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# How to determine Ice cooling rates2

## How to determine Ice cooling rates

(OP)
I have an application where I need to use an ice bath to store cold for an application requiring a constant feed of cold water just above freezing and while I can determine the mass of the ice required to prevent equipment short-cycling with a variable load, I'm not confident in my ability to determine how much surface area of ice I require in order to balance my incoming heat load and maintain a water temperature just above freezing.

The design will have an unknown length of copper pipe with refrigerant flowing through it so that ice builds up on the outside of the pipe with two ice sensors to ensure a minimum and maximum thickness of ice covering the pipes. There will be two water circuits pulled from this tank that both want water as close to freezing as possible and will each return water with an unknown rate and temperature anywhere from 3GPM to 20GPM with a temperature range between 38F and 70F.

There will be some water movement in the bath, but ideally it would rely on the suction and return of the feeds to draw the water across the ice. I do not know how to best quantify that effect on the thermal transfer between the ice and the water. All that being said, is there any general guideline for how to translate cooling capacity rate of ice as related to the surface area of ice? In this specific case, I am looking to make multiple 60kBTU circuits and need to know how much ice surface area of ice is required to cool the water at 60kBTU.

### RE: How to determine Ice cooling rates

You need a cooling capacity of 205 kW, conversely, that's 36.9 kg/min of ice.

Seems to me that nothing short of actively cooling it with a refrigerator of some sort is going to hack it. 205 kW equates to about 60 tons of conventional air conditioning

TTFN (ta ta for now)
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### RE: How to determine Ice cooling rates

60 kBTU per minute? Hour?

### RE: How to determine Ice cooling rates

What is "just above" freezing? 33F?, 34?, 35?

This looks to be really quite difficult to achieve, especially with your range of flows and temps. Water that close to freezing is very difficult to work with.

Does it need to be pure water? Can't you add some glycol to it and lower the freezing point instead?

Are those the max and min combined?, i.e. 3gpm at 38F and 20GPM at 70F? Or some other combination? So first work out your min and max heat load. but if it is that's a huge turndown to try and cope with.

Also your cooling pipes will have a different thickness of ice from the start of the entry into the water bath to the end point.

Some sort of cold air HX would seem better to me.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: How to determine Ice cooling rates

You get the maximum energy storage with slush. this is often pure water at 30-31F being stirred aggressively to prevent freezing into a solid mass. Working with solid ice is very difficult as the heat transfer rates change enormously, solid ice is a lousy conductor.
You need to figure out the combinations of flow and delta T that you need to work with in order to get min/max heat loads.
I have seen HX designed for this service, it is a specialized field.

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### RE: How to determine Ice cooling rates

(OP)
sorry for the delayed response. I checked the notify me box but it didn't do anything.

Its 60kBTUh - 5Ton. per stage. I plan on three stages. Thats what, about 17.5kW per stage.

I know fast moving water with crushed ice/slush would give the most surface area and therefore the highest transfer rate per pound of ice.

What I ultimately want to know is how much surface area of ice do I need to achieve my 17.5kW of cooling of the water.

The temperatures and flows of the two are the ranges. There are two individual pumps that each feed from the tank and go to a load before returning to the tank. Most likely one will be at 12-16 GPM and returning water temperature at 43F and the other will flow in the 2-6 GPM range and return water temperature at 66F.

I'd like to get the water as cold as close to 32F as practical, but 34F would still be acceptable.

I don't need any special quality of water, but I do not want to use glycol to lower the freezing point because it both will risk ice buildup on the device I need to cool which is to be avoided.

We made a tank that has ~100' of 1/2" copper tubing on a 5T circuit and have found that we are both building ice BUT the water temperature has stabilized over 40F. To me, I take that to mean the surface area of the ice is too small and this ice-water thermal transfer is not sufficient to cool the water.

I was hoping there would be a better way than me trying to empirically test how fast water melts ice by surface area. I don't think I need to be completely optimized to have a perfectly engineered precise surface area of ice, but I do want to figure out if our design is even practical... can I do this with 50-100SF of ice, or is this 50,000-100,000... that is a significant difference, my gut says that 50-100SF range is likely in the correct range based on the fact I"m currently under 5SF of area with the 100' of 1/2 tubing with a thin coating of ice, but I'd feel more comfortable if I didn't just "go with my gut".

### RE: How to determine Ice cooling rates

I'm trying to understand why you aren't doing this the way it's normally done. A multistage chiller keeping a reasonably sized tank of water/glycol at whatever temp you need it to be. Then you draw off whatever amount of "cooling" you need for the process?

Extremely flexible.
Fairly compact.
Highly efficient.
Maintainable by almost anyone.
No tightrope balance garbage.
Approachable, even by management!

This method allows you to design the entire system knowing just the heat load.

Keith Cress
kcress - http://www.flaminsystems.com

### RE: How to determine Ice cooling rates

(OP)
For a couple reasons.

1. The load is both moderately variable over a short duration and over the course of the year has a >10:1 load change. The system used to use direct refrigerant, but the variable loading and the resulting cycling was both terrible for process consistency which caused problems with temperature stability as well as premature compressor failures.
2. We are also required to maintain a cooling fluid temperature over the freezing point of water, so I cannot get any colder than normal ice-water, but I also do not want it to raise even momentarily over 37F and ideally under 35F.

The idea of an ice-bank seems perfect as it could allow for energy storage to prevent compressor short-cycling, provide a stable temperature buffer, and potentially allow for compressors to be load-shed for PLC demand response if needed. The "problem" is that we started with ~100' of copper tubing as the seed for the ice which is roughly 1" in diameter and with that we are only able to stabilize the system with 4T of demand instead of 5T and only with a water temperature at 37F instead of hopefully 34F. I assume the answer is "more ice surface area"... what I don't know is if I need to increase the surface area by 20%, 200%, or 20,000%.

### RE: How to determine Ice cooling rates

I suspect you need more agitation of the water to make up for the poor thermal conductivity of ice and water.

### RE: How to determine Ice cooling rates

(OP)
that was the first thing we tried. Technically there is always room for "more" movement, but I do not believe it is our solution here. I've tried to survey the water temperature around a number of locations and the water temperature does not have a large variation (generally +/- 1F)

I'm fairly convinced this is a surface area issue and I need more surface area, but I have no clue if "more" means. Is it 2sf more or 20,000sf more.

Empirically, I saw that the water temperature actually increase when we allowed the compressors to run continuously. What would happen is that ice would build up and once it formed a solid block, the temperature of the water would actually increase.

We have some other design issues with this current tank so we are planning on making a new tank, but before we can do anything I think we need to know how much surface area of ice we need in order to achieve a stead state of 5T of cooling rate.

I know I can't get an exact number because I can't define how much water movement we have, but it would be nice to at least have something rough to hang my hat on.

### RE: How to determine Ice cooling rates

Thanks for the info.
Still seems..

1) Direct refrigerant. Well heck ya that's hard to do. I'd expect pretty high instability since it's not a thermal mass like water delivers.

Doesn't count.

2) Not hard at all with a correctly done multi staged compressor system. I just installed one that had four 20hp scroll compressors. One was unloadable by half. That meant the system could operate as if it was:
10hp, 20hp, 30hp, 40hp, 50hp, 60hp, 70hp, 80hp. Feeding an 800 gallon tank which makes a serious thermal line in the sand. No short cycling ever.

Keith Cress
kcress - http://www.flaminsystems.com

### RE: How to determine Ice cooling rates

You're discovering why not many people do it this way.

Operating this close to the liquid / solid boundary is very hard. It's like trying to get 99C water at atmospheric sea level pressure without bubbles or boiling. virtually impossible.
I was responsible for some water bath heaters a few years ago and the highest atmospheric pressure heater I could get was 90C. Then you needed to pressurise it and I got 105C. The bursting disc went on one one day and it erupted like a geyser for about 20 minutes! but the point is the same - that close to the change of state and it gets very difficult to control.

What does your tube arrangement look like? I'm struggling to see how long the incoming water has to flow past the ice and how does the temperature range change.

the glycol tank idea still sounds good to me as you can maintain this much easier at your desired temperature I think.

your comment "because it both will risk ice buildup on the device I need to cool which is to be avoided." doesn't make sense to me. If its water at somehow 34 to 35F or a water glycol mix at 34-35 F - what's the difference?

I was trying to work out how this works thermodynamically. You have warmish water that needs to loose energy. It encounters ice. The way to cool the liquid is to melt the ice thus absorbing energy as it changes state. You now have some water at your higher temp plus some water at basically 33F. But to get from 40-70F down to 34F you need to melt a lot of ice. But then the ice need to regenerate for the next gallon water. you don't then have a stable ice surround.

40F might be as low as you can go without a huge area of ice compared to the water flow.

Then it becomes how do you control the thickness.

Maybe some sort of tilted flat plate which you put the cooling tubes behind, it grows a set thickness of ice and then you gently pour / trickle your water accross it at different flow rates per flat plate depending on incoming temperature to avoid it freezing at the bottom?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: How to determine Ice cooling rates

(OP)
Definitely sorry if I offended anyone in my responses. That is definitely not my intent.

When the tank was built, we didn't consider the water-ice barrier to be a capacity constraint at all and instead designed it for ease of fabrication... the tank is a cylinder with the return at the top and flowing at a tangential angle to induce a swirl and the two pump suction ports on the bottom. The cooling circuits are three concentric circular coil rings. The coils on the same circuit are roughly 3" apart. The first thing we did to troubleshoot was to install a pump down at the bottom of the tank to push the water back up and continue with the swirl. That pump definitely improved things and now the water water is moving a lot and the temperature is consistent across the tank +/-1F other than right against the ice coils.

Once running, we could see that this setup was a problem and we have tested out a number of improvements and come to the conclusion that the tank needs a complete redesign from the tank shape to the coil length and shape. The one thing that appears clear to me is that we simply do not have enough ice surface area to allow for thermal transfer. We will do things like increase the tank volume to allow for a longer time to cool in the tank and install baffles to force more contact time and more uniform mixing across all the coils, but what at the core of this design is "how much surface area of ice is required" and that is what I'm trying to get an answer on.

Using liquid only or using direct refrigerant are options to consider, but the ice bath solution is the ideal one if it can be made to work as the direct refrigerant one or the liquid-only solutions have their own practical issues with our requirements. I just can't get even a conservative estimate for what total sf of ice I should plan for to make this solution work. If it requires 100sf, we can do it, if it requires 100,000sf... we can't and have to deal with the downsides of the other solutions.

### RE: How to determine Ice cooling rates

There is a lot of circular thinking going on here. You want to achieve as large a heat flow as possible and yet you want to maintain your tank at as close to freezing as possible. These are contrary goals and therefore impossible.
The mistake you are making is to equate the desire for 34F water coming out of your tank to mean that your tank must be uniformly 34F, top to bottom. This is, of course, impossible if you are adding 70F water to the tank at a significant rate. Mixing the tank simply short circuits some of this 70F water directly to your outlet.

It also means that you are not using the ice as a heat storage medium at all. The ice is just a heat transfer medium, for no benefit. If you were using ice for heat storage, to increase peak cooling capacity above that of your refrigeration unit, then the amount of ice in your tank would have to fluctuate accordingly.

When water is at 34F, the ability of ice to cool it further is almost zero (at 32F it actually is zero). This is why you are looking at almost an infinite surface area required. In order to get heat to flow there must be a delta T. More heat flow means more delta T. For this reason most heat exchangers are set-up for counter-current flow, which your tank is definitely not. There was a recent thread about cooling a quench tank that had similar problems.

There are a number of ways to design a system that works but your current approach is not one of them.

### RE: How to determine Ice cooling rates

(OP)
Sorry for the confusion. I do not care about the temperature uniformity within the ice bath tank. I care that the water I draw out of that tank is always 34F and never goes over a maximum of 35F nor under a minimum of 32F. My intention in mentioning the current uniformity of the temperature of the water in the ice bath was to indicate that there is sufficient water mixing in the tank that I cannot further increase the thermal transfer of the water and ice simply by mixing the water any more. Before we added the mixing pump and used only the return feed to mix the water, there was a significant thermal gradient within the tank.

My intention is to use the ice as both a heat storage medium AND a heat transfer medium. I do intend on having the ice fluctuate and didn't specifically mention that part because the storage side is straight forward and I figure that as long as the minimum ice level has enough surface area to meet the heat transfer rates required, the larger ice level will also meet that rate.

I realize I am probably not sufficiently explaining what I'm looking for but its essentially the numbers or formula behind this statement you gave:
"When water is at 34F, the ability of ice to cool it further is almost zero (at 32F it actually is zero). " - I can't find those numbers or the formula to quantify that "ability of ice to cool [water at a given temperature]."

I just found one place online recently that mentioned something like 500 BTU/(sf*F*h) as a general rule for a coiled tube heat exchanger in liquid water, and using that, I can estimate that I'd need 60sf of surface area to transfer 60,000 BTU with a 2F temperature differential. That happens to work out nicely with the ice mass I want for melting as storage as that would generate a surface area of 68SF at the smallest mass and 90SF at the largest.

I'm glossing over all the details about how I know that the ice at the core will be colder than 32F and that the cooling capacity of the compressors changes with the temperatures of the medium which I understand and am considering such details in the design, but at the core, I know I need to have a grasp of what ice's rate of cooling is for ice cooling water and without that I don't know if I need a surface area of 60sf or one of 600,000sf to ensure we have a continuous supply of 34f water for any demand load from 1BTU up to 120,000BTU.

### RE: How to determine Ice cooling rates

I don't think you've offended anyone - this is quite an interesting problem.

I do think though a bit like composite pro that you may well already be at or close to what is practical to achieve with this set up.

A diagram helps enormously for everyone to understand what you have.

My interpretation is that you current set up is a tank with three coils inside? You have also introduced a return flow path presumably bottom to top.
So you have a certain flow through and certain return flow re circualting the water. What are those values relative to each other?

My guess is that you need the recirc to be about 10 times the flow through to work best, especially when you have a high inlet temp.

However when you do even a little bit of research, you find that the water ice interface zone is a complex, uncertain area of physics and not studied well.

But whatever it is as the temperature difference between the ice and the water gets smaller and smaller the required surface area will get bigger and bigger, probably exponentially.

You have a perfect set up now to do a lot of experimentation in terms of approach temperatures, throughput, recirc flow, chiller flow / power.
I suspect you will find that even with a very low through flow compared to recirc flow, you will struggle to get the temperature down to your aimed for 34F. There is clearly going to be an effect from different flows over the same square area, even with the same approach temperature.

Ultimately with your different flows and temperatures you will need a varying surface area, i.e. more cylinders at higher flow / temperature and less at lower flow / lower return temperatures.

It is very interesting to get into the mechanics of this and sometimes you find that no one really knows because they've never tried to do it that way.

Maybe it will work / be effective, maybe it won't. Please let us know how it goes.

But I do think the glycol mix idea and keep it all liquid is a far easier thing to control so long as your bulk supply is big enough and you circulate it well. IMHO.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: How to determine Ice cooling rates

(OP)
"However when you do even a little bit of research, you find that the water ice interface zone is a complex, uncertain area of physics and not studied well.
But whatever it is as the temperature difference between the ice and the water gets smaller and smaller the required surface area will get bigger and bigger, probably exponentially."

Yup... I started looking around and was shocked that I couldn't find anything and figured it was just my inability to search in the right academic corner. If I can't find anything else, I plan on playing around with our current setup to see how long that ice takes to melt in our current setup if we remove the load and the cooling to get an idea of what the transfer rate is at these approximate conditions... it isn't perfect, but better than nothing.

I like the idea of ice because, as long as I can get the energy transfer rate large enough to stabilize at 34-35F, then I don't have to worry about going too cold or going too warm and can cycle the compressors and even allow for load-shedding possibilities. The critical issue I believe is just having a sufficient minimum surface area of ice. My concern with liquid only is that with a max of 2F temperature rise, I only get ~16kBTU of storage per 1000 GAL of water and that means that translates into a large storage tank which also translates into a large heat loss just from the tank. This solution should work, but it would require some different compressors and one of the nice things about having three identical 5T units is that when one goes down for mechanical reasons we should still have enough capacity to continue to operate mostly normally.

Knowing my max flow is 20GPM and that as we increase water flow rates the return temperatures drop some, I figure a tank with 400GAL of liquid water. would allow for at least 20 minutes of time in the tank before it makes its way back to the pump instead of what is likely 5 minutes now. I'm thinking that instead of a simple cylinder which would require lots of internal mixing to get the water in contact with the ice, I want to make a rectangle and put the water in at one end and take it out on the other side. It would have baffles to force the water path to go under one baffle then over the next repeating a number of times. The refrigerant circuits would run perpendicular to that path and effectively follow the same path the water would be flowing. The idea is to allow plenty of time and surface for ice-water contact without having to force the circulation like we do in the cylinder. Assuming that ~70 SF of ice surface is sufficient per 5T circuit, I would start with making the refrigerant loop spaced to prevent freezing solid when operated using the ice sensors we have and then plot the baffles and tank around that to meet the 400GAL sizing. My problem is that this all works nicely with 70 SF, but if that is 700SF or 7000SF then this solution looks much less attractive.

### RE: How to determine Ice cooling rates

(OP)
I don't think it is arbitrary at all, but I'll restate it in case that helps. I didn't leave specific numbers at the beginning because I'd rather have a formula than just a value so I can apply it under other conditions (like if I instead increased the water temperature to 35F).

"How much surface area of ice @32F is required to provide 60,000 BTU of cooling on 34F water?"

The only thing I left as arbitrary is the shape of the ice and the flow of the water which I'll let anyone who can answer the question above define those details.

### RE: How to determine Ice cooling rates

(OP)
if this was a batch process, I'd consider crushed ice a viable solution, but this is a continuous process with a variable load up to 120,000 BTU.

Beyond the fact that crushing ice is more complicated to produce than ice rods and requires moving parts which would be more susceptible to breaking down, I don't know how crushed ice can be reliably controlled with the precision required to maintain the temperatures so close to freezing without potentially freezing the system solid if there is a lot of crushed ice in the tank and the heat load suddenly stops.

My concern with surface area is to the extend that i have no clue what the cooling capacity of ice is and my problem isn't a simple "I have 100# of water at 45F and want to cool it to 33F, how many pounds of ice do I need?"

My specific application question was about using ice to cool at a rate of 5T, but at its core, I'm generally curious about "how FAST does ice cool water" and that is something that apparently doesn't actually have a known formula or property.

### RE: How to determine Ice cooling rates

Seems to me that you have this problem regardless of the form of the ice. Crushed ice has the highest possible surface area, so it'll have the best thermal transfer. How are you even getting the existing ice form into water; that requires mechanical or human work.

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg
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### RE: How to determine Ice cooling rates

If this is a continuous process, in my opinion, you need to throw this ice based concept in the garbage and find an alternate route.

### RE: How to determine Ice cooling rates

Ditto! I can't think of a bigger waste of time and the company's money. This is a classic wild ass effort that will take months of resources before it all gets sh!t-canned and done reliably. People do this all the time reliably and efficiently without ice.

Keith Cress
kcress - http://www.flaminsystems.com

### RE: How to determine Ice cooling rates

(OP)
so what you three are saying is that you don't know the answer, so you would rather avoid the question?

As I mentioned, this was originally direct refrigerant, but that solution is not capable of the turndown ratio and response time required. I won't get into all the reasons why refrigerants and anti-freeze are not ideal solutions for the process. I'm evaluating an alternative idea which involves ice and would be perfectly workable if the heat transfer of the ice was sufficient, the first attempt showed it wasn't. The question is straight forward and you can either help answer the question or not... "how much surface area of ice is required to remove 5T of energy from 34F water assuming the water remains at 34F and the ice remains at 32F?" With that information, I can evaluate if ice is a practical solution for us or not.

That being said, if you have an alternative solution that will provide cold water that is maintained between 32.1F and 35F when you have any heat load between 100 and 120,000BTU which can change >10,000BTU/min and involves return water temperatures between 35F and 70F and is capable of running 24/7, I'm all ears.

### RE: How to determine Ice cooling rates

ABL33,

No, what they are saying is that this is an unexplored area of engineering FOR A REASON. They aren't trying to avoid the question - they are trying to suggest alternative means that are certain to work. There are simply easier, more consistent, and less expensive ways of doing what you want without needing to go to an ice slurry design.

#### Quote (ABL33)

That being said, if you have an alternative solution that will provide cold water that is maintained between 32.1F and 35F when you have any heat load between 100 and 120,000BTU which can change >10,000BTU/min and involves return water temperatures between 35F and 70F and is capable of running 24/7, I'm all ears.

Then lend me your ears, because there is solution that does not require ice. Itsmoked provided this with his "reasonably sized tank" comment. Your short-cycling compressor means that your tank is too small - the temperature is swinging too quickly when the compressor kicks on. The only way to solve this would be, as previously suggested, a multi-stage compressor, a larger tank, or ideally a combination of both. Each source can pull and return water up to 20 gpm and 70F EACH, by your OP. You have, as I understand it, a possibility of a Q = (40 gpm)(8.34 lb/gal)(1 BTU/lbF)*(70F-32F) = ~12,700 BTU/min heat load. BTW, please give heat loads in units of energy/time. Saying there is a 120,000 BTU requirement means NOTHING.

That heat load, when applied to your proposed 400 gallon tank with no cooling, results in a dT/min of ~3.8 F. I assume that your compressor is sized slightly larger than that heat load, so when it kicks on AND your heat load is low (i.e. 6 gpm return and lower temperature), your tank will hit setpoint in about a minute or less, short cycling the compressor. If your current tank is anywhere near 400 gallons, its no wonder you are having issues.

You DON'T NEED a chiller that has the same turndown as your heat load turndown. You simply need to size the chiller and reservoir tank volume such that the lowest turndown on the chiller will give it a full cycle time. This can be aided with correct setpoint selection and proper deadbands on the controls tuning.

If you must pursue the ice thing, here are a few things I found that may help you:
If you want to dig deeper on ice melting mechanics, I direct you the following paper (though it only explored natural convection melting of ice).
https://lib.dr.iastate.edu/cgi/viewcontent.cgi?art...

If you really want to continue with the ice idea, you may want to look into systems like DeepChill, which generates very small particle size ice slurry. There are no existing models I know of to predict film coefficients for water-ice forced convection, so trial-and-error with smaller sized ice is the best you'll get.
https://www.sunwell.com/deepchill/

### RE: How to determine Ice cooling rates

#### Quote (abl33)

provide cold water that is maintained between 32.1F and 35F when you have any heat load between 100 and 120,000BTU which can change >10,000BTU/min and involves return water temperatures between 35F and 70F and is capable of running 24/7, I'm all ears.

What makes you think an ice slurry based solution can do all of that? You're going to need to come up with a whole additional system to provide ice.

You've said your thermal load is 60,000BTUh per stage, x 3, for a total of 180,000BTUh. If your system cools your process water at 100% efficiency, you're going to melt 1250lb per hour of ice- which means you need to make 1200 lb per hour of ice. For reference, a typical restaurant-grade ice machine will make roughly 10lb per hour of ice cubes.

Anyway, back to your main question- no one is providing a simple direct answer because the answer to your question depends on a pretty good list of factors that will be difficult or impossible for you to measure (i.e. mean water velocity over the ice surface). And even if you could measure them, the process you're laying out is unlikely to be energy efficient or cost effective - we're trying to help you.

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