Natural convection from leaves at realistic Grashof numbers

Abstract. The boundary layer resistance of model leaves was measured in still air, at a range of leaf-to-air temperature differences. The results were compared to those calculated from standard formulae for natural convection. The agreement between observed and calculated was only satisfactory when Grashof numbers exceeded about 105. At the lower Grashof numbers, which often prevail in nature, the observed rates of heat transfer considerably exceeded those calculated.     

The effect of gravity on surface temperatures of plant leaves

A fundamental study was conducted to develop a facility having an adequate air circulation system for growing healthy plants over a long-term under microgravity conditions in space. To clarify the effects of gravity on heat exchange between plant leaves and the ambient air, surface temperatures of sweet potato and barley leaves and replica leaves made of wet paper and copper were evaluated at gravity levels of 0.01, 1.0, 1.5 and 2.0 g for 20 s each during parabolic aeroplane flights. Thermal images were captured using infrared thermography at an air temperature of 26 degrees C, a relative humidity of 18% and an irradiance of 260 W m-2. Mean leaf temperatures increased by 0.9-1.0 degrees C with decreasing gravity levels from 1.0 to 0.01 g and decreased by 0.5 degrees C with increasing gravity levels from 1.0 to 2.0 g. The increase in leaf temperatures was at most 1.9 degrees C for sweet potato leaves over 20 s as gravity decreased from 1.0 to 0.01 g. The boundary layer conductance to sensible heat exchange decreased by 5% when the gravity decreased from 1.0 to 0.01 g at the air velocity of 0.2 m s-1. The decrease in the boundary layer conductance with decrease in the gravity levels was more significant in a lower air velocity. Heat exchange between leaves and the ambient air was more retarded at lower gravity levels because of less sensible and latent heat transfers with less heat convection.     

Boundary Layer Resistance and Temperature Distribution on Still and Flapping Leaves: II. Field Experiments

The forced convection of heat from reed (Phragmites communis) leaves was observed in their natural environment. The leaves were painted with liquid crystals, which displayed or indicated their temperature without any interference with natural air flow. Temperature differences as large as 15 C were observed between the leading and trailing edges of the nontranspiring, painted leaves. The turbulence of the natural wind decreased the boundary layer resistance around the leaf to about 40% of the resistance in a laminar steady wind.     

Modelled influences of non-exchanging trichomes on leaf boundary layers and gas exchange

The two main resistances in the exchange of gases between plants and the atmosphere are stomatal and boundary layer resistances. We modeled boundary layer dynamics over glabrous and pubescent leaves (assuming non-exchanging trichomes) with leaf lengths varying from 0.01 to 0.2 m, and windspeeds of 0.1-5.0 m x s(-1). Results from theoretical and semi-empirical formulae were compared. As expected, boundary layer thickness decreased with decreasing leaf length and increasing windspeed. The presence of trichomes increased leaf surface roughness, resulting in lowered Reynolds numbers at which the boundary layer became turbulent. This effect is especially important at low windspeeds and over small leaves, where the Reynolds number over glabrous surfaces would be low. We derived a new simple dimensionless number, the trip factor, to distinguish field conditions that would lead to a turbulent boundary layer based on the influence of trichomes. Because modeled rates of CO2 and H2O(v) exchange over turbulent boundary layers are one or more orders of magnitude faster than over laminar boundary layers, a turbulent boundary layer may lead to increased carbon uptake by plants. The biological trade-off is potentially increased transpirational water loss. However, in understory habitats characterized by low windspeeds, even a few trichomes may increase turbulence in the boundary layer, thus facilitating photosynthetic gas exchange. Preliminary field data show that critical trip factors are exceeded for several plant species, both in understory and open habitats.     

Disappearance of overstorey and understorey litter in an open eucalypt forest

Litter accumulation dynamics and first year rates of disappearance were investigated for leaves of overstorey and understorey species in the mixed eucalypt forest in the Griffith University study area, Queensland, Australia. The average biomass of the litter layer, was 10.2 t/ha. The wood and overstorey leaf litter formed 62.7% of the accumulated litter biomass, and were spread continuously across the ground. The distribution of shrub litter was discontinuous, being concentrated in localized patches beneath individual plants. The litter bag and tethered leaf techniques were used to measure the rate of disappearance of overstorey and shrub leaves. The ‘pairedquadrat’ technique was used to measure the weight loss of the grasses. The small leaves of the dominant shrub, Pultenaea villosa Willd. disappeared most rapidly, followed by the overstorey leaves, grasses and Acacia leaves. Fragmentation by physical factors and litter fauna appeared to be the major factors responsible for the disappearance of the overstorey leaves during the first year of exposure. The data suggest that removal of leaf constituents by leaching and microbial decomposition were more important for the shrub litter than the overstorey leaves. Fractional disappearance rates (loss constants) obtained from the short term weight loss measurements, and calculated using the steady-state model of litter accumulation (k=L/X), overestimated the rate of litter disappearance and litter decomposition. For the overstorey leaves in particular, the loss constants also overestimated the rate of loss of material from the litter layer since the fragmented and consumed tissues accumulated in the fraction of comminuted fragments before moving into the humus/soil subsystem. A compartment model of the components of the litter layer in the mixed eucalypt forest is presented. It incorporates overstorey and understorey litter accession, accumulation and disappearance data. The adoption of a two dimensional decomposition/accumulation matrix is suggested as an appropriate framework within which to simulate the dynamics of the litter subsystem in mixed eucalypt forest ecosystems.     

Boundary layer properties of highly dissected leaves: an investigation using an electrochemical fluid tunnel

Abstract. A method for modelling heat and mass transfer by diffusion-controlled electrode reactions in a fluid tunnel is described. In this procedure, a nickelplated leaf functions as a test electrode, and the convective transfer of ions to the leaf cathode in an electrolyte-filled flow tunnel is measured as a function of flow rate. The method permits the simulation of water vapour and heat transfer, and in particular, the determination of boundary layer conductances, by analogy with observed ion transfer. The approach is applicable to many problems in modelling heat and mass transfer between leaves and their surroundings, and is especially useful in examining the properties of leaves in which surface characteristics or overall shape are complex. Using this method, the properties of the highly dissected leaves of Achillea lanulosa with regard to forced convection were investigated. The leaves showed high transfer conductances, indicating that the effective unit of heat transfer was probably the individual leaf subelements. Conductances tended to be greater and effective characteristic dimensions smaller for the larger, more open leaves of a lower altitude population in contrast with leaves from high altitude plants. While the results provide insight into the properties of these complex leaf shapes, difficulties in interpreting the findings are discussed, and a number of exploratory approaches are suggested for data analysis and interpretation.     

Quantification of excess water loss in plant canopies warmed with infrared heating

Here we investigate the extent to which infrared heating used to warm plant canopies in climate manipulation experiments increases transpiration. Concerns regarding the impact of the infrared heater technique on the water balance have been raised before, but a quantification is lacking. We calculate transpiration rates under infrared heaters and compare these with air warming at constant relative humidity. As infrared heating primarily warms the leaves and not the air, this method increases both the gradient and the conductance for water vapour. Stomatal conductance is determined both independently of vapour pressure differences and as a function thereof, while boundary layer conductance is calculated using several approaches. We argue that none of these approaches is fully accurate, and opt to present results as an interval in which the actual water loss is likely to be found. For typical conditions in a temperate climate, our results suggest a 12–15% increase in transpiration under infrared heaters for a 1 °C warming. This effect decreases when stomatal conductance is allowed to vary with the vapour pressure difference. Importantly, the artefact is less of a concern when simulating heat waves. The higher atmospheric water demand underneath the heaters reflects naturally occurring increases of potential evapotranspiration during heat waves resulting from atmospheric feedback. While air warming encompasses no increases in transpiration, this fully depends on the ability to keep humidity constant, which in the case of greenhouses requires the presence of an air humidification system. As various artefacts have been associated with chamber experiments, we argue that manipulating climate in the field should be prioritized, while striving to limit confounding factors. The excess water loss underneath infrared heaters reported upon here could be compensated by increasing irrigation or applying newly developed techniques for increasing air humidity in the field.     

Effects of Leaf Shape and Boundary Layer Thickness on Photosynthesis in Cotton (Gossypium hirsutum)

In upland cotton (Gossypium hirsutum L.) certain varieties are available with the mutant character “okra” leaves. These deeply lobed leaves were found to have thinner boundary layers than their normal analogues. Apparent photosynthesis and transpiration measurements were made in field-grown stands under a variety of light intensities and carbon dioxide levels to assess the effect of leaf boundary layer diffusion resistance on photosynthetic efficiency. The thinner boundary layers associated with deeply lobed “okra” cotton failed to euhance carbon fixation rates per unit land area. It was concluded that the leaf boundary layer resistance under field conditions is small compared with the total CO₂ diffusion resistance.     

Foliar trichomes, boundary layers, and gas exchange in 12 species of epiphytic Tillandsia (Bromeliaceae)

We examined the relationships between H2O and CO2 gas exchange parameters and leaf trichome cover in 12 species of Tillandsia that exhibit a wide range in trichome size and trichome cover. Previous investigations have hypothesized that trichomes function to enhance boundary layers around Tillandsioid leaves thereby buffering the evaporative demand of the atmosphere and retarding transpirational water loss. Data presented herein suggest that trichome-enhanced boundary layers have negligible effects on Tillandsia gas exchange, as indicated by the lack of statistically significant relationships in regression analyses of gas exchange parameters and trichome cover. We calculated trichome and leaf boundary layer components, and their associated effects on H2O and CO2 gas exchange. The results further indicate trichome-enhanced boundary layers do not significantly reduce transpirational water loss. We conclude that although the trichomes undoubtedly increase the thickness of the boundary layer, the increase due to Tillandsioid trichomes is inconsequential in terms of whole leaf boundary layers, and any associated reduction in transpirational water loss is also negligible within the whole plant gas exchange pathway.     

Effect of blood flow on near-the-wall mass transport of drugs and other bioactive agents: a simple formula to estimate boundary layer concentrations

Transport of bioactive agents through the blood is essential for cardiovascular regulatory processes and drug delivery. Bioactive agents and other solutes infused into the blood through the wall of a blood vessel or released into the blood from an area in the vessel wall spread downstream of the infusion/release region and form a thin boundary layer in which solute concentration is higher than in the rest of the blood. Bioactive agents distributed along the vessel wall affect endothelial cells and regulate biological processes, such as thrombus formation, atherogenesis, and vascular remodeling. To calculate the concentration of solutes in the boundary layer, researchers have generally used numerical simulations. However, to investigate the effect of blood flow, infusion rate, and vessel geometry on the concentration of different solutes, many simulations are needed, leading to a time-consuming effort. In this paper, a relatively simple formula to quantify concentrations in a tube downstream of an infusion/release region is presented. Given known blood-flow rates, tube radius, solute diffusivity, and the length of the infusion region, this formula can be used to quickly estimate solute concentrations when infusion rates are known or to estimate infusion rates when solute concentrations at a point downstream of the infusion region are known. The developed formula is based on boundary layer theory and physical principles. The formula is an approximate solution of the advection-diffusion equations in the boundary layer region when solute concentration is small (dilute solution), infusion rate is modeled as a mass flux, and there is no transport of solute through the wall or chemical reactions downstream of the infusion region. Wall concentrations calculated using the formula developed in this paper were compared to the results from finite element models. Agreement between the results was within 10%. The developed formula could be used in experimental procedures to evaluate drug efficacy, in the design of drug-eluting stents, and to calculate rates of release of bioactive substances at active surfaces using downstream concentration measurements. In addition to being simple and fast to use, the formula gives accurate quantifications of concentrations and infusion rates under steady-state and oscillatory flow conditions, and therefore can be used to estimate boundary layer concentrations under physiological conditions.     

Ozone concentration in leaf intercellular air spaces is close to zero

Transpiration and ozone uptake rates were measured simultaneously in sunflower leaves at different stomatal openings and various ozone concentrations. Ozone uptake rates were proportional to the ozone concentration up to 1500 nanoliters per liter. The leaf gas phase diffusion resistance (stomatal plus boundary layer) to water vapor was calculated and converted to the resistance to ozone multiplying it by the theoretical ratio of diffusion coefficients for water vapor and ozone in air (1.67). The ozone concentration in intercellular air spaces calculated from the ozone uptake rate and diffusion resistance to ozone scattered around zero. The ozone concentration in intercellular air spaces was measured directly by supplying ozone to the leaf from one side and measuring the equilibrium concentration above the other side, and it was found to be zero. The total leaf resistance to ozone was proportional to the gas phase resistance to water vapor with a coefficient of 1.68. It is concluded that ozone enters the leaf by diffusion through the stomata, and is rapidly decomposed in cell walls and plasmalemma.     

Breakdown of Ficus and Eucalyptus leaves in an organically polluted river in India: fungal diversity and ecological functions

1. At two organically polluted sites in the River Nethravathi, banyan and eucalypt leaves were colonized by one or two species of aquatic hyphomycetes. A total of three or four species were identified at the two sites in samples of water and naturally occurring leaves.
2. Spore production from stream‐exposed leaves by aquatic hyphomycetes was lower by a factor of up to 1 million compared with an earlier study in geographically close but unpolluted streams.
3. Exponential decay rates and loss rates of phosphorus and calcium, were not statistically different from an earlier study in unpolluted streams. Nitrogen increased during decomposition more slowly in the current study.
4. The microbial community on both leaves released enzymes active against starch, pectin, cellulose and xylan.
5. Banyan leaves conditioned for 12 weeks were more palatable to the gastropod Notopala sp. than unconditioned leaves.
6. Together with earlier data from unpolluted streams, the study provides evidence that organic pollution severely restricts diversity of aquatic hyphomycetes and their reproductive output, but does not have an equally strong effect on ecological functions generally associated with this group.     

Estimates of the diffusion resistance of some large sunflower leaves in the field

Studies were made of resistance to gaseous exchange between large sunflower leaves and the bulk air in a crop canopy. Two components of the diffusive pathway for mass and sensible heat were evaluated; A) the resistance from the interior of the leaf to the leaf surface, and B) the resistance from the surface of the leaf through the leaf boundary air layer to the bulk air.     

NOCTURNAL THERMAL EXCHANGE OF CITRUS LEAVES

Turrell , F. M., S. W. Austin , and R. L. Perry . (U. California, Riverside & Los Angeles.) Nocturnal thermal exchange of citrus leaves. Amer. Jour. Bot. 49(2) : 97–109. Illus. 1962.—Cooling rates of leaves were measured with fine thermocouples inserted within the leaf laminae. From these rates, total thermal conductances were calculated for leaves of intact greenhouse-grown lemon cuttings, in the dark, in still air and moving air, and in open laboratory rooms of warm to freezing temperatures. Thermal conductances were also calculated for leaves of 4 commercial varieties of citrus picked from mature trees in the grove and measured in low light, in still air, in a microcosm at warm, constant temperatures. The total conductances were fractionated, first, by determining transpiration rates of detached leaves from both sources, in darkness and in still or moving air, through similar temperature ranges and humidities. From transpiration rates, transpiration conductances were calculated. Second fractions (radiation conductances) were calculated for lemon leaves from far-infrared reflectances; and the third fractions (free-convection conductances) were calculated by subtraction of the sum of the radiation and transpiration conductances from the total. A free-convection-conductance coefficient was calculated for lemon, and then applied to 3 other varieties of citrus for which infrared reflectances were unavailable, to obtain their free-convection conductances. These together with experimentally determined transpiration and total conductances permitted calculation of their radiation fractions. The conductances have been tested for 6 different measured microclimates in which the calculated leaf temperatures averaged ± 0.6 C of the measured temperatures, an error compatible with the precision of field temperature measurements. Total thermal conductances of lemon leaves were higher in both warm, still and warm moving air than in cold, whereas the radiation and free-convection fractions were about equal in still air. The transpiration fractions were very small in warm, still or warm moving air but negligible in cold. In cold still and cold moving air, all the conductances were larger for orange fruit than for lemon leaves. Leaves of plants native to tropical rain forests were more efficient in heat transfer than were leaves from the temperate zone.     

A model of sensible heat transfer across the boundary layer of animal hair coat

• 1.1.|A mechanistic model that predicts the sensible heat loss through the boundary layer of animal hair coat in relation to the climatic environment and hair coat properties is presented.
• 2.2.|The predicted sensible heat loss is positively related with hair density but is negatively related with depth of hair coat.
• 3.3.|Wind speed is a major determinant of the rate of heat loss across the boundary layer especially at low air temperatures.

     

Stomatal control of transpiration from a developing sugarcane canopy

Abstract. Stomatal conductance of single leaves and transpiration from an entire sugarcane (Saccharum spp. hybrid) canopy were measured simultaneously using independent techniques. Stomatal and environmental controls of transpiration were assessed at three stages of canopy development, corresponding to leaf area indices (L) of 2.2, 3.6 and 5.6. Leaf and canopy boundary layers impeded transport of transpired water vapour away from the canopy, causing humidity around the leaves to find its own value through local equilibration rather than a value determined by the humidity of the bulk air mass above the canopy. This tended to uncouple transpiration from direct stomatal control, so that transpiration predicted from measurement of stomatal conductance and leaf-to-air vapour pressure differences was increasingly overestimated as the reference point for ambient vapour pressure measurement was moved farther from the leaf and into the bulk air. The partitioning of control between net radiation and stomata was expressed as a dimensionless decoupling coefficent ranging from zero to 1.0. When the stomatal aperture was near its maximum this coefficient was approximately 0.9, indicating that small reductions in stomatal aperture would have had little effect on canopy transpiration. Maximum rates of transpiration were, however, limited by large adjustments in maximum stomatal conductance during canopy development. The product of maximum stomatal conductance and L. a potential total canopy conductance in the absence of boundary layer effects, remained constant as L increased. Similarly, maximum canopy conductance, derived from independent micrometeorological measurements, also remained constant over this period. Calculations indicated that combined leaf and canopy boundary layer conductance decreased with increasing L such that the ratio of boundary layer conductance to maximum stomatal conductance remained nearly constant at approximately 0.5. These observations indicated that stomata adjusted to maintain both transpiration and the degree of stomatal control of transpiration constant as canopy development proceeded.     

Tribological altruism: A sacrificial layer mechanism of synovial joint lubrication in articular cartilage

Boundary lubrication is characterized by sliding surfaces separated by a molecularly thin film that reduces friction and wear of the underlying substrate when fluid lubrication cannot be established. In this study, the wear and replenishment rates of articular cartilage were examined in the context of friction coefficient changes, protein loss, and direct imaging of the surface ultrastructure, to determine the efficiency of the boundary lubricant (BL) layer. Depletion of cartilage lubricity occurred with the concomitant loss of surface proteoglycans. Restoration of lubrication by incubation with synovial fluid was much faster than incubation with culture media and isolated superficial zone protein. The replenishment action of the BL layer in articular cartilage was rapid, with the rate of formation exceeding the rate of depletion of the BL layer to effectively protect the tissue from mechanical wear. The obtained results indicate that boundary lubrication in articular cartilage depends in part on a sacrificial layer mechanism. The present study provides insight into the natural mechanisms that minimize wear and resist tissue degeneration over the lifetime of an organism.     

Water Vapour and Heat Transfer in Leaves

Factors connected with the formation of water droplets in leavesby distillation from the mesophyll to the epidermis were investigatedin a number of species. It was concluded that in illuminatedleaves water droplets form principally on the inner walls ofguard and subsidiary cells, and sometimes below the anticlinalwalls of epidermal cells, because these sites are cooler thanthe rest of the leaf. Under more isothermal conditions any waterdroplets that had formed disappeared. With increasing waterstress water droplets did not form so readily, though distillationwas occurring. Few water droplets were observed in leaves outof doors that had open stomata. Significant temperature gradientswere measured across leaves with thermocouples, but these werelarger than were gradients calculated from measured thermalconductivities of leaves. The evaporation resistances of theinner walls of the epidermis and of the mesophyll were foundto be similar. This led to the conclusion that the hydrophobicityof the surfaces of these tissues is similar. Water transferin leaves in the vapour phase was found to be more responsiveto temperature than to water stress gradients. leaf, evaporation, distillation, heat loss, transpiration     

Effect of Joule Heating and Thermal Radiation in Flow of Third Grade Fluid over Radiative Surface

This article addresses the boundary layer flow and heat transfer in third grade fluid over an unsteady permeable stretching sheet. The transverse magnetic and electric fields in the momentum equations are considered. Thermal boundary layer equation includes both viscous and Ohmic dissipations. The related nonlinear partial differential system is reduced first into ordinary differential system and then solved for the series solutions. The dependence of velocity and temperature profiles on the various parameters are shown and discussed by sketching graphs. Expressions of skin friction coefficient and local Nusselt number are calculated and analyzed. Numerical values of skin friction coefficient and Nusselt number are tabulated and examined. It is observed that both velocity and temperature increases in presence of electric field. Further the temperature is increased due to the radiation parameter. Thermal boundary layer thickness increases by increasing Eckert number.     

The air space of an egg: an embryonic "cold nose"?

Experiments have been performed to measure the cooling rates of air space and equatorial regions of the incubated egg. The air space has a low specific heat so that it cools faster than the rest of the egg when an incubating bird leaves the nest. This rapid cooling of the air space reduces the water loss that would occur when a bird leaves the nest by 50% when compared with the water loss from an equivalent area of the rest of the shell. The overall influence of the air space is probably to reduce water losses during incubation by 10–15%.