# Maximum mass flow in a shell & tube heat exchanger

• LEO31
LEO31
I’ve been trying to understand what’s the maximum mass flow that can be used in a already existing shell&tube heat exchanger.
The only information i have available is the datasheet of the heat exchanger above mentioned and the fact that we want to increase the hot fluid flow from 30 ton/h to 40 t/h, with a virtually unlimited supply of cold fluid available.
Many thanks in advanced to whomever might be able to enlighten me

The maximum mass flow is limited by structural considerations. You could get near infinite flow with near infinite pressure drop. But the shell would explode, the tubes would either collapse or explode, and the tube sheets would be shoved down to the end. In the real world, you need to calculate the pressure drop at the increased flow.

Start by studying the datasheet and estimating the pressure drops at the increased flows. You can do this by assuming turbulent flow, so the new pressure drop will be proportional to the square of the ratio of the flow rates. Do this check for both the hot and cold side flows.

Then look at the pressure drops in the associated valves and piping, and the pump curves of the pumps supplying the flow. Do not be surprised if you find a limitation elsewhere in the system that would prevent getting the desired flow. I once had a job that started with a request to check the size of a replacement pipe, and ended by replacing the entire steam and condensate system for a paper machine.

You also need to estimate the increase in heat transfer coefficient. The increase in flow will be larger than the increase in heat transfer coefficient, so the temperature rise/fall will be less. You need to check for the possibility that the system will not meet the desired ##\Delta T## at the increased flow. At the very least, alert your management that this is a possibility, that you are checking it to the best of your ability, but are not guaranteeing the result.

LEO31, russ_watters and erobz
Don't be surprised by 'unexpected' results when trying to increase heat transfer by 33%.

There can be other problems with trying to increase throughput.

I was the Controls Engineer commissioning a new plant that sold both solid and liquid sweeteners to the food canning industry.

One of their products was corn syrup. It was pumped out of huge tanks (500,000 pound capacity), thru tube-and-shell heat exchanger, and dispensed to tanker trucks. If you have ever worked with corn syrup, you know you don't want to handle it cold, its viscosity is too high.

A few days were spent trying to kill the temperature oscillation in the heat exchanger. I finally stayed overnight and dug into the situation. Even with the steam flow fixed at maximum to the heat exchanger, the output temperature was oscillating wildly,

Turned out that we were getting slug flow thru the heat exchanger! Fortunately there was enough mixing in the plumbing for a constant temperature at the dispense point to the trucks.

Have Fun,
Tom

LEO31

In a basic version of this problem there are two equations to work with. ##T_s## is the temperature of the surrounding environment (assumed to be a constant) ## T_i, T_o## are the mean inlet and outlet temperatures of the internal flow. ##P## is the perimeter of the pipe, ##L## its length and ##\bar{h}## the average convection coefficient over the length of the tube. ##c_p## is the specific heat of the fluid, and ##\dot m ## the mass flowrate. This analysis gives the following result:

$$\frac{T_s - T_o}{T_s - T_i} = e^{ -\frac{PL\bar{h}}{c_p} \frac{1}{\dot m} } \tag{1}$$

And the heat rate(power) ##q## extract from the flow is given by:

$$q = \dot m c_p ( T_i - T_o) \tag{2}$$

Assuming ##\dot m ## is what you are trying to manipulate to create the desired change, sub (1) into (2):

$$q = \dot m c_p ( T_i - T_s ) \left( 1 - e^{-(PL\bar{h})/( c_p \dot m)} \right)$$

The basic shape of this function is the following:

Depending on where you currently are on the curve (in your system), you may struggle to find performance change through the variation of ##\dot m ##(if that is what you are after).

Last edited:
LEO31
How many tube passes and how many shell passes are there? What is the geometry and fluid flow rates of the exchanger? What are the hot and cold fluids?

LEO31
Chestermiller said:
How many tube passes and how many shell passes are there? What is the geometry and fluid flow rates of the exchanger? What are the hot and cold fluids?
Thank you all for all your answers, I really do appreciate them.

Datasheet data:
• 6 tube passes and 1 shell pass
• Shell diameter of 550 mm
• Tubes with an outer diameter of 25 mm and an average thickness of 4.5 mm
• 169 tubes with a pitch of 33 mm
• 11 baffles with a 370 mm spacing
• cold fluid: 203 ton/h of water as a cold fluid that goes from 28°C to 38°C
• hot fluid: 30 ton/h of 70% w/w sulfuric acid that we want to bring from 184°C to 45°C

There are 3 key points that I’ve analyzed so far:
1. Nozzels diameters: by ensuring that the increase in mass flow rate doesn’t lead to velocities that are too high to be allowed at the inlets or outlets (no concerns here)
2. Pressure drops: the data sheet indicates that the maximum allowable pressure drop is 7000 Pa. Although my calculations show that the new mass flow rate would take us above that value, I believe I could get a higher allowed pressure drop by examining the pump settings
3. Lastly I’ve calculated the new overall heat transfer coefficient relative to the new mass flow rate, so that I could then find the new heat transfer area needed and compare it with the fixed geometrical area that’s available. Regarding the latter point, I found values of required area higher than the available area, which leads me to think that the desired temperature jump is too large and therefore I should settle for a lower ΔT value and use a second heat exchanger.
Again, I really do appreciated your time !

erobz and Tom.G
LEO31 said:
Thank you all for all your answers, I really do appreciate them.

Datasheet data:
• 6 tube passes and 1 shell pass
• Shell diameter of 550 mm
• Tubes with an outer diameter of 25 mm and an average thickness of 4.5 mm
• 169 tubes with a pitch of 33 mm
• 11 baffles with a 370 mm spacing
• cold fluid: 203 ton/h of water as a cold fluid that goes from 28°C to 38°C
• hot fluid: 30 ton/h of 70% w/w sulfuric acid that we want to bring from 184°C to 45°C

There are 3 key points that I’ve analyzed so far:
1. Nozzels diameters: by ensuring that the increase in mass flow rate doesn’t lead to velocities that are too high to be allowed at the inlets or outlets (no concerns here)
2. Pressure drops: the data sheet indicates that the maximum allowable pressure drop is 7000 Pa. Although my calculations show that the new mass flow rate would take us above that value, I believe I could get a higher allowed pressure drop by examining the pump settings
3. Lastly I’ve calculated the new overall heat transfer coefficient relative to the new mass flow rate, so that I could then find the new heat transfer area needed and compare it with the fixed geometrical area that’s available. Regarding the latter point, I found values of required area higher than the available area, which leads me to think that the desired temperature jump is too large and therefore I should settle for a lower ΔT value and use a second heat exchanger.
Again, I really do appreciated your time !
It sounds like you’ve got all the bases covered. I’m not sure I could add to this.

LEO31

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