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

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°.