Excluding blowup at zero points of the potential by means of Liouville-type theorems

We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for the equation $u_t= \Delta u+V(x)f(u)$, we rule out the possibility of blowup at zero points of the potential $V$ for monotone in time solutions when $f(u)\sim u^p$ for large $u$, both in the Sobolev subcritical case and in the radial case. This solves a problem left open in previous work on the subject. Suitable Liouville-type theorems play a crucial role in the proofs

A study of a nonlocal problem with Robin boundary conditions arising from technology

From Wiley via Jisc Publications RouterHistory: received 2020-08-03, rev-recd 2021-02-18, accepted 2021-02-22, pub-electronic 2021-05-04Article version: VoRPublication status: PublishedIn the current work, we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (micro‐electro‐mechanical system) device, when the ends of the device are attached or pinned to a cantilever. Initially, the steady‐state problem is investigated estimates of the pull‐in voltage are derived. In particular, a Pohožaev's type identity is also obtained, which then facilitates the derivation of an estimate of the pull‐in voltage for radially symmetric N‐dimensional domains. Next a detailed study of the time‐dependent problem is delivered and global‐in‐time as well as quenching results are obtained for generic and radially symmetric domains. The current work closes with a numerical investigation of the presented nonlocal model via an adaptive numerical method. Various numerical experiments are presented, verifying the previously derived analytical results as well as providing new insights on the qualitative behavior of the studied nonlocal model

Combustion and direct energy conversion in a micro-combustor

The push toward the miniaturization of electromechanical devices and the resulting need for micro-power generation (milliwatts to watts) with low-weight, long-life devices has led to the recent development of the field of micro-scale combustion. Since batteries have low specific energy (~200 kJ/kg) and liquid hydrocarbon fuels have a very high specific energy (~50000 kJ/kg), a miniaturized power-generating device, even with a relatively inefficient conversion of hydrocarbon fuels to power, would result in increased lifetime and/or reduced weight of an electronic or mechanical system that currently requires batteries for power. Energy conversion from chemical energy to electrical energy without any moving parts can be achieved by a thermophotovoltaic (TPV) system. The TPV system requires a radiation source which is provided by a micro-combustor. Because of the high surface area to volume ratio for micro-combustor, there is high heat loss (proportional to area) compared to heat generation (proportional to volume). Thus the quenching and flammability problems are more critical in a micro-scale combustor. Hence innovative schemes are required to improve the performance of micro-combustion. In the current study, a micro-scale counter flow combustor with heat recirculation is adapted to improve the flame stability in combustion modeled for possible application to a TPV system. The micro-combustor consists of two annular tubes with an inner tube of diameter 3 mm and 30 mm long and an outer tube of 4.2 mm diameter and 30 mm long. The inner tube is supplied with a cold premixed combustible mixture, ignited and burnt. The hot produced gases are then allowed to flow through outer tube which supplies heat to inner tube via convection and conduction. The hot outer tube radiates heat to the TPV system. Methane is selected as the fuel. The model parameters include the following: diameter d , inlet velocity u , equivalence ratio àand heat recirculation efficiency ÷ between the hot outer flow and cold inner flow. The predicted performance results are as followings: the lean flammability limit increased from 7.69% to 7.86% and the quenching diameter decreased from 1.3 mm to 0.9 mm when heat recirculation was employed. The overall energy conversion efficiency of current configuration is about 2.56

Improved micro-contact resistance model that considers material deformation, electron transport and thin film characteristics

This paper reports on an improved analytic model forpredicting micro-contact resistance needed for designing microelectro-mechanical systems (MEMS) switches. The originalmodel had two primary considerations: 1) contact materialdeformation (i.e. elastic, plastic, or elastic-plastic) and 2) effectivecontact area radius. The model also assumed that individual aspotswere close together and that their interactions weredependent on each other which led to using the single effective aspotcontact area model. This single effective area model wasused to determine specific electron transport regions (i.e. ballistic,quasi-ballistic, or diffusive) by comparing the effective radius andthe mean free path of an electron. Using this model required thatmicro-switch contact materials be deposited, during devicefabrication, with processes ensuring low surface roughness values(i.e. sputtered films). Sputtered thin film electric contacts,however, do not behave like bulk materials and the effects of thinfilm contacts and spreading resistance must be considered. Theimproved micro-contact resistance model accounts for the twoprimary considerations above, as well as, using thin film,sputtered, electric contact

Computational Studies of Premixed Flame Characteristics with Surface Effects.

As a fundamental study to understand characteristics in catalyst-assisted combustion, numerical simulations of two canonical models are performed. For a stagnation-point flow combustor with a catalytic surface, parametric studies are conducted to investigate the effects of strain rate, equivalence ratio and heat loss on the combustion and extinction modes. The steady results showed that catalysis largely extends the strain-induced extinction limit, while suppressing the gas phase reaction at lower strain rates. The temperature versus strain rate response curves exhibit multiple branches of stable solutions, implying a possibility of hysteresis behavior in a coupled homogeneous-heterogeneous reactor. In the lean extinction limit investigation, results show that the level of flammability extension by surface reaction depends strongly on the mixture dilution, such that the benefit of catalyst-assisted lean combustion can be fully realized only with a diluted system. These observations are explained by consideration of characteristic time scales calculated from the fuel consumption rate. The extinction response to an oscillatory strain rate also shows consistent behavior. Experimental validation was carried out to demonstrate simulation conclusions. It was found the substrate surface heat loss condition is a key factor to match simulation result with experimental results. Radiation and conductive heat loss through the surface in the experiment could be modeled as one effective heat loss coefficient, and that coefficient is relevant to both the flow rate (related with strain rate) and the surface temperature at that time. Thus an iteration process could be used to find the extinction condition for a fixed flow rate. Parametric studies on heat loss, equivalence ratio and device dimension for micro-channel flow configuration are conducted to research the combustion stability at near quenching conditions. A parallel DNS code supplemented by flame position capturing ability is applied. The results show the flame quenching condition is mainly affected by channel width and equivalence ratio at current parameter range. Channel wall heat loss shows influence on flame propagation speed but not on quenching conditions. Flame shape is affected by both equivalence ratio and heat loss. This research is expected to provide insight into improving the combustion stability and efficiency of catalyst-assisted combustors.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61655/1/jingjinz_1.pd

IN SITU INFRARED DIAGNOSTICS FOR A MICRO-SCALE COMBUSTION REACTOR

The development of centimeter to millimeter scale engines and power supplies have created a need for micro-scale combustion diagnostics. Fuel concentrations, product concentrations, and temperature are useful measurements in determining combustion behavior, chemical efficiency, and flame structures. However, to the present there have been few efforts to develop non-intrusive diagnostic techniques appropriate for application in such small engines. Non-intrusive measurements in these engines are complicated by short path length and lack of optical access. In this thesis in situ FTIR spectroscopy is used to measure temperature and concentrations of fuel, and carbon dioxide in a micro-combustor. The measurements are made through silicon walls spaced a few millimeters apart. This is possible because silicon is transmissive in the infrared. Experimental issues, including the optical setup, limitations associated with etaloning, calibration, and interpretation of the resulting spectra using wide-band models are discussed in detail

UNDERSTANDING THE ROLE OF HEAT RECIRCULATION IN ENHANCING THE SPEED OF PREMIXED LAMINAR FLAMES IN A PARALLEL PLATE MICRO-COMBUSTOR

This dissertation investigates the role of heat recirculation in enhancing the flame speeds of laminar flames stabilized in a parallel plate reactor by: 1) developing analytical models that account for conjugate heat transfer with the wall and 2) making measurements of temperature profiles in a simulated microcombustor using non-intrusive FTIR spectroscopy from which heat recirculation is inferred. The analytical models have varying degrees of complexity. A simple heat transfer model simulates the flame by incorporating a concentrated heat release function along with constant temperature wall model. The next level model accommodates conjugate heat transfer with the wall along with a built in heat loss model to the environment. The heat transfer models identify the thermal design parameters influencing the temperature profiles and the Nusselt number. The conjugate heat transfer model is coupled with a species transport equation to develop a 2-D model that predicts the flame speed as an eigenvalue of the problem. The flame speed model shows that there are three design parameters (wall thermal conductivity ratio ( &kappa ), wall thickness ratio ( &tau ) and external heat loss parameter ( NuE )) that influence the flame speed. Finally, it is shown that all these three parameters really control the total heat recirculation which is a single valued function of the flame speed and independent of the velocity profile (Plug or Poiseuille flow). On the experimental side, a previously developed non-intrusive diagnostic technique based on FTIR spectroscopy of CO2 absorbance is improved by identifying the various limitations (interferences from other species, temperature profile fitting, ... etc) and suggesting improvements to each limitation to make measurements in a silicon walled, simulated microcombustor. Methane/Air and Propane/Air flames were studied for different equivalence ratios and burning velocities. From the temperature profiles it can be seen that increasing the flame speed pushes the flames further up the channel and increases the combustors inner gas and outer wall temperatures (measured using IR thermography). The temperature profiles measured are used to make a 2-D heat recirculation map for the burner as a function of the equivalence ratio and burning velocity. The experimental results are compared to the analytical models predictions which show a linear trend between flame speed and heat recirculation