tailieunhanh - Heat Transfer Mathematical Modelling Numerical Methods and Information Technology Part 15

Tham khảo tài liệu 'heat transfer mathematical modelling numerical methods and information technology part 15', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Thermal Characterization of Solid Structures during Forced Convection Heating 549 Th ny nz Thx nx ny nz - T nx ny nz Th x nx ny nz - T nx ny nz nx ny nz - T nx ny nz Th y nx ny nz - T nx ny nz Th nx ny nz - T nx ny nz Th-z nx ny nz - T nx ny nz 32 where Thx nx ny nz is the heater gas temperature at A1 nx ny nz etc. To achieve a compact description the temperature differences between a given cell and its adjacent cells are also collected into assistant vectors TK nx ny nz T nx - 1 ny nz - T n ny nz T nx 1 ny nz - T nx ny nz T nx ny -1 nz - T nx ny nz T nx ny 1 nz - T nx ny nz T nx ny nz - 1 - T nx ny nz T n ny nz 1 - T nx ny nz 33 We need only those values of TK nx ny nz where adjacent cells exist. Therefore Tk nx ny nz vectors will be filtered by the G nx ny nz vectors. In those positions where the G nx ny nz vector is zero the value of the TK nx ny nz will be disregarded. The solid-gas interfaces are chosen by h nx ny nz . By the application of the assistant vectors and matrixes 29-33 this gives us the general expression of the differential equation system which best describes the model dT nx ny nz _ h nx ny nz T A nx ny nz Th nx ny nz G nx ny nz T T x ny nz 34 dt C nx ny nz If we do not maximize the number of the cell neighbours in the model then the assistant vectors 29 30 31 and 33 would be matrices with 6xN dimensions N is the cell number therefore Eq. 34 and its implementation would be more complex. Application example In the last section we present an application of our model which is the convectional heating of a surface mounted component . during the reflow soldering in Fig 15. We investigate how change the temperature of the soldering surfaces of the component if the heat transfer coefficients are different around the component see more details in Illés Harsányi 2008 . The model was implemented using MATLAB software. We have defined a nonuniform grid with 792 thermal cells the applied resolution is the same as in Fig the x-y projection in