Heat release of sewage tank, hot water injected from geothermal wells and heavy oil wells, and groundwater seepage in fractured rock mass form the temperature effect of seepage and heat transfer. Different fracture patterns in geological structures are illustrated in Fig. ![]() As there are various kinds of fractures in the natural rock mass of the aforementioned projects, new fractures and faults will come about in the initial excavation and drilling process. There are many areas, such as disposal of high-level radioactive waste, geothermal exploitation engineering, heavy oil exploitation engineering, and so on, all of which are associated with the coupling of water and heat in fractured rock mass and their overall construction. The direction of the flowing water and transferring heat of the fracture exerts a dominant effect on the temperature of the rock mass than the length.Īt present, the coupling of water and heat in fractured rock mass is a hot research topic of domestic and international scholars. ![]() The findings indicate that: When the model goes into a stable state under four working conditions, the rock on the x = 0–2 m mostly forms a heat transfer path from left to right the x = 2–4 m primarily forms a heat transfer path from bottom to top, and the temperature gradient reveals that the isotherm of 40–45 ☌ is highly similar to the shape of four different fractures, indicating that flowing water and transferring heat in the fracture configuration dominate the temperature field of the right side rock mass. Based on the conceptive model of flowing water and transferring heat in curved fractured rock mass, the influence of flowing water and transferring heat in “I”, “L”,, and shaped fractures on the temperature field of rock mass is calculated by using discrete element program. Compared with straight fracture flowing water and transferring heat, there are few relevant literatures about the heat transfer of curved fracture water flow. Stat.Domestically and internationally, the effect of fracture flowing water and transferring heat on the temperature field of surrounding rock in high-level radioactive waste repositories is a popular research area. Zhao, C., Song, J.S.: Exact heat kernel on a hypersphere and its applications in kernel SVM. In Technical report 150, Department of Statistics, Stanford University (1969) Stephens, M.: Techniques for directional data. (Eds.) Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics. Sommer, S., Arnaudon, A., Kuhnel, L., Joshi, S.: Bridge simulation and metric estimation on landmark manifolds. Small, C.G.: The Statistical Theory of Shape. Saloff-Coste, L.: A note on Poincaré, Sobolev, and Harnack inequalities. Mardia, K.V., Jupp, P.E.: Directional Statistics. Jensen, M.H., Sommer, S.: Simulation of conditioned semimartingales on riemannian manifolds. Hundrieser, S., Eltzner, B., Huckemann, S.: Finite sample smeariness of fréchet means and application to climate. Hsu, E.P.: Stochastic Analysis on Manifolds. Hotz, T., Huckemann, S.: Intrinsic means on the circle: uniqueness, locus and asymptotics. Hansen, P., Eltzner, B., Huckemann, S., Sommer, S.: Diffusion Means in Geometric Spaces. ![]() Grigor’yan, A., Noguchi, M.: The heat kernel on hyperbolic space. Grigor’yan, A.: Heat kernel upper bounds on a complete non-compact manifold. arXiv: 1801.06581 (2019)įréchet, M.: Les éléments aléatoires de nature quelconque dans un espace distancié. Huckemann, S.F.: A smeary central limit theorem for manifolds with application to high dimensional spheres. 116(11), 1660–1675 (2006)Įltzner, B.: Geometrical smeariness - a new phenomenon of Fréchet means. Google-Books-ID: 0v1VfTWuKGgC (1984)ĭelyon, B., Hu, Y.: Simulation of conditioned diffusion and application to parameter estimation. arXiv:1807.11072 (2019)Ĭhavel, I.: Eigenvalues in Riemannian Geometry. Alonso-Orán, D., Chamizo, F., Martínez, A.D., Mas, A.: Pointwise monotonicity of heat kernels.
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