On the Influencing Mechanism of Geothermal Fluids on the Dynamic Changes of Groundwater Flow and Heat Transfer Temperature

Nowadays, people are paying increasing attention to the rational exploitation of geothermal resources. To develop and utilize geothermal resources in a scientific way, it is important to understand the change patterns of key geohydrological parameters such as seepage velocity and temperature. As part of the effort, this paper analyzes and studies the influencing mechanism of geothermal fluids on the dynamic changes of groundwater flow and heat transfer temperature. First, a differential equation of heat conduction of geothermal fluids and a groundwater flow-geothermal fluids thermal coupling model were constructed to study the seepage state and the heat transfer of groundwater flow in the energy extraction process. Then, an analytical model for the influence of groundwater seepage on heat transfixion was established, directly showing the relevant mechanism. The experimental results proved the effectiveness of the constructed model.

Application of Jacobi Polynomial and Multivariable Aleph- Function in Heat Conduction in Non-Homogeneous Moving Rectangular Parallelepiped

The present paper deals with an application of Jacobi polynomial and multivariable Aleph-function to solve the differential equation of heat conduction in non-homogeneous moving rectangular parallelepiped. The temperature distribution in the parallelepiped, moving in a direction of the length (x-axis) between the limits x = −1 and x = 1 has been considered. The conductivity and the velocity have been assumed to be variables. We shall see two particular cases and the cases concerning Aleph-function of two variables and the I-function of two variables.

Analysis of 2D heat conduction in nonlinear functionally graded materials using a local semi-analytical meshless method

<abstract> <p>This paper proposes a local semi-analytical meshless method for simulating heat conduction in nonlinear functionally graded materials. The governing equation of heat conduction problem in nonlinear functionally graded material is first transformed to an anisotropic modified Helmholtz equation by using the Kirchhoff transformation. Then, the local knot method (LKM) is employed to approximate the solution of the transformed equation. After that, the solution of the original nonlinear equation can be obtained by the inverse Kirchhoff transformation. The LKM is a recently proposed meshless approach. As a local semi-analytical meshless approach, it uses the non-singular general solution as the basis function and has the merits of simplicity, high accuracy, and easy-to-program. Compared with the traditional boundary knot method, the present scheme avoids an ill-conditioned system of equations, and is more suitable for large-scale simulations associated with complicated structures. Three benchmark numerical examples are provided to confirm the accuracy and validity of the proposed approach.</p> </abstract>

Analysis for the Joining of Light Alloys by Numerical Experiment

The current paper deals with the application of numerical experiment of joining light alloys. Modelling and numerical simulation and finite element method in the ANSYS program were used to investigate the course of thermal cycles, the joining process of light alloys by welding. Joining process of light alloys by welding is defined as a moving point source of heat, which generates temperature fields of various kinds, depending on the time and thickness of the material being welded. The paper is therefore devoted to: Thermal energy transfer and solution to differential equation of heat conduction, Initial and boundary conditions for temperatures distribution of a moving point source of heat, Generation (definition) of thermal cycle. Another part of the paper deals with the analysis of the heat-affected zone. Of the result of the solution will be expressed as the temperature field generated in the base material during the welding process.

Heat Localization in the Medium in Blow-Up Regime

The existence of the effect of heat metastable localization in the medium in the blow-up heating regime was experimentally proved. This is the regime in which the heating energy for a finite period of time tends to infinity. Previous theoretical studies have shown that in this case some regions, inside of which the temperature increases, may arise, while their size remains constant or decreases with time (heat localization regions). These regions exist as long as there is some energy input from the outside. An installation for the experimental study of the thermal blow-up regimes in a solid was developed. The object of research was an aluminum rod with a heater at its end. The temperature distribution along the rod was measured with thermocouples. The temperature of the rod end could vary according to the given law. Calibration of the installation was performed. The sensitivity of thermocouples was determined. The inertia of the heating and cooling process was estimated. The mathematical description of the thermal processes, occurring during the experiment, was made. The nonlinear equation of heat conduction for the rod was solved, with the heat exchange with the environment by convection and radiation taken into account. The thermal regime at the boundary, which is necessary to create the thermal structures, was determined. The temperature distribution in the rod in the blow-up regime and non-blow-up regime was measured. In the blow-up regime the heat front (the coordinate of the point with the temperature equal to half the maximum temperature) initially shifts from the heat source, and then in the opposite direction, and the size of the area under heating decreases. In the non-blow-up regime the size of the heated region increases all the time. The predicted effect was supposed to be used in installations for thermonuclear fusion where the target was heated by laser radiation pulses of a special shape. This effect can also be used for localized heating in cutting and welding, when the adjacent regions are not to get very hot, and in other similar situations.

MATHEMATIC SIMULATION OF GENERALIZED PROBLEM OF HEAT-EXCHANGE IN THE BODIES WITH HEMISPHERICAL SHAPE

The article presents the first mathematical model for calculating temperature fields of hemispherical bodies, which approximately simulates operation of the diamond-drilling bit and takes into account angular velocity of drilling operations and finite velocity of heat conduction, and which was created as a physicomathematical boundary problem for hyperbolic equation of heat conduction with the Dirichlet boundary conditions. Besides, a new integral transformation was formulated for the two-dimensional finite space, with the help of which and with the help of finite element method and Galerkin method a temperature field was found in the form of convergence series.

Simplified Grinding Temperature Model Study

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.