|M.Sc Student||Lapchev Denis|
|Subject||Low Reynolds Number Flow in Spiral Micro-Channels|
|Department||Department of Mechanical Engineering||Supervisor||Research Professor E Daniel Weihs|
|Full Thesis text|
As a result of the development of microprocessors and MEMS technology, new problems are faced, involving need of efficient heat removal from the chips and MEMS systems. A common solution is to use micro-channels heat exchangers for this purpose. One of the problems in the micro-channels is the high pressure drop, which lowers efficiency of the heat exchanger. Pressure drop is caused by many factors including dimensions, geometry, roughness, etc. Geometry is one of the parameters that can be easily controlled, which demands more in-depth study.
We study the behavior of an incompressible fluid flowing in spiral micro-channels, which serve as a good area covering pattern. We propose the study of flow in a three-dimensional orthogonal curvilinear spiral coordinate system of micron size, where two of the dimensions are orthogonal spirals, and third one is height (z). As a first stage of solution, the equations of motion equations for incompressible, time independent flow will be developed, in spiral coordinates. The small size of the channels suggests low Reynolds number flow in the system, which reduces the Navier-Stokes set of equations to the Stokes equations for creeping flow. The goal of the research is to obtain theoretical solutions of the Stokes equations in spiral coordinates, and calculate velocity profiles and pressure drop in several practical configurations of the channels.
The results show that both pressure and velocity have exponential dependence on the expansion / contraction parameter k and on α, the streamwise position along the channel. In both expanding and converging channels, the pressure drop is increased when the expansion/contraction parameter k is increased. It has same value in both expanding and contracting channels due to reversible nature of Stokes equations.