Design method of concrete block cooling system based on fast and accurate numerical reconstruction technology
A concrete block and cooling system technology, applied in computer-aided design, calculation, complex mathematical operations, etc., can solve the problems of complex temperature field calculation process, large calculation load, long calculation time, etc., to achieve reduced solution scale, fast and accurate calculation , Calculate the effect of fast
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Embodiment 1
[0077] Embodiment 1: Consider the section cooling problem of the concrete block that contains five cooling water pipes, the area equation is
[0078] {(x 1 ,x 2 )|01 ,x 2 )<3m},
[0079] where x 1 and x 2 respectively represent the abscissa and ordinate of points on the area, and the boundary and internal data collection points are as follows figure 2 As shown, Ip represents the internal point, Bp represents the boundary point, the radius of the water pipe is 5cm, and the equivalent distance between the water pipes is about 1.6m.
[0080] The equivalent heat conduction equation and boundary conditions are:
[0081]
[0082] where T a represents the ambient air temperature, T w Indicates the water temperature, Γ 1 represents the square boundary of the concrete block section, Γ 2 Indicates the circular boundary of the contact between the concrete block section and the water pipe, the unit of temperature is °C, assuming that the thermal conductivity of concrete is a...
Embodiment 2
[0087]Example 2: Consider the data reconstruction of heat conduction in a cube, where the side length is 1m, and a slender water pipe is embedded in the center of the cube, and the radius of the water pipe is 5cm. The exact solution can be expressed as:
[0088]
[0089] where is the thermal conductivity coefficient. Figure 5 When τ=1d, the curves of the temperature values on the three test lines of the local radial basis function (LRBF) collocation method (LRBF) with time are given, and the results are compared with the finite element method (FEM). The three test lines are: (x 1 ,0.45,0.45), (x 1 ,0.75,0.75), (x 1 ,0.15,0.15). Figure 6 The absolute error comparisons of the two are given. It shows the accuracy of the local radial basis function collocation method in dealing with three-dimensional problems. It should be mentioned that when solving this three-dimensional problem, the degree of freedom of the finite element method is 51846, which is far more than 1728 ...
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