John H. Lienhard

Boiling and Evaporation in Small Diameter Channels

Since the 1950s, the research and industrial communities have developed a body of experimental data and set of analytical tools and correlations for two-phase flow and heat transfer in passages having a hydraulic diameter greater than about 6 mm. These tools include flow regime maps, pressure drop and heat transfer correlations, and critical heat flux limits, as well as strategies for robust thermal management of HVAC systems, electronics, and nuclear power plants. Designers of small systems with thermal management by phase change will need analogous tools to predict and optimize thermal behavior in the mesoscale and smaller sizes. Such systems include a wide range of devices for computation, measurement, and actuation in environments that range from office space to outer space as well as living systems. This paper examines important processes that must be considered when channel diameters decrease, including flow distribution issues in single, parallel, and split flows; flow instability in parallel passages; manufacturing tolerance effects; single-phase heat transfer; nucleation processes; boiling heat transfer and pressure drop; and wall conductance effects. The discussion focuses on engineering issues for the design of practical systems.

The decay of turbulence in thermally stratified flow

The decay of grid-generated turbulence in the presence of strong thermal stratification is studied in a continuously stratified, open-loop wind tunnel at Brunt–Vaisala frequencies up to 2.5s −1 . The data include one-point statistical measurements through moments of fourth order and associated power- and cross-spectra. Cross-channel phase measurements are used to analyse the scales of correlation of velocity and temperature. The present data are considerably more coherent than previous salt-stratified data, and the structural form of stratified turbulence is thus more clearly manifested. No internal wave effects are observed at any stage of the decay. Stratified turbulence is found to be a two-scale process dominated by buoyancy forces at large scales of motion and dissipative effects at small scales. The two-scale structure is used to develop universal buoyancy scalings for the decay of the vertical heat flux, the scalar variance, and the molecular dissipation rates, and, in particular, for the vertical velocity decay. Velocity and temperature spectra satisfy universal equilibrium scaling at high wavenumbers, but show buoyancy effects at small wavenumbers. The flow remains isotropic at high wavenumbers over the entire range of turbulent decay studied. Cospectral and phase data are used to validate the two-scale model of the turbulence. The flow may show large-scale restratification while active turbulence persists at smaller scales, so that the vanishing of the vertical transport does not represent extinction of turbulent motion. Additionally, an original universal equilibrium scaling is developed for the cross-spectrum. Lengthscale evolution is measured, and the overturning and buoyancy lengthscales (associated with potential and kinetic energy, respectively) are found to characterize flow development. The role of the Prandtl number is assessed by comparison to previous works, and the Prandtl number is found to have a significant influence upon stratified turbulence evolution.

Entropy Generation Analysis of Desalination Technologies

Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies. Entropy generation analysis, and specifically, Second Law efficiency, is an important tool for illustrating the influence of irreversibilities within a system on the required energy input. When defining Second Law efficiency, the useful exergy output of the system must be properly defined. For desalination systems, this is the minimum least work of separation required to extract a unit of water from a feed stream of a given salinity. In order to evaluate the Second Law efficiency, entropy generation mechanisms present in a wide range of desalination processes are analyzed. In particular, entropy generated in the run down to equilibrium of discharge streams must be considered. Physical models are applied to estimate the magnitude of entropy generation by component and individual processes. These formulations are applied to calculate the total entropy generation in several desalination systems including multiple effect distillation, multistage flash, membrane distillation, mechanical vapor compression, reverse osmosis, and humidification-dehumidification. Within each technology, the relative importance of each source of entropy generation is discussed in order to determine which should be the target of entropy generation minimization. As given here, the correct application of Second Law efficiency shows which systems operate closest to the reversible limit and helps to indicate which systems have the greatest potential for improvement.

Convective Heat Transfer by Impingement of Circular Liquid Jets

The impingement of circular, liquid jets provides a convenient method of cooling surfaces. Here, jet impingement cooling of uniformly heated surfaces is investigated analytically and experimentally for stable, unsubmerged, uniform velocity laminar jets in the absence of phase change. Analytical and numerical predictions are developed for a laminar radial film flow. Experiments using undisturbed laminar jets were performed to determine local Nusselt numbers from the stagnation point to radii of up to 40 diameters. Turbulent transition in the film flow is observed experimentally at a certain radius. Beyond this transition radius, a separate turbulent analysis is constructed. Integral method results are compared to numerical results, and Prandtl number effects are investigated. The predictions are found to agree well with the measurements for both laminar and turbulent flow. Predictive formulae are recommended for the entire range of radii.

Technical evaluation of stand-alone solar powered membrane distillation systems

Abstract Economic evaluation was carried out to understand the main contributors to water production cost in solar-powered membrane distillation (SP-MD) systems. Three SP-MD systems (Direct Contact (DCMD), Air Gap (AGMD), and Vacuum (VMD)) were modeled and economically analyzed. A parametric study was conducted on the AGMD, the most frequently used SP-MD configuration, to understand the relationships between various design and operation parameters and water production cost. The parametric study results show that, in the AGMD system, increasing the feed inlet temperature had a significant effect in lowering the cost while higher feed flow rate resulted in increased water production cost. This study also shows that higher effective membrane length and lower air gap width and feed channel depth reduce the cost of water. Finally, the choice of MD configuration (AGMD, VMD, DCMD) in SP-MD systems will impact the final water cost.

Quantifying the potential of ultra-permeable membranes for water desalination†

In the face of growing water scarcity, it is critical to understand the potential of saltwater desalination as a long-term water supply option. Recent studies have highlighted the promise of new membrane materials that could desalinate water while exhibiting far greater permeability than conventional reverse osmosis (RO) membranes, but the question remains whether higher permeability can translate into significant reductions in the cost of desalinating water. Here, we address a critical question by evaluating the potential of such ultra-permeable membranes (UPMs) to improve the performance and cost of RO. By modeling the mass transport inside RO pressure vessels, we quantify how much a tripling in the water permeability of a membrane would reduce the energy consumption or the number of required pressure vessels for a given RO plant. We find that a tripling in permeability would allow for 44% fewer pressure vessels or 15% less energy for a seawater RO plant with a given capacity and recovery ratio. Moreover, a tripling in permeability would result in 63% fewer pressure vessels or 46% less energy for brackish water RO. However, we also find that the energy savings of UPMs exhibit a law of diminishing returns due to thermodynamics and concentration polarization at the membrane surface.

Laminar film condensation on plane and axisymmetric bodies in nonuniform gravity

Expressions are developed for the condensate film thickness and the local Nusselt number on arbitrary axisymmetric bodies, including vertical plates and cylinders. The expressions are the same as the Rohsenow-Nusselt expressions except that they are based on an “effective gravity” that corrects both for variable gravity and for the form of the body. The limitations on the expressions are: that radii of curvature greatly exceed the film thickness, that Prandtl numbers are never much less than unity, and that the ratio of sensible to latent heats is not large. These criteria include almost all practical situations. Several applications are developed.

On the existence of two ‘transition’ boiling curves

Abstract The idea that there are two ‘transition’ boiling curves accessible to a given liquid boiling on a given surface, is advanced. A variety of saturated, subcooled, pool, and flow boiling data are shown to be consistent with, and explainable in terms of, the idea. Some of the data are hitherto unpublished results. The two boiling curves are extensions of the nucleate and film boiling curves, and they are related to nucleate and film boiling phenomenologically.

An upper bound for the critical boiling heat flux

The great value of boiling and condensation in process heat transfer is that they yield the highest known heat transfer coefficients. People who have to transfer a great deal of energy rapidly, under fairly low driving temperature differences, usually turn to these processes. The authors therefore constantly face the question. What is the upper limit on these heat fluxes - how far can they be driven.

Stagnation-Point Heat Transfer During Impingement of Laminar Liquid Jets: Analysis Including Surface Tension

The stagnation-zone characteristics of an impinging liquid jet are of great interest because the maximum heat transfer coefficient occurs in that region. This is an analytical study of the fluid flow and heat transfer in the stagnation zone of an unsubmerged liquid jet. The role of surface tension is emphasized. Stagnation-zone transport is strongly dependent on the potential flow above the boundary layer. Numerical solutions for a laminar unsubmerged jet are obtained, using a simulation method for steady, inviscid, incompressible flow with surface tension