fundamentals of heat and mass transfer solutions manual phần 5

TÌM: (a) Trên Tx tọa độ, phác thảo các bản phân phối nhiệt độ cho các trường hợp sau đây: điều kiện ban đầu (t ≤ 0), điều kiện trạng thái ổn định (t → ∞) giả định nhiệt độ tối đa vượt quá T2, và hai thời gian trung gian, các tính năng nhãn quan trọng (b) Đối với mạng ba nút được hiển thị, lấy được phương trình hữu hạn, | PROBLEM Cont. Hence Rt 0 _ 9 _ 9 4236 w m z 2 _ 1---- K W m2 and Tb Too Pelec Rb Rt0 17 C 1200W W C COM M ENTS 1 The boundary layer thickness at the trailing edge of the fin is l 2 __ Ỗ 5w2 Rew2 0 84 111111 s -1 . Hence the assumption of parallel flow over a flat plate is reasonable. 2 If a finned heat sink is not employed and heat transfer is simply by convection from the w2 xw2 base surface the corresponding convection resistance would be K W. which is only twice the resistance associated with the fin array. The small enhancement by the array is attributable to the large value of h and the correspondingly small value of Pf. Were a fluid such as air or a dielectric liquid used as the coolant the much smaller thermal conductivity would yield a smaller h a larger and hence a larger effectiveness for the array. PROBLEM KNOWN Plate dimensions and freestream conditions. Maximum allowable plate temperature. FIND a Maximum allowable power dissipation for electrical components attached to bottom of plate b Effect of air velocity and fins on maximum allowable power dissipation. SCHEMATIC ASSUMPTIONS 1 Steady-state conditions 2 Constant properties 3 Negligible heat loss form sides and bottom 4 Transition Reynolds number is 5 X 105 5 Isothermal plate. PROPERTIES Table Aluminum T - 350 K k - 240 W m-K Table Air Tf 325 K 1 atm V X IO 6 m2 s k W m-K Pr . ANALYSIS a The heat transfer from the plate by convection is elec q hAs Ts Too For II 15 m s n_UooL ReL V 15m 978x105 m2 s Rex c Hence transition occurs on the plate and Nul 5-871ÌPr1 3 -4 5 I -871 .1 3 1263 h Nul Ị 12630028W m-K w m2-K L m The heat rate is q w m2-K 2 350-300 K 2137 w. b The effect of the freestream velocity was considered by combining the Correlations Toolpad for the average coefficient associated with flow over a flat plate with the .