Mathematical Modelling for Predicting Thermal Properties of Selected Limestone

Abstract

Due to a lack of geotechnical and geothermal studies on Jordanian limestone, this paper aims to provide the thermal properties, including thermal conductivity, thermal diffusivity, and specific heat, using the Hot Disk Transient Plane Source (TPS) 2200 method. It also aims to provide a set of mathematical models through which the thermal properties can be indirectly predicted from the rocks’ physical and engineering properties. One hundred cylindrical rock specimens with a height of 20 cm and a diameter of 10 cm were extracted and prepared. The results showed that the thermal conductivity values ranged between (1.931–3.468) (W/(m*k)), thermal diffusivity (1.032–1.81) (mm2/s), and specific heat (1.57–2.563) ((MJ)/(m3*K)). The results also suggest a direct relationship between conductivity and diffusivity and an inverse relationship between conductivity and specific heat. On the other hand, the results indicate the direct relationship between the conductivity and diffusivity, and the inverse relationship between the specific heat and density, hardness, sound velocity, and rock strength; the opposite happens when the rock’s porosity is considered. Simple regression, multivariate regression, and the backpropagation–artificial neural network (BP–ANN) approach were utilized to predict the thermal properties of limestone. Results indicated that the ANN model provided superior prediction performance compared to other models.