Temperature evolution of two parallel composite cylinders with contact resistances and application to thermal dual-probes

• Published in: International journal of heat and mass transfer 2014-02, Vol.69, p.481-492
• Main Authors: Macher, W., Kömle, N.I., Bentley, M.S., Kargl, G.
• Format: Article
• Language: English
• Subjects: Bessel functions expansion; Contact; Evolution; Heat capacity; Heated composite cylinder; Heaters; Mathematical analysis; Mathematical models; Needles; Numerical inverse Laplace transform; Specific heat; Thermal dual-probe; Thermal surface conductance; Thermal surface resistance
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2013.10.047

Thermal dual-probes are frequently used to measure the heat capacity and diffusivity of soil samples. These probes mostly consist of two thin parallel needles, one serving as a heater and the other as a temperature sensor. Originally a simple infinite line source model was applied to describe the temperature evolution around the heated needle and to evaluate dual-probe measurements. Quite recently an analytical approach by Knight et al. (2012) for the infinitely long dual-probe made it possible to take the finite radius and heat capacity of the probes into account. In the present article this theory is extended to allow for surface resistances at the boundaries between the probes and the sample and, in addition, facilitating a subdivision of the probes into cylindrical cores and surrounding tubular sheaths, which is a rough representation of the needles’ inner structure. In comparison with computer simulations by finite element solvers, the extended semi-analytical approach enables us to determine the influence of contact resistances with shorter computation time, providing an efficient method for the evaluation of dual-probe measurements.