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Design and Optimization of Thermal Systems Episode 1 Part 10

Tham khảo tài liệu 'design and optimization of thermal systems episode 1 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling of Thermal Systems 197 PROBLEMS Note In all problems dealing with model development list the assumptions approximations and idealizations employed give the resulting governing equations and whenever possible give the analytical solution. Symbols may be used for the appropriate physical quantities. 3.1. An energy storage system consists of concentric cylinders the inner being of radius R1 the outer of radius R2 and both being of length L as shown in Figure P3.1. The inner cylinder is heated electrically and FIGURE P3.1 supplies a constant heat flux q to the material in the outer cylinder as shown. The annulus is packed with high conductivity metal pieces. Assuming that the system is well insulated from the environment and that the annular region containing the metal pieces may be taken as isothermal a Obtain a mathematical model for the system. b If the maximum temperature is given as Tmax obtain the time for which heating may be allowed to occur employing the usual symbols for properties 3.2. Solid plastic cylinders of diameter 1 cm and length 30 cm are heat treated by moving them at constant speed U through an electric oven of length L as shown in Figure P3.2. The temperature at the oven walls is Ts and the air in the oven is at temperature Ta. The convective heat transfer coefficient at the plastic surface is given as h and the surface I. L s -o o o OiO o -Ư h Ia-r----- FIGURE P3.2 198 Design and Optimization of Thermal Systems emissivity as e. The cylinders are placed perpendicular to the direction of motion and are rotated as they move across the oven. Develop a simple mathematical model for obtaining the temperature in the plastic cylinders as a function of the temperatures Ts and Ta h L and U for design of the system. Clearly indicate the assumptions and approximations made. 3.3. A chemical industry needs hot water at temperature Tc ATc for a chemical process. For this purpose a storage tank of volume V and surface area A is employed. Whenever hot .