3차원 비정렬격자을 이용한 전열해석 방법론

Abstract

Heat transfers and related phenomena can be described by the second order partial differential equation, which cannot generally be solved except a simple domain. To make matters worse, the solution significantly dependents on the boundary conditions. The equations with analytical methods are solvable for only a limited number of cases. The known solutions are extremely useful in helping to understand heat transfer phenomena, but they rarely can be applied in engineering or design, because these solutions are not sufficiently practical. The engineer and designer have generally been forced to use numerical methods instead. To obtain an numerical solution, a discretization method, which approximates the differential equations by a system of algebraic equations is used. The approximations are applied to small domains in space and time so the numerical solution provides results at discrete locations in both space and time. The accuracy of numerical solutions is dependent on the quality of discretizations and size of cells used. The higher accuracy, the higher numerical resource are required. The balance between the accuracy and difficulty of the numerical methods is critical. The final linear equations by discretization are solved with matrix solver, which takes the most of the computation time. To reduce the computation time, the effective method for matrix solver is required. This study provides an overview of discretization, and matrix solver for the 3-dimensional numerical heat transfer.