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Analytical Solution of Heat Pulse Method in a Parallelepiped Sample Space with Inclined Needles
Author(s) -
Liu Gang,
Li Baoguo,
Ren Tusheng,
Horton Robert,
Si Bing C.
Publication year - 2008
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj2007.0260
Subject(s) - parallelepiped , thermal diffusivity , adiabatic process , materials science , thermal conductivity , line source , thermal , mechanics , analytical chemistry (journal) , optics , geometry , composite material , thermodynamics , physics , chemistry , mathematics , chromatography
The heat pulse method enables estimation of soil thermal diffusivity ( k ), volumetric heat capacity ( C ), thermal conductivity, and water content. The heater needle and temperature‐sensing needle may deflect during probe insertion into soils. The impact of needle deflection on estimates of C and k has not been fully studied theoretically or experimentally. We defined θ to be the polar angle of needle deviation from the z axis and φ to be the azimuthal angle in the x–y plane. Transient‐state analytical solutions were derived for an inclined and pulsed finite line source in a parallelepiped sample with zero surface temperature and adiabatic boundary conditions. For a heat pulse sensor with 6‐mm needle spacing and a heater needle of 4‐cm length in a given parallelepiped (5 by 5 by 5 cm, assumed to be filled with air‐dry sand), model errors in C and k were about −11.3 and 12.1%, respectively, for an inclined heater needle with θ = 1° and φ = 0°. Model errors in C and k were about −11.2 and 12.1%, respectively, for an inclined sensor needle with θ = 1° and φ = 180°. When −6 ≤ θ ≤ 6° for either the heater or the sensor needle, the temperature curves could be approximated rather well by a pulsed infinite line source model with a modified probe spacing that accounted for the inclination. For various heating durations and strengths, the errors in both k and C were relatively constant when all other parameters were fixed; however, the errors in both C and k decreased monotonically and slowly as k increased. The model errors in C and k were similar for four soil conditions with different thermal properties in the range −6 ≤ θ ≤ 2°.