Russian Federation
The article considers mathematical models of calculation of thermal conductivity in a constant cross-section rod, change of a liquid temperature along the length of the pipe and calculation of two-dimensional temperature field of liquid under the flow in the pipe. The mathematical model of fluid flow in the tube is realized in the form of a program for computers. The results of modeling of processes of heat conduction and heat exchange are presented. The task of simulation of heat exchange processes using numerical method of solving the Cauchy problem in the form of finite differences is considered in detail. This approach makes it possible to calculate the value of the studied parameter at any point of the object under investigation. The numerical method involves obtaining a system of algebraic equations for unknown variables and an algorithm for solving these equations. The main dependencies describing the process of thermal conductivity in the rod of the final length are given. The results of the calculation of the temperature change by the length of the rod are presented in a graphical presentation. The main dependencies describing the process of temperature change of the liquid flowing through the pipe are given. The results of the calculation of temperature pressure change over the length of the pipe are presented in a graphical presentation. The problem statement and mathematical model of the process of flow of incompressible liquid in the pipe are considered in detail. On the basis of the developed mathematical model, a computer model, implemented in the form of a program for computers, was created. The results of calculation, using the method of running, of two-dimensional temperature field of liquid along the pipe length are presented. The temperature dependence of the liquid in the various nodal points of the pipe section along the length of the pipe is presented in a graphical form.
heat exchange, heat conductivity, temperature field, numerical method, mathematical model, computing model, computing program
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