing the thickness and the width. Simulations were repeated for silicon carbide, PMMA, and Parylene. Among the beams with the fixed dimension, plastic materials show the fastest write time, with the lowest energy cost. The study of high particle energy collision shows these particles do not cause fast undesired buckling for silicon and silicon carbide. The heat through collision dissipates in less than 10 nsec which is much smaller than the smallest buckling time. However, high energy electron collision causes buckling in PMMA and parylene limiting their use in high radiation applications.

Momentum and Heat Transfer in Laminar Flow Past a Circular Cylinder with Slip and Temperature Jump Boundary Conditions

Vorticity transport and energy equations are solved numerically in a laminar gas flow past a circular cylinder. The slip boundary condition and temperature jump are applied at the cylinder wall. Heat transfer and the velocity at the cylinder wall are studied by Knudsen and Reynolds number variations. As Knudsen number increases the slip increases at the wall and the heat flux between the cylinder wall and the flow decreases.

Simulation of Femto-Satellite Heat Transfer

The time dependent temperature of a femto-satellite configuration based on assembled silicon wafers in low earth orbit is calculated using the radiation heat transfer equations. The results show that due to the low thermal mass of the system, the satellite will experience changes in temperature greater than 100 K from direct sunlight to being in eclipse. Calculation of the available solar power without attitude control shows the system will have about 100 mW available power. This power usage will slightly decrease the temperature swings in the system. I. Introduction Continued progress in micro- and nano-technology has renewed interest in satellite configurations built around micro- and nano-systems. 1 Recent progress in guidance systems 2 and propulsion systems, 3-5 as well as sustained experience in using micro-systems in the space environment 6-8 has demonstrated that these technologies are approaching the maturity required for integration into space systems. Proposed configurations for femto-satellites (satellites with a mass of less than 0.1 kg) use the approach of integrating micro-systems at the wafer level, and then integrating multiple wafers into a single spacecraft. A potential challenge in using these systems is thermal management. The small mass of the satellite will lead to large thermal transients as the satellite moves in and out of direct sunlight. On-board power usage will also be higher on a specific mass basis, indicating that power usage may play a role in stabilizing the temperature swings. The current work simulates the unsteady heat transfer to obtain an estimate for the temperature range in these systems.

Simulation of Actuation in Micro-Thermal Switches

The opening and closing of a RF MEMS switch is simulated using the governing thermal and structural equations. The system is a bridge with a length of 250 microns, a width of 50 microns, and a thickness of 1 micron, in air with a pressure of 5 kPa. Simulations are performed for two different materials: silicon and silicon nitride. Three heating models are used: Distributed heat, concentrated heat at the center, and concentrated heat at the sides of the top plate. The steady state results show that the maximum deflection variation at the center of the bridge versus the total heat changes at the top corresponds to a linear system. For distributed heat, for a specific deflection at the center, closed bridge needs less heat at the top than the free bridge. Variation in the length of the contact results in negligible changes in the maximum deflection. Transient results show that silicon nitride has faster response in comparison with silicon. Silicon nitride has a smaller closing time and opening time in comparison with silicon for the same value of heat, due to the larger expansion coefficient of silicon nitride. Adding concentrated heat at the center yields a larger displacement than adding heat to the sides and show better dynamic behavior. When the heating is changed to a concentrated heat load at the center the required heat is an order of magnitude less than heat added to the sides.Copyright

Simulation of Thermal Positioning in Micro- and Nano-Scale Bridge Structures

Heat transfer in a thermally-positioned doubly-clamped bridge, at the micro- and nano-scale, is simulated to investigate the effect of convective cooling on the mechanical response of the system. The mechanical response of the system is defined as the displacement at the center of the bridge. The heat conduction equation is solved numerically using a finite difference method to obtain the temperature distribution in the bridge. Then, thermal stress due to the temperature difference with respect to the wall temperature is calculated. The thermo-structural equation is solved numerically to get the displacement along the beam. Two systems are compared: one doubly clamped beam with a length of 100 microns, a width of 10 microns, and a thickness of 3 microns, and a second beam with a length of 10 microns, a width of 1 micron, and a thickness of 300 nanometers, in air at a pressure from 0.01 Pa to 2 MPa. Conduction within the beam as well as convection between the beam and the gas are considered. A constant heat load with respect to the time is applied to the top of the beam varying from 10 to 600 μW/μm2 . The simulations use both free molecular and continuum models to define the convective coefficient, h. The simulations are performed for three different materials: silicon, silicon carbide, and diamond. The numerical results show that the displacement and the response of thermally-positioned nano-scale devices are strongly influenced by ambient cooling. The displacement depends on the material properties, the geometry of the beam, and the Biot number. In the free molecular model, the displacement varies significantly with the pressure at high Biot numbers, while it does not depend on cooling gas pressure in the continuum case. The significant variation of displacement starts at Biot number of 0.1 which occurs at gas pressure of 27 KPa in nano-scale. As the Biot number increases, the dimensionless displacement, δ* = δk/q″ αl2 decreases. The displacement of the system increases significantly as the bridge length increases, while these variations are negligible when the bridge width and thickness change. Thermal noise analysis shows silicon carbide has the most physically meaningful displacements in comparison with silicon and cvd diamond.Copyright