Tham khảo tài liệu 'heat transfer mathematical modelling numerical methods and information technology part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Population Balance Model of Heat Transfer in Gas-Solid Processing Systems 429 Kin T t MíẠt- T 1 -ỷ M0 ins T - t 2 0 p 1 85 where Mo in 108 m3 is the total number of particles in a unit volume and ip is the ratio of particles having different temperatures. Fig. 4 shows that there may remain rather significant inhomogeneities in the temperature distribution of particles in the bed. These inhomogeneities are decreasing with increasing interparticle collision frequency therefore the particle-particle interaction play important role in homogenization of temperature inside the population of particles. 8 ơ2 r 6 4 T 100 2 102 102 103 103 103 103 104 0 .5 10 Fig. 4. Time evolution of the variance of temperature distribution of the particle population Fig. 5 presents the time evolution of the temperatures of characteristic parts of the bubbling bed . mean temperature of particles the temperatures of the bubble phase and the gas in the emulsion phase as well as the temperatures of the wall and liquid in the jacket. In this case the input temperature of gas was 180 C and the initial temperature of gas in the emulsion and bubble phases were of the same values. It is seen how the temperature profiles vary in interconnections of the different parts of the bed. In steady state under the given heat transfer resistance conditions of the particle population the wall and liquid is heated practically only by the gas in the emulsion phase while the bubbles flow through the bed without losing heat assuring only the well stirred state of the emulsion phase. Fig. 5. Time evolution of the temperatures of characteristic parts of the bubbling bed in interrelations with each other 430 Heat Transfer - Mathematical Modelling Numerical Methods and Information Technology In Fig. 5 bubble temperature transient is shown only for the bed output indicating here a rather sharp front. Naturally the temperature front of bubbles evolves progressively along the bed as it
