Aquecimento e Fusão de Nanopartículas Cerâmicas - Análise de Tempo de Voo e Distância

PROBLEM 526 KNOWN Diameter and initial temperature of nanostructured ceramic particle Plasma temperature and convection heat transfer coefficient Properties and velocity of particles FIND a Timeinflight corresponding to 30 of the particle mass being melted b Timeinflight corresponding to the particle being 70 melted c Standoff distances between the nozzle and the substrate associated with parts a and b SCHEMATIC LSTD Dp 50 m Ti 300 K T 10000K h 30000 Wm2K ASSUMPTIONS 1 Constant properties 2 Negligible radiation PROPERTIES Given k 5 WmK 3800 kgm3 cp 1560 JkgK hsf 3577 kJkg Tmp 2318 K ANALYSIS a To determine whether the lumped capacitance assumption is appropriate the Biot number is calculated as 2 6 3 30000 Wm K 50 10 m 6 6 5 Wm K h ro hD Bi k k 005 Since Bi 01 the lumped capacitance approximation is valid The particle heating process can be divided into two stages Stage 1 Heating to the melting temperature The timeofflight for the first stage is found from Equation 55 1 mp 3 6 2 ln ln 6 3800 kgm 50 10 m 1560 Jkg K 300 K 10000 K ln 6 30000 Wm K 2318 K 10000 K i i s Vc Dc T T t hA h T T 000038 s Stage 2 Melting to 30 liquid The second stage involves heat transfer to the particle which is isothermal at its melting point temperature Hence Continued PROBLEM 526 Cont 203 mp mp 3 6 3 2 03 005 005 3800kgm 50 10 m 3577 10 Jkg 000015 s 30000Wm K 10000 2318 K sf sf s Vh Dh E t q hA T T h T T Therefore the required timeofflight is ttot03 t1 t2 03 000038 s 000015 s 000053 s b The calculation for the second stage may be repeated for 70 liquid yielding t2 07 000034 s Therefore the required timeofflight is ttot 07 t1 t2 07 000038 s 0000341 s 000072 s c The required standoff distances are STD03 tot03 35 ms 000053 s 0019 m 19 mm L Vt STD07 tot07 35 ms 000072 s 0025 m 25 mm L Vt COMMENTS 1 Assuming the particles to have an emissivity of p 04 and radiation is exchanged with surroundings at an assumed temperature of Tsur 300 K the radiation heat transfer coefficient may be found from Equation 19 as 2 2 8 2 2 mp sur mp sur 2 4 W 04 567 10 2318 300 K 2318K 300K m K r p h T T T T 320 Wm2K Hence hr hconv and radiation heat transfer is negligible 2 To deliver a partiallymolten droplet to the substrate standoff distances on the order of 20 mm need to be maintained This is a reasonable requirement 3 See I Ahmed and TL Bergman Simulation of Thermal Plasma Spraying of Partially Molten Ceramics Effect of Carrier Gas on Particle Deposition and Phase Change Phenomena ASME Journal of Heat Transfer vol 123 pp 188196 2001 for more information