Boundary Layers of Air Adjacent to Cylinders

Abstract

Using existing heat transfer data, a relatively simple expression was developed for estimating the effective thickness of the boundary layer of air surrounding cylinders. For wind velocities from 10 to 1000 cm/second, the calculated boundarylayer thickness agreed with that determined for water vapor diffusion from a moistened cylindrical surface 2 cm in diameter. It correctly predicted the resistance for water vapor movement across the boundary layers adjacent to the (cylindrical) (3,7,13,16,17,29). Here we will consider that a hypothetical or effective boundary layer of uniform thickness surrounds a cylinder. This highly simplified approach sacrifices a detailed description; e.g., the complicated dependency of heat transfer on angular position around a cylinder (16, 29) is not incorporated. However, relatively simple relations are obtained for estimating the boundarylayer thickness controlling heat and gas fluxes from cylindrical plant surfaces. THEORYWe will define a thermal boundary layer of effective thickness a such that the temperature goes from that at the surface of the cylinder (T,) to that of the ambient air (Ta) across this hypothetical distance. Assuming that there are no heat sources within the boundary layer, and for the case of cylindrical symmetry (and no change along the axis of the cylinder, which is assumed to be infinitely long), the heat conducted per unit area and per unit time in a radial direction to or away from the surface can be represented as follows:Boundary-layer theory (3,17,29) has been applied to the study of the energy and gas fluxes for leaves, which are generally treated as flat plates (5,8,21,24,28 where JH is the average heat flux at the surface of a cylinder of radius r, and k is the thermal conductivity coefficient (13,16). Heat transfer from objects is also described by JH = h(T, -Ta), where h is the conventional heat transfer coefficient averaged over the cylindrical surface (8,13,16

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Plant Biomechanics: An Engineering Approach to Plant Form and Function.

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Importance of Aerodynamic Resistance to Water Use Efficiency in Three Conifers under Field Conditions

“…A combination of relatively low stomatal resistances (< 300 seconds per centimeter) and low wind speeds (< 30 centimeters per second) led to substantial contributions of the aerodynamic resistance (R",) Several investigations have examined the magnitude of the aerodynamic, or boundary air layer, resistance to heat and mass transfer for a variety of leaves, or leaf replicas (3, 8-12, 14, 15, 18, 19). Only a few of these studies have attempted to estimate the quantitative influence of this resistance on transpiration and photosynthesis under field conditions (13,14,16). No attempt has been made to estimate the quantitative importance of this resistance based on simultaneous measurements of the aerodynamic properties and gas exchange rates of leaves or shoots under natural field conditions.…”

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