A mathematical model describing the evaporating meniscus in a capillary tube has been formulated incorporating the full three-dimensional Young–Laplace equation, Marangoni convection, London–van der Waals dispersion forces, and nonequilibrium interface conditions. The results showed that varying the dimensionless superheat had no apparent effect on the meniscus profile. However, varying the dispersion number produced a noticeable change in the meniscus profile, but only at the microscopic level near the tube wall. No change in the apparent contact angle was observed with changes in the dimensionless superheat or dispersion number. In all cases, the dimensionless mean curvature was asymptotic to a value equal to that for a hemispherical meniscus. The local interfacial mass flux and total mass transfer rate increased dramatically as the dispersion number was increased, suggesting that surface coatings can play an important role in improving or degrading capillary pumping. The model also predicted that the local capillary pressure remains constant and equal to 2σ/rc regardless of changes in the dimensionless superheat and dispersion number. It should be noted that the results in this study are theoretical in nature and require experimental verification.
Successful analysis and modeling of micro heat pipes requires a complete understanding of the vapor–liquid interface. A thermodynamic model of the vapor–liquid interface in micro heat pipes has been formulated that includes axial pressure and temperature differences, changes in local interfacial curvature, Marangoni effects, and the disjoining pressure. Relationships were developed for the interfacial mass flux in an extended meniscus, the heat transfer rate in the intrinsic meniscus, the “thermocapillary” heat-pipe limitation, as well as the nonevaporating superheated liquid film thickness that exists between adjacent menisci and occurs during liquid dry out in the evaporator. These relationships can be used to define quantitative restrictions and/or requirements necessary for proper operation of micro heat pipes. They also provide fundamental insight into the critical mechanisms required for proper heat pipe operation.
Biomass has been considered as an alternative fuel to firing coal in utility boilers because of its vast availability and renewable nature. However, the use of biomass as a full or partial replacement for coal needs a careful evaluation of its impact on the boiler performance and the best approach for implementation. In the past, biomass has been implemented in a cofiring mode and is injected into the coal pipe providing a portion of the heat input. Another approach of utilizing biomass is through reburning. In this application, biomass can be directly injected above the burner zone as a reburn fuel, which utilizes the renewable energy and can lead to reduced NO X emissions. In addition, this approach reduces the requirements for mill and/or burner modifications. This paper reviews (1) the process conditions and burner flame structures for biomass cofiring as a function of the heat input and (2) the process requirements and impacts of biomass reburning on the boiler combustion performance. The study indicates that a successful implementation of biomass as an alternative fuel requires a case-by-case examination of the biomass properties such as its fuel factor, F, defined as the ratio of the air-to-fuel demand to the heating value, and its combustion moisture factor, M C , defined as the ratio of the fuel hydrogen content to the fuel carbon content.
A mathematical model of the evaporating extended meniscus in a V-shaped channel was developed to investigate the effect of wedge half-angle and vapor mass transfer on meniscus morphology, fluid flow, and heat transfer. The liquid was unsaturated, flowed down the wedge due to gravity, and evaporated into atmospheric air. The average Nusselt number was found to decrease as the wedge half-angle increased, primarily because of an increase in the average wall-interface temperature difference. The mean curvature changed from zero at the interline to a constant, at a distance approximately three times the adsorbed layer thickness from the wall. The capillary pressure calculated from first principles was nearly twice as large as that determined from a semicircular approximation of the mean curvature. We believe that this was partially due to the presence of the van der Waals attraction near the wall. Downstream from the inlet, both thermocapillary convection and pressure recovery in the liquid caused the interline to move downward toward the wedge apex and then upward away from the apex until the piezometric pressure gradient was equal to zero. The locus of liquid dry out points were estimated based on axial locations where the piezometric pressure gradient was equal to zero; this represented a point of zero flow in the channel. As expected, the points where dry out occurred, moved closer to the inlet as the surface mass flux was increased. Nomenclature a = aspect ratio, r 0 /L Ca = capillary number E = evaporation number F = surface mass transfer number G = arc-length function g = gravity vector H = mean curvature of the vapor-liquid interface h = heat transfer coefficient at a given axial location /z ave = average heat transfer coefficient h fg = latent heat of vaporization h m = mass transfer coefficient / = identity tensor / = mass flux at the interface k = thermal conductivity in the liquid M = Marangoni number M A = magnitude of the normal vector MI = magnitude of the tangent vector m = summation index Nw ave = average Nusselt number h = unit normal vector to the interface pointing into the vapor phase P = pressure Pr = Prandtl number R = radial location of the vapor-liquid interfacê va P = g as constant divided by the molecular weight of the vapor r = radial spatial coordinate r 0 = interline location at the wedge inlet T = temperature i = unit tangent vector to the interface u = radial velocity v = azimuthal velocity v = velocity vector w = axial velocity z = axial spatial coordinate z steps = number of steps in the axial direction V = gradient operator a = wedge half-angle /3= wedge inclination angle with respect to the gravity vector y = change in surface tension with respect to temperature Ar = radial spatial increment Az = axial spatial increment A0 = azimuthal spatial increment 8 = adsorbed layer thickness l* r = unit vector in the radial direction j) z = unit vector in the axial direction 8 e = unit vector in the azimuthal direction e = azimuthal coordinate with an origin at the wall, a -0 £ 0 = angle assoc...
An extended version of the Bejan model of irreversible power plants is proposed using a log-mean temperature difference (LMTD) representation for both the high and low-temperature heat exchangers. The analysis focuses on minimizing the irreversibilities associated with the hot and cold heat exchangers. The results indicate that the maximum power output, external conductance allocation ratio, and second law efficiency are functions of the number total heat exchanger transfer units (N), and are asymptotic to Bejan’s original results as N → O. This asymptote represents a global power output maximum and occurs for either extremely high cycle flow rates or cycle phase change processes in both heat exchangers. The LMTD representation also shows that under optimal conditions, more conductance should be allocated to the low-temperature heat exchanger as N increases.
Biomass reburn is a low NOx alternative to cofiring that effectively uses the high volatility and high char reactivity of biomass for NOx reduction. In this paper, computational fluid dynamics (CFD) and thermal modeling, and a NOx prediction model were used to evaluate the impacts of sawdust/coal reburn on the performance of a 250 MW opposed-fired boiler burning bituminous coal as the primary fuel. The results showed that the reburn system maintained overall boiler performance with a 50 – 70 °F reduction in the furnace exit gas temperature. Predicted losses in thermal efficiency were caused by the lower biomass fuel heating value (similar to biomass cofiring) and increase in unburned carbon. The higher unburned carbon emissions were attributed to an order of magnitude larger biomass mean particle size relative to bituminous coal. Thus, LOI emissions can be improved significantly by reducing the biomass mean particle size. The NOx predictions showed that for reburn rates above about 19%, adding dry sawdust biomass to a coal reburn system can improve NOx reduction; i.e., using pure dry sawdust as reburn fuel at 30% of the total heat input can lead to NOx levels about 30% less than those for pure coal reburn under for similar firing conditions.
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