A fluid whose properties are essentially those of o-dichlorobenzene is vaporised in the tubes of a forced convection reboiler. Estimate the local heat-transfer coefficient at a point where 5 per cent of the liquid has been vaporised. The liquid velocity at the tube inlet is 2 m/s and the operating

Question

A fluid whose properties are essentially those of o-dichlorobenzene is vaporised in the tubes of a forced convection reboiler. Estimate the local heat-transfer coefficient at a point where 5 per cent of the liquid has been vaporised. The liquid velocity at the tube inlet is 2 m/s and the operating pressure is 0.3 bar. The tube inside diameter is 16 mm and the local wall temperature is estimated to be [latex]120^{\circ} C[/latex].

Accepted Answer

Physical properties:

[latex] ext { boiling point } 136^{\circ} C[/latex]

[latex] ho_{L}=1170 kg / m ^{3}[/latex]

[latex]\mu_{L}=0.45 mNs / m ^{2}[/latex]

[latex]\mu_{v}=0.01 mNs / m ^{2}[/latex]

[latex] ho_{v}=1.31 kg / m ^{3}[/latex]

[latex]k_{L}=0.11 W / m ^{\circ} C[/latex]

[latex]C_{p L}=1.25 kJ / kg ^{\circ} C[/latex]

[latex]P_{c}=41 bar[/latex]

The forced-convective boiling coefficient will be estimated using Chen’s method.

With 5 per cent vapour, liquid velocity (for liquid flow in tube alone)

[latex]=2 imes 0.95=1.90 m / s[/latex]

[latex]R e_{L}=\frac{1170 imes 1.90 imes 16 imes 10^{-3}}{0.45 imes 10^{-3}}=79,040[/latex]

[latex] ext { From Figure } 12.23, j_{h}=3.3 imes 10^{-3}[/latex]

[latex]P r=\frac{1.25 imes 10^{3} imes 0.45 imes 10^{-3}}{0.11}=5.1[/latex]

Neglect viscosity correction term.

[latex]\begin{aligned}h_{f c} &=\frac{0.11}{16 imes 10^{-3}} imes 3.3 imes 10^{-3}(79,040)(5.1)^{0.33} \&=3070 W / m ^{2 \circ} C\end{aligned}[/latex] (12.15)

[latex]\begin{aligned}\frac{1}{X_{t t}} &=\left[\frac{0.05}{1-0.05} ight]^{0.9}\left[\frac{1170}{1.31} ight]^{0.5}\left[\frac{0.01 imes 10^{-3}}{0.45 imes 10^{-3}} ight]^{0.1} \&=1.44\end{aligned}[/latex] (12.69)

[latex] ext { From Figure 12.56, } f_{c}=3.2[/latex]

[latex]h_{f c}^{\prime}=3.2 imes 3070=9824 W / m ^{2 \circ} C[/latex]

Using Mostinski’s correlation to estimate the nucleate boiling coefficient

[latex]h_{n b}=0.104 imes 41^{0.69}\left[h_{n b}(136-120) ight]^{0.7}[/latex] (12.63)

[latex] imes\left[1.8\left(\frac{0.3}{41} ight)^{0.17}+4\left(\frac{0.3}{41} ight)^{1.2}+10\left(\frac{0.3}{41} ight)^{10} ight][/latex]

[latex]h_{n b}=7.43 h_{n b}^{0.7}[/latex]

[latex]h_{n b}=800 W / m ^{2 \circ} C[/latex]

[latex]R e_{L} f_{c}^{1.25}=79,040 imes 3.2^{1.25}=338,286[/latex]

[latex] ext { From Figure } 12.57, f_{s}=0.13 ext {, }[/latex]

[latex]h_{n b}^{\prime}=0.13 imes 800=104 W / m ^{2}{ }^{\circ} C[/latex]

[latex]h_{c b}=9824+104=\underline{\underline{9928} W / m ^{2}{ }^{\circ} C }[/latex]

Question 12.9: A fluid whose properties are essentially those of o-dichloro...

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