Analysis of Convection in the Presence of Apparent Slip

Friday, November 6 • 2:30 PM – UTEB, Rm. 175

Analysis of Convection in the Presence of Apparent Slip

Marc Hodes

Associate Professor of Mechanical Engineering Tufts University, Medford, Massachusetts

Abstract: A liquid flowing over a structured surface in the form of, e.g., ridges parallel to the flow, may be suspended in the unwetted (Cassie) state. I will introduce the physical principles and micro/nanotechnology that are exploited to trap a liquid in this state, where the no-slip boundary condition does not apply. This complicates the solution of the Stokes (or Navier-Stokes) equations for the velocity profile as it imposes different types of boundary conditions along the solid-liquid interface and the liquid-gas interface (meniscus). The vast majority of previous research on such flows considered them adiabatic. We study them in the presence of heat transfer, where the thermal energy equation is too subjected to non-standard boundary conditions. We have solved a variety of diffusive “inner” problems in the vicinity of the structures, where a boundary condition that the flow or temperature field is 1-dimensional infinitely far away from the structures may be imposed. These yield expressions for the apparent hydrodynamic and thermal slip lengths that manifest themselves as Robin boundary conditions on the outer problems that span the whole domain, e.g., a parallel plate channel. Additionally, in the outer thermal problems, advection must be considered. I will present our conformal map and convolution theory-based analytical solution to an inner thermal problem that captures the effects of evaporation and condensation along menisci. Then, I will discuss our analytical results for the Nusselt number (Nu) governing an outer thermal problem where arbitrary and asymmetric hydrodynamic and thermal (apparent) slip are imposed on a thermally-developing Couette flow. Nu is in the form of Airy and exponential function-containing infinite series, where the first term corresponds to the thermally-developed flow limit. Lastly, I will discuss our present work on the effects of thermocapillary stress and meniscus curvature on both types of apparent slip lengths.

Biographical Sketch: Marc Hodes received his M.S. in Mechanical Engineering from the University of Minnesota, where he performed research on dielectric liquid cooling of microelectronics. In 1998, he received his Ph.D. in Mechanical Engineering from the Massachusetts Institute of Technology, where his research addressed salt deposition (fouling) in supercritical water oxidation reactors used for the destruction of hazardous organic wastes. After holding a succession of appointments from Postdoctoral Member of Technical Staff to Manager over a 10 year period at Bell Labs, he joined the Mechanical Engineering Department at Tufts University in the Fall of 2008 as an Associate Professor. Professor Hodes’ research interests are in heat and mass transfer and, over the course of his career, four thematic areas have been addressed, i.e., 1) the thermal management of electronics, 2) mass transfer in supercritical fluids, 3) analysis of thermoelectric modules and 4) analysis of convection in the presence of apparent slip. Current research is in two areas. First, analytical solutions for apparent hydrodynamic and thermal slip lengths for liquid flows over diabatic structured surfaces that capture the effects of curvature, thermocapillary stress or evaporation and condensation at menisci are being developed. Secondly, enhanced aircooled heat sinks are being developed by deriving semi-analytical optimization formula for longitudinal-fin geometry heat sinks that capture the effects of non-uniform heat transfer coefficients and by developing manufacturing methods for novel “three-dimensional” geometries. Students conducting research with Professor Hodes enroll in part of all of his 4 course sequence of undergraduate fluid mechanics, undergraduate heat transfer, thermal management of electronics and graduate heat transfer. Since joining Tufts University in the fall of 2008 Professor Hodes’ research has been supported by the Department of Energy, NSF, DARPA, Science Foundation Ireland, the Wittich Energy Sustainability Research Initiation Fund, Tufts University and domestic and foreign industrial partners.

For additional information, please contact Prof. Michael T. Pettes at (860) 486-2855, or Laurie Hockla at (860) 486-2189,


Published: November 6, 2015

Categories: Events and Seminars, Seminars

Available Archives