Modelling effective thermal conductivity coeficient of Salix viminalis L. dried pieces

Abstract

The effective thermal conductivity coefficient (λef) of willow Salix Viminalis L. dried pieces was studied by drying the willow at various temperatures. The willow was acquired from the energy crop plantation of the University of Agriculture in Krakow. The dried pieces of willow were covered with insulating coating and then heated in thermal chamber with constant drying agent (air) velocity under various conditions of drying air temperature: 313.15-343.15 K (40-70 °C). The experiment set up caused the longitudinal direction of the heat flow. Single piece of willow was heated in 15 minutes period. With the use of two thermocouples the temperature of single sample was measured in the two points: on the surface and at half-height in the middle. The specific density and porosity of the willow particles were measured with AccuPyc II 1340 and GeoPyc 1360 pycnometers. On basis of the Fourier equation of heat transfer and concept of reverse problem formulation the thermal conductivity coefficient (λ) was calculated. The effective thermal conductivity coefficient (λef) was determined using a general model, in which porosity and density of the willow pieces were covered. The effect of the drying agent temperature on the (λef) coefficient was investigated. The rise in the air temperature led to an increase in the (λef) coefficient rate in the experiments. At the 15th minute the (λef) coefficient varied from 0.038 (W⋅m-1⋅K-1) at 313.15 K (40 °C) temperature and 0.086 (W⋅m-1⋅K-1) at 343.15 K (70 °C). The performance of the model was evaluated by comparing the correlation coefficient (R2), root mean square error (RMSE), mean absolute percentage error (MAPE) and the chi-square (χ2) between the observed and the predicted effective thermal conductivity coefficient (λef) ratios. The calculated statistical parameters varied over the studied temperature range: RMSE was below 0.014, MAPE ranged from 6 to 17 %, R2 ranged from 0.91 to 0.97, χ2 below 0.019 showed good model adjustment to the experimental data.