Question

steam saturated at 68.9 kPa (10 psia) is condensing on a vertical tube 1.22 m (4.0 ft) long having an OD of 0.0254 m (1.0 in.) and a surface temperature of 86.11 ºC (187 ºF). Calculate the average heat-transfer-coefficient using English and SI units.

Answer 1

In SI Units

At pressure P = 68.9 kPa (saturated steam)

Saturation temperature Tsat = 89.44 °C

Tw = 86.11 °C

T = Tsat - Tw = 89.44 - 86.11 = 3.33 K

Tf = (Tsat + Tw) / 2 = (89.44 + 86.11) / 2 = 87.8 °C

Latent heat hfg = 2657.8 - 374.6 = 2283.2 kJ/kg x 1000J/kJ

= 2283200 J/kg

Liquid density _L = 966.7 kg/m3

Vapor density _v = 0.391 kg/m3

Viscosity of liquid _L = 3.24 * 10^-4 Pa-s

Thermal conductivity k = 0.675 W/m-K

Length L = 1.22 m

Nusselt number Nu = 1.13 [_L² g h_fg L³ / kT]^0.25

Nu = 1.13 [966.7² * 9.81 * 2283200 * 1.22³ /3.24 * 10^-4 * 0.675* 3.33]^0.25

hL/k = 17077.35

h * 1.22 / 0.675 = 17077.35

h = 9448.53 W/m2-K

In English Units

At pressure P = 10 psia (saturated steam)

Saturation temperature Tsat = 193 °F

Tw = 187 °F

T = Tsat - Tw = 193 - 187 = 6°F

Tf = (Tsat + Tw) / 2 = (193 + 187) / 2 = 190 °F

Latent heat hfg = 1143.3 - 161 = 982.3 Btu/lbm

Liquid density _L = 60.3 lbm/ft3

Viscosity of liquid _L = 0.784 lbm/ft-h

Thermal conductivity k = 0.390 Btu/ft-h-°F

Length L = 4 ft

Nusselt number Nu = 1.13 [_L² g h_fg L³ / kT]^0.25

Nu = 1.13 [60.3² * 32.174 * 982.3 * 4³ /0.784 * 0.390* 6]^0.25

hL/k = 17077.35

h * 4 / 0.390 = 17077.35

h = 1665.04 Btu/h-ft2-°F