12. Heat Exchangers Chemical engineering 170

Explain the different mechanisms of heat transfer: Review: Heat Transfer Explain the different mechanisms of heat transfer: Conduction Convection Radiation

Review: energy balances Where would you use each equation? 𝑄 = 𝑚 C P Δ𝑇 𝑄 = 𝑚 Δ 𝐻

Heat exchangers In industrial settings, we transfer heat using a heat exchanger.

Heat Duty Heat exchangers have a hot side and a cold side 𝑸 𝒅𝒖𝒕𝒚 : heat that flows from one side or the other

Finding heat duty In an oil refinery, an oil stream is heated to a higher temperature using a heat exchanger with steam being condensed to water as the heat source. You have complete information about both streams. Describe two different ways of finding the heat duty (two different equations you could use).

Finding heat duty Oil (Cold Stream) Water (Hot Steam) In an oil refinery, an oil stream is heated to a higher temperature using a heat exchanger with steam being condensed to water as the heat source. You have complete information about both streams. Describe two different ways of finding the heat duty (two different equations you could use). Oil (Cold Stream) Water (Hot Steam) Mass flow rate: 960 𝑙 𝑏 𝑚 /𝑚𝑖𝑛 Heat capacity: 0.74 𝐵𝑇𝑈 𝑙𝑏𝑚 °𝐹 Inlet temperature: 35 °𝐹 Outlet temperature: 110 °𝐹 Mass flow rate: 57.6 𝑙 𝑏 𝑚 /𝑚𝑖𝑛 Heat of vaporization: 925 𝐵𝑇𝑈 𝑙𝑏𝑚 Vaporization temperature: 35 °𝐹

Sizing heat exchangers 𝑄 𝑑𝑢𝑡𝑦 = 𝑈 𝑜 𝐴Δ 𝑇 𝑎𝑣𝑔 Overall heat transfer coefficient Heat transfer area Temperature difference between hot and cold streams (averaged)

Typical units 𝑄 𝑑𝑢𝑡𝑦 = 𝑈 𝑜 𝐴Δ 𝑇 𝑎𝑣𝑔 𝑾 ? 𝒎 𝟐 𝑲 °𝑭 𝑩𝑻𝑼 𝒉𝒓 𝒇 𝒕 𝟐

Typical units 𝑄 𝑑𝑢𝑡𝑦 = 𝑈 𝑜 𝐴Δ 𝑇 𝑎𝑣𝑔 𝑾 𝒎 𝟐 𝑲 𝑩𝑻𝑼 𝒉𝒓 𝒇 𝒕 𝟐 °𝑭

Average temperature difference Why do we need to average the temperature difference? 𝑻 𝒉𝒐𝒕,𝒊𝒏 𝑻 𝒄𝒐𝒍𝒅,𝒐𝒖𝒕 𝑻 𝒄𝒐𝒍𝒅,𝒊𝒏 𝑻 𝒉𝒐𝒕,𝒐𝒖𝒕 1 2

Log Mean Temperature difference For a simple heat exchanger (the only kind we’ll be using): Δ 𝑇 𝑙𝑜𝑔𝑚𝑒𝑎𝑛 = Δ 𝑇 1 −Δ 𝑇 2 ln Δ 𝑇 1 Δ 𝑇 2 Δ 𝑇 1 = 𝑇 ℎ𝑜𝑡,𝑜𝑢𝑡 − 𝑇 𝑐𝑜𝑙𝑑,𝑖𝑛 Δ 𝑇 2 = 𝑇 ℎ𝑜𝑡,𝑖𝑛 − 𝑇 𝑐𝑜𝑙𝑑,𝑜𝑢𝑡

Finding heat duty A chemical process creates a very hot waste stream. We will use a stream of cold water to cool it before it can be released. We have the following information about the two streams:

Finding heat duty Waste Stream (Hot) Cooling Water (Cold) A chemical process creates a very hot waste stream. We will use a stream of cold water to cool it before it can be released. We have the following information about the two streams: Waste Stream (Hot) Cooling Water (Cold) Inlet temperature: 50 °𝐶 Outlet temperature: 30 °𝐶 Heat capacity: 2 𝑘𝐽 𝑘𝑔 °𝐶 Density: 10 𝑘𝑔 𝑚 3 Flow rate: 0.5 𝑚 3 /𝑠 Inlet temperature: 20 °𝐶 Outlet temperature: 25 °𝐶 Heat capacity: 4.17 𝑘𝐽 𝑘𝑔 °𝐶 Density: 997 𝑘𝑔 𝑚 3 We also know that for this heat exchanger, 𝑈 𝑜 =284 𝑊 𝑚 2 °𝐶 . Find (a) the exchanger’s heat duty, (b) Δ 𝑇 𝑙𝑜𝑔𝑚𝑒𝑎𝑛 , (c) the required heat transfer area.