We are interested in how the microscale geometry and compositional and conductivity gradients in coolants affect net heat transport in liquid-cooled electronics applications. Rates of heat transfer from the semiconductor devices are a significant limitation to the processing capabilities of these devices. Liquid cooling has shown promise in improving the rates of heat transport in these devices. Although the experimental capability to design and fabricate specific microstructures in materials has advanced significantly in the past few decades, a description of their effective thermal behavior on the microscale has not kept pace. Current modeling of these multi-physics systems has focused on direct computational approaches, but they are limited due to the need to resolve the finest length-scales (microns) over the length scale of the full application (centimeters). We employ an asymptotic approach to formulate effective transport equations that capture the dominant net fine-scale physical effects on the application length scale. This modeling approach provides an efficient means to determine how competition of different microscale effects can change macroscale behavior.
Although the promise of environmentally friendly, low-cost energy harnessing for heating and cooling of residential properties has been known for nearly 30 years, the adoption of the technology in the United States has been slow. The installation costs for current residential geothermal systems are currently cost-prohibitive, with a typical return-time on investment on the order of 8-10 years. A significant portion of this cost is in the installation of large networks of piping to harness the geothermal energy. Our focus in this research program is to develop mathematical models to quantify how the length of the piping is related to the operational parameters of the system. One means to improve the economic competitiveness of these systems is to reduce the installation footprint. The power rating and the unknown temperature variation in the axial direction together determine the required length of pipe needed for the system to function properly. However, the temperature profile in the fluid is necessarily coupled to the thermal behavior in the soil from which the energy is transferred. In order to fully understand how these systems work, a requirement for design optimization, the temperature profile in both the soil and the fluid need to be solved simultaneously. This is a difficult modeling task, so it is no surprise that some simplifications in the modeling have been attempted in order to understand different aspects of the system. We have developed a model for the simple case of a single tubing, but we are ready to consider the effects of using a network of tubing under the soil, and to understand the impact of the network on the effective energy harnessed from the soil after use over several decades.
Collaborators: Prof. S. Evans, Department of Mechanical Engineering, WPI, K. Maher, New England Geothermal Professionals Association (NEGPA)
With an increasing
population in the US, there is a greater need to control public
health risks from chemical and microbiological contaminants. As one
example, there are over 1000 contaminated soil and aquifer sites on
the EPA's national priority list, and many other sites that pose a
risk to neighboring populations. While the means to remediate soils
have been of interest since the 1980's, their main limitation centers
on delivering the remediation agent (either chemical or biological)
to the location in a timely manner. Developing new technologies is
also challenging, since the time-scale for a typical small-scale, in
situ experiment is on
the order of weeks to months. The bottleneck lies in the transport of
the agent through the soil. Previous modeling attempts have been
phenomenological, with the results dependent on the local soil
conditions and the underlying chemical process. We extend the work in
this area to include higher-order effects of elasticity in the solid
clay medium with the electrokinetic and viscous effects of the flow.
These effects are relevant in natural and engineered filtration
problems, since the deformations, although small locally, can lead to
large deformations over the length of the filter or within an aquifer
system, which affects the desired performance of the system.
Collaborators: Prof.
B. Vernescu, Department of
Mathematical Sciences, WPI, and Prof.
J.D. Plummer, Department
of Civil and Environmental Engineering, WPI.
In
recent years, ink-jet printers have become a common and economical
standard for producing high-quality printed text and graphics. These
printers typically employ several different jets simultaneously, each
made up of a different colour of ink; arbitrary colours can therefore
be generated by mixing the output of the jets in different
proportions. Since only one drop size is typically generated, the
efficient control of drop formation is an inherent requirement in the
overall performance of the system. The limitation on resolution of
these devices is down to the reliable control of the smallest drop
size while the printing rate depends on the ability to control the
break-up phenomena both spatially and in time. A further application
requiring the delicate control of jet dynamics is found in the
fabrication of high-density microelectronic devices.
To focus
on the competition between the thermally-driven and inertially-driven
instability mechanisms, we consider a symmetrically heated sheet
(rather than a radially symmetric jet), which results in no net
bending. The application of the laser results in a prescribed initial
temperature profile from which the sheet evolves. The spatial
location of rupture is controlled through interfacial temperature
gradients. We find that this heating, along with a standard
modulation in the axial velocity from the nozzle, results in a better
control of drop size than in the isothermal problem; the evaporation
time scale is assumed to be much longer than the viscous time scale
here. We show that the time to rupture may be minimised by varying
the phase difference between the initial velocity profile and the
initial temperature profile. For sufficiently large temperature
differences, the phase difference between the initial velocity and
temperature profiles determines the rupture location.
Collaborators: Mark Bowen, Waseda University, Tokyo,
Japan.