A jacketed, agitated reactor consists of a vertical cylinder 1.5 m diameter, with a hemispherical base and a flat, flanged, top. The jacket is fitted to the cylindrical section only and extends to a height of 1 m. The spacing between the jacket and vessel walls is 75 mm. The jacket is fitted with a

Question

A jacketed, agitated reactor consists of a vertical cylinder 1.5 m diameter, with a hemispherical base and a flat, flanged, top. The jacket is fitted to the cylindrical section only and extends to a height of 1 m. The spacing between the jacket and vessel walls is 75 mm. The jacket is fitted with a spiral baffle. The pitch between the spirals is 200 mm. The jacket is used to cool the reactor contents. The coolant used is chilled water at $10^{\circ} C$ ; flow-rate 32,500 kg/h, exit temperature $20^{\circ} C$ .

Estimate the heat transfer coefficient at the outside wall of the reactor and the pressure drop through the jacket.

Accepted Answer

[latex] ext { The baffle forms a continuous spiral channel, section } 75 mm imes 200 mm ext {. }[/latex]

[latex] ext { Number of spirals }= ext { height of jacket/pitch }=\frac{1}{200} imes 10^{-3}=5[/latex]

[latex] ext { Length of channel }=5 imes \pi imes 1.5=23.6 m[/latex]

[latex] ext { Cross-sectional area of channel }=(75 imes 200) imes 10^{-6}=15 imes 10^{-3} m[/latex]

[latex] ext { Hydraulic mean diameter, } d_{e}=\frac{4 imes ext { cross-sectional area }}{ ext { wetted perimeter }}[/latex]

[latex]=\frac{4 imes(75 imes 200)}{2(75+200)}=109 mm[/latex]

[latex] ext { Physical properties at mean temperature of } 15^{\circ} C ext {, from steam tables: } ho=999 kg / m ^{3} ext {, }[/latex]

[latex]\mu=1.136 mNm ^{-2} s , P r=7.99, k_{f}=595 imes 10^{-3} Wm ^{-1} C ^{-1}[/latex]

[latex] ext { Velocity through channel, } u=\frac{32,500}{3600} imes \frac{1}{999} imes \frac{1}{15 imes 10^{-3}}=0.602 m / s[/latex]

[latex]Re =\frac{999 imes 0.602 imes 109 imes 10^{-3}}{1.136 imes 10^{-3}}=57,705[/latex]

Chilled water is not viscous so use equation 12.11 with C = 0.023, and neglect the viscosity correction term.

[latex]N u=0.023 R e^{0.8} \operatorname{Pr}^{0.33}[/latex] (12.11)

[latex]h_{j} imes \frac{109 imes 10^{-3}}{595 imes 10^{-3}}=0.023(57,705)^{0.8}(7.99)^{0.33}[/latex]

[latex]h_{j}=1606 Wm ^{-2 \circ}{ }^{\circ} C ^{-1}[/latex]

Use equation 12.18 for estimating the pressure drop, taking the friction factor from Figure 12.24. As the hydraulic mean diameter will be large compared to the roughness of the jacket surface, the relative roughness will be comparable with that for heat exchanger tubes. The relative roughness of pipes and channels and the effect on the friction factor is covered in Volume 1, Chapter 3.

[latex] ext { From Figure } 12.24, ext { for } R e=5.8 imes 10^{4}, j_{f}=3.2 imes 10^{-3}[/latex]

[latex]\Delta P=8 j_{f}\left(\frac{L}{d_{e}} ight) ho \frac{u^{2}}{2}[/latex] (12.18)

[latex]\begin{aligned}\Delta P &=8 imes 3.2 imes 10^{-3}\left(\frac{23.6}{109} imes 10^{-3} ight) 999 imes \frac{0.602^{2}}{2} \&=1003 N / m ^{2}\end{aligned}[/latex]

Question 12.14: A jacketed, agitated reactor consists of a vertical cylinder...

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