高等传热学课程作业
Homework 5.5
1. Sphere or bubble motion in a liquid: ? Radius = 0.04 mm ? water properties at 25 C ? find terminal velocity for
– solid sphere, use stainless steel with density = 8238 kg/m3 – air bubble
– ethanol droplet in the water (assume does not mix and the ethanol viscosity is 1.20 x 10-3 Ns/m2) – Hint: drag=buoyancy
? For each case, do these conditions satisfy the assumptions of the derivation? Hint: Red<0.5, Red=u0d/ν, u0 is the coming flow velocity. A: 25℃水，?w?996.95 kg/m3，??9.027?10?4Ns/m2
空气密度?g?1.185kg/m3，乙醇密度?e?789.3kg/m3 拖曳力D?6?R?U?，??
4重力G??R3?sg
34浮力B??R3?wg
33?'?2?
3?'?3?a) 对于固体小球，有G?B?D
44即?R3?sg??R3?wg?6?R?U 3342Rg(?s??g)3∴U?=0.028m/s
6?
Re??UD?20.42?0.5 ?b) 对于气泡，有G?D?B
424即?R3?sg??6?R?U??R3?wg 3331
高等传热学课程作业
42Rg(?w??g)3∴U?=0.0058m/s
4?Re??UD?4.21?0.5 ?3?'?2??0.857
3?'?3?c) 对于乙醇，有G?D?B，??
44即?R3?sg?0.857?6?R?U??R3?wg 3342Rg(?w??e)3∴U?=9.35×10-4m/s 0.857?6?
Re??UD?0.682?0.5 ?
2. Bubble growth (homogeneous)
a. Assuming inertia controlled growth, estimate the interfacial velocity of a 0.2 mm diameter bubble growing in water at atmospheric pressure and 120°C.
b. Estimate the bubble size and the time for transition from inertia to heat transfer controlled growth (R+=1=t+ (this is an order of magnitude approximation)). A: a) 查表知，
?v?1.122 kg/m3，?l = 943.1 kg/m3，hfg?2200 kJ/kg，Tv?120℃，Tsat=100℃
惯性控制生长阶段
?2?vhfg(Tv?Tsat(P?))?R(t)???t
?lTsat(P?)?3?dR?2?vhfg?Tv?Tsat(P?)??u(R)????dt?3?lTsat(P?)?1/212
?0.59 m/s
b) 查表知，T??120℃，?l?17.1?10?8m2/s
Ja??T??Tsat??lcp,l?vhfg?32.47
2
高等传热学课程作业
?2?vhfg?T??Tsat(P?)??A????3??T(P)lsat??? B?12?l1/2?0.591
??Ja?0.026
A?A2根据R?R2,t?t2得
B R?B2A? 0.0012m，
BB2t?A2? 0.002s
3