tailieunhanh - Design and Optimization of Thermal Systems Episode 1 Part 9

Tham khảo tài liệu 'design and optimization of thermal systems episode 1 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 172 Design and Optimization of Thermal Systems local temperature. Here V2 d2 dx2 d2 dy2. For the solid region the energy equation is PQ n ksN T dT where the subscript s denotes solid material properties. The Boussinesq approximations have been used for the buoyancy term. The pressure work and viscous dissipation terms have been neglected. The boundary conditions on velocity are the no-slip conditions . zero velocity at the solid boundaries. At the inlet and outlet the given velocities apply. For the temperature field at the inner surface of the enclosure continuity of the temperature and the heat flux gives T Ts and where n is the coordinate normal to the surface. Also at the left source an energy balance gives Q L -k Ỉ k dT dy where Qs is the energy dissipated by the source per unit width. Similar equations may be written for other sources. At the outer surface of the enclosure walls the convective heat loss condition gives -k Ỉ h T - T ơn At the inlet the temperature is uniform at Ti and at the outlet developed temperature conditions dT dy 0 may be used. Therefore the governing equations and boundary conditions are written for this coupled conduction-convection problem. The main characteristic quantities in the problem are the conditions at the inlet and the energy input at the sources. The energy input governs the heat transfer processes and the inlet conditions determine the forced airflow in the enclosure. Therefore v H T and Qs are taken as the characteristic physical quantities. The various dimensions in the problem are nondimensionalized by H and the velocity V by v. Time T is nondimensionalized by H v to give dimensionless time t T v H . The nondimensional temperature 0 is defined as T - T Q 0 T where AT - AT k Here AT is taken as the temperature scale based on the energy input by a given source. The energy input by other sources may be nondimensionalized by Qs. Modeling of Thermal Systems 173 The governing equations and the boundary conditions may now