A simplified method for the numerical calculation of nonstationary heat transfer through a flat wall
DOI:
https://doi.org/10.15587/1729-4061.2017.96090Keywords:
nonstationary heat transfer, flat wall, simplified numerical computation, small computational gridAbstract
The nonstationary operation modes of power equipment lead to the nonstationary regimes of heat exchange, in particular heat transfer. The transient processes, related to the accumulation of energy in the heat-transmitting surfaces, which manifest themselves in this case, may affect manageability of the work of equipment.
Although in many cases, with a proper approximation, the heat exchange surfaces can be represented in the form of a simple variant of an infinite plate, the existing methods and tools for solving the problems on nonstationary heat transfer are built from the positions of universalism, introducing unjustified complications and hampering the generalization of numerical results obtained. We developed a simplified discrete analog to solve the one-dimensional problems on nonstationary heat transfer through an infinite plate. The realized approach allowed us to obtain the analog and results of calculations based on it in the dimensionless form, which substantially facilitates their generalization.
A high stability of computational process is demonstrated relative to the selection of a number of nodes in computational grid and calculation step by time. The possibility of using the maximally small computational grids (3 nodes) makes it possible, at the current calculation step by time. To obtain an analytical solution for determining the temperatures at the surfaces of the plate at initial use of boundary conditions of the third kind. As a result, accumulated energy can be defined as a difference in the heat fluxes at the surfaces of the plate. Performing the calculations on the maximally small grids might be useful to solve the inverse problems on thermal conductivity.
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