Leaf temperature error from heat conduction along thermocouple wires

Abstract

Heat conduction through the wires is one source of thermocouple (TC) error. Leaf temperature measurement may be affected by this error if the leaf-to-air temperature difference is large and contact between TC and leaf is inadequate. Selection of small diameter TCs with low thermal conductivity, as well as good contact with the leaf, are possible solutions to the problem. A laboratory experiment was carried out to determine conduction error as a function of TC-type, wire diameter, insulation and length of contact between wire and leaf. Most of the tests were conducted with a thin plastic plate, as a leaf-substitute, to ensure repetitiveness. Some measurements were also made with in vivo pepper and tomato leaves, to determine a correction factor. Different lengths of the TC wires were glued to the plate, or leaf, to ensure good contact. Controllable temperature differences were established with a thermo-electric cooler. A conduction error, τ, of 1% (relative to the leaf-to-air temperature difference) is to be expected when a length of about 22 mm of AWG 40 (0.08 mm diameter), teflon-insulated type-T (copper–constantan) thermocouple is glued to a leaf. Removing the insulation reduces this length to 14 mm, and replacing the insulated type-T thermocouple by an insulated type-K (chromel–alumel) thermocouple of the same gage, requires about 10 mm for the same 1% error. An approximate theoretical solution was obtained, which relates relative measurement error, τ, to normalized glued length, ξ, in the form τ = exp{− ξ}. This relationship can be used to estimate errors with other TCs.