Measurement of Thermophysical Properties of Loose Coal Based on Multi-dimensional Constant Temperature Boundary Unsteady Heat Transfer Model

Abstract

Based on the unsteady state heat transfer model, production solution method is proposed to calculate the thermal diffusivity and thermal conductivity of loose coal. By constructing the heat transfer model of the infinite large plate and the infinitely long cylinder, the temperature rise formula of the production solution method is established. The measured temperature rise is then used by the MATLAB programming software to inversely calculate the thermophysical parameters of the loose coal. During the experiment, a constant temperature boundary was constructed using an incubator and a high thermal conductivity copper cylindrical case. The experiment selected anthracite, bituminous coal in Panyi Mine, and bituminous coal in Lizuo Mine for thermophysical property measurement. The results show that the relative deviation between each measurement result and related literature is within 5 %, and each sample is tested three times. The deviations are less than 5 %, which verify the stability of the test method. Finally, the experimental model was established in the ANSYS FLUENT simulation software, and the thermophysical parameters of the measured coal samples were substituted into the model for simulation calculation. It was found that the simulation temperature rise was consistent with the measured temperature rise.

Appendix: Derivation of Eq. 3

• 1. The temperature response of an infinite plate at a given surface temperature. For the infinite plate whose thermophysical properties are constant with initial temperature T₀ and thickness l, one side (x = l) temperature suddenly changes from T₀ to T_w, and the other side x = 0) is always maintained adiabatic. In the slab during reaction time τ, the temperature of any thickness x is T. The temperature response is

  $$ \Theta_{\text{p}} (x,\tau ){ = }\frac{{T_{w} - T}}{{T_{w} - T_{0} }}{ = }\sum\limits_{n = 1}^{\infty } {( - 1)^{n + 1} \cdot \frac{4}{(2n - 1)\pi } \cdot \cos \left( {\frac{(2n - 1)\pi x}{2l}} \right) \cdot e^{{\frac{{ - (2n - 1)^{2} \pi^{2} }}{4}Fo}} }. $$

• 2. The temperature response of an infinitely long cylinder at a given surface temperature.

  For the infinitely long cylinder whose thermophysical properties are constant with initial temperature T₀ and radius R, its surface temperature suddenly changes from T₀ to T_w. In the cylinder during the reaction time τ, the temperature of any radius r is T. The temperature response is

  $$ \Theta_{\text{c}} (r,\tau ) = \frac{{T_{w} - T}}{{T_{w} - T_{0} }} = \sum\limits_{n = 1}^{\infty } {\frac{{2J_{0} \left( {\mu_{n} \frac{r}{R}} \right)}}{{\mu_{n} J_{1} (\mu_{n} )}} \cdot e^{{ - \mu_{n}^{2} Fo}} }. $$

  The experimental model is a short cylinder, its upper surface is in adiabatic condition, and its other surface is in constant temperature condition. To meet the above conditions, the product solution method can be used to obtain the temperature response of any point (x,r, τ) within the short cylinder:

  $$ \begin{aligned} \Theta (r,x,\tau ) & = \frac{\theta (r,x,\tau )}{{\theta_{0} }} = \Theta_{p} (x,\tau ) \cdot \Theta_{\text{c}} (r,\tau ) \hfill \\ & = \left( {\sum\limits_{n = 1}^{\infty } {( - 1)^{n + 1} \cdot \frac{4}{(2n - 1)\pi } \cdot \cos \left( {\frac{(2n - 1)\pi x}{2l}} \right) \cdot e^{{\frac{{ - (2n - 1)^{2} \pi^{2} }}{4}Fo}} } } \right) \hfill \\ & \quad \cdot \left( {\sum\limits_{n = 1}^{\infty } {\frac{{2J_{0} \left( {\mu_{n} \frac{r}{R}} \right)}}{{\mu_{n} J_{1} (\mu_{n} )}} \cdot e^{{ - \mu_{n}^{2} Fo}} } } \right) \hfill \\ \end{aligned}. $$