On Spreading Resistances and Apparent Slip Lengths for Rectangular and Elliptical Pillars - Kane, Daniel. (2017)
Abstract: In the diffusion limit, solutions exist for the temperature and velocity fields when isothermal and no-slip boundary conditions, respectively, are imposed on elliptical surfaces on an otherwise zero-flux plane of a half-space domain containing far field Dirichlet boundary conditions. We utilize these results to tabulate thermal and hydrodynamic spreading resistances on half spaces as a function of the aspect ratio of the ellipse and of the aspect ratio of the ellipse and its orientation, respectively. Then, via computations, we quantitatively assess the accuracy of these expressions for rectangular isothermal and no-slip surfaces when the square root of their area is used as a characteristic length scale to nondimensionalize the spreading resistances. We then provide numerically computed thermal and hydrodynamic spreading resistances and apparent slip lengths for elliptical and rectangular surfaces centered on the base of a square, semi-infinite domain (flux channel).; Thesis (M.S.)--Tufts University, 2017.; Submitted to the Dept. of Mechanical Engineering.; Advisor: Marc Hodes.; Committee: Marc Hodes, Yuri Muzychka, and Jeffrey Guasto.; Keywords: Mechanical engineering, and Engineering.