Boundary Layer Flow Past a Stretching Surface in a Porous Medium Saturated by a Nanofluid: Brinkman-Forchheimer Model

In this study, the steady forced convection flow and heat transfer due to an impermeable stretching surface in a porous medium saturated with a nanofluid are investigated numerically. The Brinkman-Forchheimer model is used for the momentum equations (porous medium), whereas, Bongiorno’s model is used for the nanofluid. Uniform temperature and nanofluid volume fraction are assumed at the surface. The boundary layer equations are transformed to ordinary differential equations in terms of the governing parameters including Prandtl and Lewis numbers, viscosity ratio, porous medium, Brownian motion and thermophoresis parameters. Numerical results for the velocity, temperature and concentration profiles, as well as for the reduced Nusselt and Sherwood numbers are obtained and presented graphically.     

Thermoregulation and the determinants of heat transfer in Colias butterflies

Summary As a means of exploring behavioral and morphological adaptations for thermoregulation in Colias butterflies, convective heat transfer coefficients of real and model butterflies were measured in a wind tunnel as a function of wind speed and body orientation (yaw angle). Results are reported in terms of a dimensionless heat transfer coefficient (Nusselt number, Nu) and a dimensionless wind speed (Reynolds number, Re), for a wind speed range typical of that experienced by basking Colias in the field. The resultant Nusselt-Reynolds (Nu-Re) plots thus indicate the rates of heat transfer by forced convection as a function of wind speed for particular model geometries.For Reynolds numbers throughout the measured range, Nusselt numbers for C. eurytheme butterflies are consistently lower than those for long cylinders, and are independent of yaw angle. There is significant variation among individual butterflies in heat transfer coefficients throughout the Re range. Model butterflies without artificial fur have Nu-Re relations similar to those for cylinders. Heat transfer in these models depends upon yaw angle, with higher heat transfer at intermediate yaw angles (30–60°); these yaw effects increase with increasing Reynolds number. Models with artificial fur, like real Colias, have Nusselt numbers which are consistently lower than those for models without fur at given Reynolds numbers throughout the Re range. Unlike real Colias, however, the models with fur do show yaw angle effects similar to those for models without fur.The independence of heat loss from yaw angle for real Colias is consistent with field observations indicating no behavioral orientation to wind direction. The presence of fur on the models reduces heat loss but does not affect yaw dependence. The large individual variation in heat transfer coefficients among butterflies is probably due to differences in fur characteristics rather than to differences in wing morphology.Finally, a physical model of a butterfly was constructed which accurately simulates the body temperatures of basking Colias in the field for a variety of radiation and wind velocity conditions. The success of the butterfly simulator in mimicking Colias thermal characteristics confirms our preliminary understanding of the physical bases for and heat transfer mechanisms underlying thermoregulatory adaptations in these butterflies.     

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.     

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.     

Air movement and heat loss from sheep. I. Boundary layer insulation of a model sheep, with and without fleece

A model sheep, made from metal cylinders and hemispheres, was heated electrically. Heat loss by forced convection in a wind tunnel was analysed in terms of the dependence of the Nusselt number (Nu) on Reynolds number (Re). For a bare trunk Nu = 0.095 Re0.684, but with fleece covering the trunk to a depth of 3.5 cm, Nu = 0.0112 Re0.875 when the mean radiative temperature of the the coat was taken as the surface temperature. Heat transfer by convection from the whole body, including legs, was described by Nu = 0.029 Re0.80. However, a bulk Nesselt number should not be used to estimate heat loss from a live sheep in a hot environment if the windspeed is below about 4 m s-1 because the relation between mean surface temperature, Nusselt number and convective heat flux is not unique.     

Buoyancy effect on forced convection in the leaf boundary layer

Abstract. Mixed convection (forced convection plus free convection) in the leaf boundary layer was examined by air flow visualization and by evaluation of the boundary layer conductance at different leaf-air temperature differences ( T _L- T _A) under low wind velocities. The visualized air flow was found to become more unstable and buoyant at higher T _L- T _A. An ascending longitudinal plume was induced along the upper surface, and the air flow along the lower surface ascended after passing the trailing leaf edge. The air flow modified by buoyancy was considered to result in an increase in boundary layer conductance ( G _A) for mixed convection, which became higher with higher T _L- T _A as compared with the conductance for pure forced convection without buoyancy. This increase in G _A appeared larger at larger Grashof number (Gr) and at smaller Reynolds number (Re). The dependences of buoyancy effect on Gr and Re were related to 'edge-effects'.     

Heat and mass exchange processes between the surface of the human body and ambient air at various altitudes

 The rates of convection and evaporation at the interface between the human body and the surrounding air are expressed by the parameters convective heat transfer coefficient h _c, in W m^–2°C^–1 and evaporative heat transfer coefficient h _e, W m^–2 hPa^–1. These parameters are determined by heat transfer equations, which also depend on the velocity of the airstream around the body, that is still air (free convection) and moving air (forced convection). The altitude dependence of the parameters is represented as an exponential function of the atmospheric pressure p: h _c∼p ⁿ and h _e∼p ^1–n, where n is the exponent in the heat transfer equation. The numerical values of n are related to airspeed: n=0.5 for free convection, n=0.618 when airspeed is below 2.0 ms^–1 and n=0.805 when airspeed is above 2.0 ms^–1. This study considers the coefficients h _c and h _e with respect to the similarity of the two processes, convection and evaporation. A framework to explain the basis of established relationships is proposed. It is shown that the thickness of the boundary layer over the body surface increases with altitude. As a medium of the transfer processes, the boundary layer is assumed to be a layer of still air with fixed insulation which causes a reduction in the intensity of heat and mass flux propagating from the human body surface to its surroundings. The degree of reduction is more significant at a higher altitude because of the greater thickness of the boundary layer there. The rate of convective and evaporative heat losses from the human body surface at various altitudes in otherwise identical conditions depends on the following factors: (1) during convection – the thickness of the boundary layer, plus the decrease in air density, (2) during evaporation (mass transfer) – the thickness of the boundary layer, plus the increase with altitude in the diffusion coefficient of water vapour in the air. The warming rate of the air volume due to convection and evaporation is also considered. Expressions for the calculation of altitude dependences h _c (p) and h _e (p) are suggested. Received: 23 June 1998 / Accepted: 10 February 1999     

RADIATION AND CONVECTION IN CONIFERS

The transfer of energy to and from a conifer branch involves solar radiation, thermal radiation from the ground, atmosphere, and surroundings, thermal emission by the branch, and free convection in still air and forced convection in wind. It is necessary to know the actual surface area of the branch, the effective area for absorbing sunlight, the effective area for absorbing long wave thermal radiation and for emission, and the free and forced convection coefficients. These parameters are determined using silver castings of blue spruce and white fir branches suspended in an evacuated radiation chamber and in a wind tunnel. The actual surface area of a branch is determined by means of an electrolytic technique. Numerical examples are given for energy transfer in a natural environment for conifers and comparison is made to a broad deciduous type of leaf. The role of transpiration in the energy transfer process is discussed.     

Boundary layer conductance of the leaves of some tropical timber trees

Abstract The boundary layer conductance of brass models of leaves exposed in a wind tunnel was determined from their cooling characteristics. Conductances were generally very low, as expected from large leaves. Nusselt numbers were calculated from the rates of heat loss, so that the results could be compared with established theory. There was generally good agreement between observed and calculated values. Leaves with veins displayed an apparent transition from a laminar to a turbulent boundary layer, and so did leaves inclined at an angle from the horizontal. In still air the observed rates of heat loss by natural convection were substantially higher than those calculated.     

Heat transfer simulation using energy conservative dissipative particle dynamics

Dissipative particle dynamics with energy conservation (eDPD) was used to investigate conduction heat transfer in two dimensions under steady-state condition. Various types of boundary condition were implemented to the conduction domain. Besides, 2D conduction with internal heat generation was studied and the heat generation term was used to measure the thermal conductivity and diffusivity of the eDPD system. The boundary conditions used include both the Neumann and Dirichlet boundary conditions. The Neumann boundary condition was applied via adiabatic surfaces and surfaces exposed to convection heat transfer. The DPD simulations were compared to analytical solutions and finite-difference techniques. It was found that DPD appropriately predicts the temperature distribution in the conduction regime. Details of boundary condition implementation and thermal diffusivity measurement are also described in this paper.     

Tansley Review No. 59 Leaf boundary layers

Studies of heat and mass exchange between leaves and their local environment are central to our understanding of plant-atmosphere interactions. The transfer across aerodynamic leaf boundary layers is generally described by non-dimensional expressions which reflect largely empirical adaptations of engineering models derived for flat plates. This paper reviews studies on leaves, and leaf models with varying degrees of abstraction, in free and forced convection. It discusses implecations of finding for leaf morphology as it affects – and is affected by – the local microclimate. Predictions of transfer from many leaves in plant communities are complicated by physical and physiological feedback mechanisms between leaves and their environment. Some common approaches, and the current challenge of integrating leaf-atmosphere interactions into models of global relevance, are also briefly addressed.     

Experimental study on convective heat transfer coefficient of the human body

1. 1. The convective heat transfer coefficient of the human body is essential to predict convective heat loss from the body.

2. 2. The object of this paper is to calculate the convective heat transfer coefficient of the human body using heat flow meters and to estimate the thermally equivalent sphere and cylinder to the human body.

3. 3. The experimental formulae of the convective heat transfer coefficient for the whole body were obtained by regression analysis for natural, forced and mixed convection.

4. 4. Diameters of the thermally equivalent sphere and cylinder of the human body were calculated as 12.9 and 12.2 cm, respectively.

Relationships among shoot sinks for resources exported from nodal roots regulate branch development of distal non-rooted portions of Trifolium repens L

Two manipulative experiments tested hypotheses pertaining to the correlative control exerted by nodal roots on branch development of the distal non-rooted portion of Trifolium repens growing clonally under near-optimal conditions. The two experiments, differing in their pattern of excision to manipulate the number of branches formed at the first 9-10 phytomers distal to the youngest nodal root, each found that after 20 phytomers of growth the total number of lateral branches formed on the primary stolon remained between five and seven regardless of where the branches formed along the stolon. Additional treatments established that nodal roots influenced branch development via relationships among shoot sinks for the root-supplied resources rather than through variation in the supply of such resources induced by fluctuations in photosynthate supply to roots from branches. Regression analysis of data pooled from treatments of both experiments confirmed that shoot-sink relationships for root- supplied resources controlled the branching processes on the non-rooted portion of plants. A disbudding treatment, which removed all the apical and axillary buds present on basal branches, but left other branch tissues intact, increased branch development of the apical region in the same way as did complete excision of the basal lateral branches. The apical buds and the elongation processes occurring immediately proximal to the buds were thus identified as strong sinks for the root-supplied resources. Such results suggest that branch development on the non-rooted shoot portion distal to the youngest nodal root is regulated by competition among sinks for root-derived resources, of limited availability, necessary for the processes of elongation of axillary buds and the primary stolon apical bud.     

极端干旱区大气边界层厚度时间演变及其与地表能量平衡的关系

主要采用ECMWF的地表和大气产品分析了中国西北极端干旱区大气边界层厚度与地表能量通量的时间变化特征,同时,结合探空加强观测分析了大气边界层演变的可能因素.得出:西北极端干旱区大气边界层厚度呈现出季节性的年际和年代际变化,夏季大气边界层厚度呈下降趋势,春、秋季节呈现出先增加后降低的趋势,冬季以阶段性降低趋势为主,20世纪80年代是大气边界层厚度的转折时期;感热通量是极端干旱区大气边界层发展的主要热力因素;由于夏季净辐射量、地气温差、粗糙度以及风速等因子随时间演变而呈降低趋势,潜热通量呈增加趋势,导致了边界层高度形成的热力作用减弱,边界层厚度降低;同时,粗糙度和风速也是大气边界层发展的主要动力因素,由于边界层粗糙度和风速降低,促使垂直风切变减小,湍流动力作用减弱,也会导致边界层厚度降低.     

Biomass partitioning and water content relationships at the branch and whole-plant levels and as a function of plant size in Elaeagnus mollis populations in Shanxi, North China

Understanding of the biomass (dry weight) allocation and water relations in populations will provide useful information on the growth patterns and resource-allocation dynamics. By destructive sampling, foliage, branch and root biomass were measured in the endangered shrub Elaeagnus mollis populations growing in Shanxi province, North China. Biomass partitioning and water content relationships were compared at the branch and whole-plant levels, and as a function of basal diameter (plant size). The biomass was mainly distributed in the bigger branches at the branch level, and in the branch wood at the whole-plant level, and branch biomass (but not foliage or root biomass) increases significantly with increasing basal diameter. As a result, branch wood became the major biomass pool, even though considerable biomass was also allocated to the roots. However, the relative water content decreased from the periphery of the crown to the interior of the shrub at the branch level, and from the aboveground to the belowground at the whole-plant level though no significant variation among foliage, branches, and roots. Yet it increased significantly for the whole-plant with increasing basal diameter. The ratio of belowground to aboveground biomass was smaller than 1.0, even as a function of basal diameter. These growth responses indicated a strong adaptation to the shrub’s growing conditions. Biomass was primarily allocated above the ground and the aboveground components grew faster than the belowground one.     

Biomass partitioning and water content relationships at the branch and whole-plant levels and as a function of plant size in Elaeagnus mollis populations in Shanxi, North China

Understanding of the biomass (dry weight) allocation and water relations in populations will provide useful information on the growth patterns and resource-allocation dynamics. By destructive sampling, foliage, branch and root biomass were measured in the endangered shrub Elaeagnus mollis populations growing in Shanxi province, North China. Biomass partitioning and water content relationships were compared at the branch and whole-plant levels, and as a function of basal diameter (plant size). The biomass was mainly distributed in the bigger branches at the branch level, and in the branch wood at the whole-plant level, and branch biomass (but not foliage or root biomass) increases significantly with increasing basal diameter. As a result, branch wood became the major biomass pool, even though considerable biomass was also allocated to the roots. However, the relative water content decreased from the periphery of the crown to the interior of the shrub at the branch level, and from the aboveground to the belowground at the whole-plant level though no significant variation among foliage, branches, and roots. Yet it increased significantly for the whole-plant with increasing basal diameter. The ratio of belowground to aboveground biomass was smaller than 1.0, even as a function of basal diameter. These growth responses indicated a strong adaptation to the shrub’s growing conditions. Biomass was primarily allocated above the ground and the aboveground components grew faster than the belowground one.     

Computer-based analysis of steady-state and transient heat transfer of small-sized leaves by free and mixed convection

In order to study convective heat transfer of small leaves, the steady‐state and transient heat flux of small leaf‐shaped model structures (area of one side = 1730 mm²) were studied under zero and low (= 100 mm s^?1) wind velocities by using a computer simulation method. The results show that: (1) distinct temperature gradients of several degrees develop over the surface of the model objects during free and mixed convection; and (2) the shape of the objects and onset of low wind velocities has a considerable effect on the resulting temperature pattern and on the time constant τ. Small leaves can thus show a temperature distribution which is far from uniform under zero and low wind conditions. The approach leads, however, to higher leaf temperatures than would be attained by ‘real’ leaves under identical conditions, because heat transfer by transpiration is neglected. The results demonstrate the fundamental importance of a completely controlled environment when measuring heat dissipation by free convection. As slight air breezes alter the temperature of leaves significantly, the existence of purely free convection appears to be questionable in the case of outdoor conditions. Contrary to the prognoses yielded by standard approximations, no quantitative effect of buoyancy on heat transfer under the considered conditions could be detected for small‐sized leaf shapes.     

Coping with branch excision when measuring leaf net photosynthetic rates in a lowland tropical forest

Measuring leaf gas exchange from canopy leaves is fundamental for our understanding of photosynthesis and for a realistic representation of carbon uptake in vegetation models. Since canopy leaves are often difficult to reach, especially in tropical forests with emergent trees up to 60 m at remote places, canopy access techniques such as canopy cranes or towers have facilitated photosynthetic measurements. These structures are expensive and therefore not very common. As an alternative, branches are often cut to enable leaf gas exchange measurements. The effect of branch excision on leaf gas exchange rates should be minimized and quantified to evaluate possible bias. We compared light-saturated leaf net photosynthetic rates measured on excised and intact branches. We selected branches positioned at three canopy positions, estimated relative to the top of the canopy: upper sunlit foliage, middle canopy foliage, and lower canopy foliage. We studied the variation of the effects of branch excision and transport among branches at these different heights in the canopy. After excision and transport, light-saturated leaf net photosynthetic rates were close to zero for most leaves due to stomatal closure. However, when the branch had acclimated to its new environmental conditions—which took on average 20 min—light-saturated leaf net photosynthetic rates did not significantly differ between the excised and intact branches. We therefore conclude that branch excision does not affect the measurement of light-saturated leaf net photosynthesis, provided that the branch is recut under water and is allowed sufficient time to acclimate to its new environmental conditions.     

An open-air system for exposing forest-canopy branches to ozone pollution

We developed a chamberless system to expose branches to elevated concentrations of ozone with little alteration of micro-meteorological conditions. In a 35-year-old stand of sugar maple (Acer saccharum Marsh.), scaffolding and a platform (14 m in height) provided access to 10 branches and ten paired controls within the canopy. Ozone was delivered to the canopy through a manifold and an array of loops (38 cm in diameter) of teflon tubing individually fitted to each branch. Ozone-enriched air was discharged through numerous small holes in each loop positioned beneath the exposed foliage. A sampling system controlled by a microcomputer monitored ozone concentrations for each loop by means of composite air samples from 12 leaves, drawn through small teflon tubes (1.65 mm diameter) attached to the petioles. On average, coefficients of variation for ozone concentrations for the sample points within each branch loop were less than 50%. Between 0900 and 1700 h for 68 d of exposure, the mean hourly ozone concentrations among the branches averaged 95nmol mol⁻¹ (±13SD), about twice the ambient mean. Frequency distributions of mean hourly concentrations during exposure were unimodal and approximately log-normal, comparable to ambient ozone concentrations. The open-air loop system enables exposure of branches to gaseous pollutants under relatively natural conditions.     

Biology of the bamboo Chusquea culeou (Poaceae: Bambusoideae) in southern Argentina

Over a period of 7 years the biology and phenotypic variability of Chusquea culeou were studied at 5 locations in cool temperate forests of southern Argentina. Excavated rhizomes had an average of 1.1 successful rhizome buds, and an average of 2.1 years elapsed between successive generations of rhizomes. Rhizome buds usually develop within the first four years after a rhizome forms. Height, volume and weight of a culm can be calculated from its diameter 1 m above the ground. Culm size, length of foliage leaf blades, and pattern of secondary branching differed among study sites. Dead culms were numerous and commonly remained erect for more than 7 years after dying. New culm shoots appear in spring and reach full size within a few months. Shoots can grow more than 9 cm/day. Less than half of the shoots survived a year; most were killed by moth larvae. Multiple primary branch buds emerge through the culm leaf sheaths in the second spring. The mean number of branch buds at mid-culm nodes varied between 34.8 and 81.5, and the mean number of primary branches was between 22.8 and 40.8. Number and length of branches, and number and length of foliage leaf blades at each node is related to the position of the node on a culm. Most branches grow about 3 cm and produce 1 to 3 foliage leaves annually. Foliage leaf blades generally live 2 years or more; few survive 6 years. Relative lengths of foliage leaf blades and their spacing along a branch permit recognition of annual cohorts.Both gregarious and sporadic flowering have been reported, and every year a few isolated plants flower and die. Length of the life cycle is unknown. Seedlings require up to 15 years to produce culms of mature size. Foliage branches may live more than 23 years, and culms may survive 33 years. Extensive loss of new shoots to predation suggests that gregarious flowering may be driven by a need to escape parasitism. C. culeou clumps expand slowly. Average annual rate of increase of the number of live culms in a clump was 4.6%. Methods of seed dispersal are undocumented. A dense stand of Chusquea culeou had an estimated phytomass of 179 tons/hectare (dry weight), 28% of which was underground. Net annual production was about 16 t/ha dry weight.