14.5.3 Sensible heat exchange

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An exchange of sensible heat occurs when leaves are either warmer or cooler than the surrounding air. The rate of exchange is proportional to the difference in temperature between a leaf and its surrounding air. Heat transfer occurs by molecular conduction across a thin boundary layer of air which is ‘attached’ to both sides of any leaf. Boundary-layer resistance to heat transfer varies according to the thickness of that layer which in turn is a function of leaf geometry (plane, cylinder, sphere) and imposed wind speed. For a flat leaf, mean boundary-layer thickness (δ) can be calculated as:

 δ= 6.5 (d/υ)1/2 (14.4)

where δ is leaf width in metres (m),  υ is wind speed in metres per second (m s–1) and δ is in millimetres (mm). Taking a case where d = 0.05 m and υ = 1 m s–1,  δ will be 1.5 mm. Other relationships will apply to different shapes.

Boundary layers around leaves remain laminar until the product of wind speed and leaf width exceeds about 0.3 m2 s–1. Above this value, boundary layers become turbulent, and will occur at a wind speed of around 6 m s–1 when d = 0.05 m (cf. the example above).

Sensible heat transfer between leaf and air can also occur by free convection. This process is much more efficient in terms of heat flux density, and arises from the circulation of fluid over an object which is in turn maintained by gradients in temperature, and hence fluid density.