DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Alina A. Alexeenko, School of Aeronautics and Astronautics, Purdue University

**Title: ***
Thermally Driven Microflows: Phenomena and Modeling Approaches
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**Abstract:**
In the early 1870s Sir William Crookes invented the first thermally-driven gas flow device: a set of vanes mounted on a spindle in a bulb evacuated to a very low pressure which rotates when sunlight shines on it. This phenomenon is based on the non-equilibrium thermal stresses that generate a bulk gas flow and a total force on the vanes which has a maximum when the mean free path of molecules is comparable to the vane size. Another manifestation of thermal stresses in gases is the thermal transpiration - a gas flow from the cold to the hot end of a tube of sufficiently small diameter. Nowadays, the availability of low thermal-conductivity materials, such as aerogel, and advances in microscale manufacturing make it possible to exploit the thermal stress phenomena to built sensors and actuators powered by radiant or resistive heating. In this talk, we will discuss modeling approaches that can be used to predict gas flows and performance of such devices. The first approach, the direct simulation Monte Carlo (DSMC) method, is a stochastic technique based on the atomistic description of a gas as a collection of moving and colliding particles. The DSMC method has proved to be a very powerful numerical tool for modeling high-speed rarefied gas flows, such as high-altitude hypersonic flight. However, this stochastic approach currently has limited application to the low-speed thermal stress flows, due to inherent statistical scatter and low signal-to-noise ratios. It also becomes increasingly computationally costly as the flow Knudsen number decreases towards the continuum flow regime. Moreover, the DSMC method is explicit in time, which imposes additional limits to its application. An alternative numerical approach is to obtain a deterministic solution, based on the discrete ordinate method, of the Boltzmann kinetic model equations. The primary advantage of this modeling technique is its high computational efficiency compared to pure stochastic methods. Last but not least, techniques for solution of the model equation are amenable to coupled microscale gas flow/heat transfer simulations.

**Place:** Science and Technology Building I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491