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Tham khảo tài liệu 'design and optimization of thermal systems episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Numerical Modeling and Simulation 247 become uniform at 0 1. Figure 4.18 shows the variation of the temperature at several locations in the plate with time T. Again the approach to steady state at large time is clearly seen. The Crank-Nicolson method is a very popular choice for such one-dimensional problems because of the second-order accuracy in time and space. Tridiagonal sets of equations are generated for one-dimensional problems and these may be solved conveniently and accurately by the Thomas algorithm to yield the desired solution. 4.3 NUMERICAL MODEL FOR A SYSTEM We now come to the numerical model for the overall system which may comprise several parts constituents or subsystems. The model may be relatively simple as is the case for systems with a small number of components such as a refrigerator or may be very involved as is the case for a major undertaking such as a power plant. The numerical model may be developed by the users themselves or it may be based on a commercially available general-purpose code such as Fidap Ansys Phoenics Simpler or Fluent. Specialized programs for specific applications are also available. Since the development of computer codes for large thermal systems is a very elaborate and time-consuming process it is often more convenient and efficient to use a commercially available program. Consequently such codes are employed extensively in industry and form the basis for the numerical simulation and design of a variety of thermal systems ranging from electronic packages to air-conditioning and energy systems. However it is important to be conversant with the algorithm used in the software and to be aware of its applicability accuracy limitations and ease with which inputs may be given to simulate different circumstances. Even if the numerical model is being developed indigenously software available on the computer or in the public domain may be employed effectively. This is particularly the case for graphics programs and standard .
