Buoyancy effect on forced convection in the leaf boundary layer

Abstract

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 (TL‐TA) under low wind velocities. The visualized air flow was found to become more unstable and buoyant at higher TL‐TA. 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 (GA) for mixed convection, which became higher with higher TL‐TA as compared with the conductance for pure forced convection without buoyancy. This increase in GA 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’.

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

“…During mixed convection, the simultaneous effects of buoyancy forces and forced convection are expected to result in more intense heat dissipation in comparison with forced convection alone (Kitano & Eguchi 1990). If the Nusselt number of quad2 is calculated by using standard relationships such as given by Schuepp (1993) ( Nu = 0·679 Pr 0·33 Re 0·5 for uniform heat flux, with Pr = Prandtl number) and if the expected heat flux C for the whole structure due to forced convection is calculated as C = Nu ρ c p κ ( T leaf – T air )/ d (with d = characteristic dimension, amounting to 41·6 mm in this case, κ = thermal diffusivity of air and the simulated mean temperature of the whole model structure applied as T leaf ) (Dixon & Grace 1983), the total heat flux of is about 84 J m −2 s. The computer simulation yielded a total heat flux of about 84·51 J m −2 s. Heat dissipation of this small quadratic object by free convection obviously does not significantly contribute to the value given by the standard relationship for forced convection despite the fact that the Gr / Re 2 indicated the presence of mixed convection (see above).…”

“…Kitano & Eguchi (1990) studied the effect of buoyancy forces on forced convection by using two different entire leaf models with maximum widths of 23 and 11·5 cm. The quantitative effects proved to differ strongly according to the conditions and could be very small even if the ratio of Gr / Re 2 indicated significant influence of buoyancy on heat transfer (Kitano & Eguchi 1990). This might be due to the location of the buoyancy plume.…”

“…This might be due to the location of the buoyancy plume. The photographs of Kitano & Eguchi (1990) showed that, under appropriate conditions, a plume can develop only at the end of the leaf (relative to the leading edge). The same flow behaviour was demonstrated for the model structures that were considered in the present study; the plume is not operative at the surface; it develops at the end of the model structure or even behind it (Fig.…”

“…Vogel (1970) found for mixed convection of complex leaf shapes, among other results, that the measured heat dissipation values were not correlated with a simple Nusselt number (relating the thickness of the boundary layer to the characteristic dimension d of an object), which is based on a weighted mean width. Kitano & Eguchi (1990) demonstrated complex buoyancy effects on heat dissipation during mixed convection and documented the modifi-cation of the flow field by the developing buoyancy plume. Heat transfer between leaf and air under the regime of mixed convection can thus not be simply calculated or estimated by approximation approaches used for purely forced convection cases.…”

Tansley Review No. 59 Leaf boundary layers

“…Even fewer are studies in the tratisition region between forced atid free convection, atid a satisfactory descriptioti of the highly complex buoyancy effects in mixed convection on leaf boutidary layers remains a challenge (Kitano & Eguchi, 1990). The relative paucity of empirical studies may result from a perception that conditions of very low wind may be rare in the natural environment, but it is precisely under such conditions that lethal temperatures are most likely to occur.…”