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SOIL PHYSICS

Analytical Solution of Heat Pulse Method in a Parallelepiped Sample Space with Inclined Needles

^a Laboratory for Plant–Soil Interaction Processes, Ministry of Education, College of Resources and Environment, China Agricultural University, No. 2 Yuanmingyuan Xi Lu, Beijing 100094, P.R. China
^b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
^c Dep. of Soil Science, Univ. of Saskatchewan, Saskatoon, SK, Canada S7N5A8

^* Corresponding author (libg{at}cau.edu.cn).

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 to be the polar angle of needle deviation from the z axis and 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 = 1° and = 0°. Model errors in C and k were about –11.2 and 12.1%, respectively, for an inclined sensor needle with = 1° and = 180°. When –6 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 2°.

Abbreviations: ABC, adiabatic boundary condition • DPHP, dual-probe heat pulse • PILS, pulsed infinite line source • ZST, zero surface temperature

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