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The virtual boundary meshfree Galerkin method (VBMGM) is given to calculate the multi-domain transient heat conduction with heat source problem. The radial basis function interpolation is used to obtain the virtual source function on the virtual boundary, the heat source, the particular solutions of the temperature, and the heat flux in the computational domain. The formula of the proposed method is gotten by the Galerkin method and the control equations of the multi-domain transient heat conduction with heat source. Therefore, there are the advantages of the Galerkin method, the boundary element method, and the meshfree method for the multi-domain transient heat conduction with heat source problem by VBMGM. The numerical meaning of the weighted values are definite for the multi-domain transient heat conduction with heat source problem through VBMGM, such as the partial derivatives of the temperature, the heat flux, the heat source, and the continuity conditions on the public boundary at time. The detailed calculation scheme of VBMGM is deducted for the multi-domain transient heat conduction with heat source problem. Two numerical examples, four subdomains with the time-dependent heat source problem and two subdomains with the constant heat source and mixed boundary condition problem, are computed. The accuracy and the stability of VBMGM for the multi-domain transient heat conduction with heat source problem are verified. [ABSTRACT FROM AUTHOR]

The boiler equipment should be able to adapt to the load requirements and overcome the interference of various external conditions. By establishing a one-dimensional single-channel general numerical calculation model suitable for flow instability analysis of ultra-supercritical boilers at 700 °C, the rules of flow in the tubes are calculated. The 7th loop and the 22nd loop of the boiler water wall are selected as typical loops, and the dynamic characteristics of the two loops are calculated. The results show that after applying different multiples of heat flux disturbance, regardless of whether metal heat storage is considered, the inlet and outlet mass flow rates of the two circuits show inverse dynamic responses and eventually return to a steady state. When considering heat storage, it takes about 63 s for the 7th loop to return to stability. The recovery and stabilization time of the 22nd loop is about 60 s. Metal thermal storage has a positive effect on the settling time of the pipe section after heat flux disturbance. And when the maximum heat flux disturbance is applied, the maximum wall temperatures of the two loops are 443.9 °C and 446.5 °C, and the boiler can operate safely and stably. [ABSTRACT FROM AUTHOR]