heat transfer vs. velocity in forced convection across sheet

[drcrash]

Is there a simple generalization about the effect of velocity on heat transfer when using simple forced convection across a sheet? How does the velocity affect the heat transfer---e.g., almost linearly, or not nearly linearly, or what?

I want to be able to heat a 2 x 2 foot sheets of 2 to 6 mm. plastic reasonably evenly and quickly. (For thermoforming, on site.) I am considering building a simple collapsible convection oven to do it, using an HVAC "draft inducer" (furnace exhaust blower) to recirculate the air, and pumping it with a 1500-watt heat gun or two to keep the air temperature up.

(An inexpensive draft inducer should give me 100 cubic feet a minute through a 1/3 square foot cross section duct over the plastic, for 300 ft/min or 5 ft./sec. airflow. Not exactly high velocity, but I'm trying to figure out whether I'd really derive much benefit from a much more expensive draft inducer's 2x or 3x more airflow.)

I don't know whether this is a reasonable thing to do, or if I should go with the usual kind of radiant-heat oven to heat the plastic.

Any thoughts?

 

[IRstuff]

Well, consider what a convection oven buys you in general.

TTFN

 

[insult2injury]

Nusselt relations are typically in the form Nu = C * Re^m * Pr^n where m is typically less than unity. The temperature difference between the air and the surface, however, does have a linear effect on the heat transfer.

I2I

 

[IRstuff]

The velocity dependence is embedded in the Reynolds number, and the heat transfer coefficient is proportional to the square root of the Reynolds number, so the overall relationship is proportional to square root of velocity.



TTFN

 

[25362]

The boundary air layer thicknesses change across the sheets' length so that the heat transferred wouldn't be uniform, and this without considering heat conduction resistances of the plastic.

As for the time taken to heat the sheets up, it all depends on the temperatures, those of the heating air probably limited by the draft inducer construction.

For unsteady state heat transfer by convection, assuming the air temperature T is constant, T₁ and T₂ are the initial and final (assumed uniform) temperatures of the sheets of mass M, specific heat C, area A, taking U as overall heat transfer coefficient, time t is estimated from:

t = (MC/UA) ln[(T-T₁)/(T-T₂)]​

 

[BigInch]

Considering that the sheets are 2'x2'x6mm, there should be no great change in heat transfer across the surface from a changing boundary thickness layers.

Going the Big Inch!

http://virtualpipeline.spaces.msn.com

 

[25362]

For air flowing at 5 fps, my estimates for the thermal -not hydrodynamic- boundary-layer thickness [δ] are: on the first 10 cm, [δ]~6 mm; at 50 cm from the leading edge, [δ]~14 mm.

The formula used for this estimation:

[δ] = 5[×](distance)[÷]Re^0.5​

where Re = (density)(velocity)(distance)[÷]kin. visc.

Definitions:

Hydrodynamic boundary layer: region where viscous forces are felt.
Thermal boundary layer: region where temperature gradients are present in the flow.

 

[sailoday28]

See the text written by Schliting.

Regards

 

[BigInch]

You guys are right. It seems to be 1/2 the average at the edge, correct?

Going the Big Inch!

http://virtualpipeline.spaces.msn.com

 

[25362]

Although my estimation of Re numbers was correctly done with absolute, or dynamic, viscosities my definition of Re should be corrected to say so, not kin. visc., as I wrongly wrote.

BigInch, I don't know about that ROT, may be it refers to pipes or tubes with inherent surface rugosities. If you find an answer please let us know about it.

On the other hand, a ROT that I have noted is that the length of pipe or tube before the growing hydrodynamic boundary layers become fully developed (e.g., when they reach the center of the pipe or tube), known as entry lengths are:

for laminar flow, 120 diameters,
for turbulent flow, 60 diameters.

 

[drcrash]

OK, this is sounding doable...

As I understand it, high-end commercial convection ovens for heating plastic generally blow the air 1 to 5 meters per second.

I'm guessing that they top out a 4 or 5 meters/second because the limiting factor is the thermal conductivity of the plastic, not the velocity of the air across its surface. Unless you heat the plastic from the inside using RF or something, it's going to take a few minutes per millimeter of plastic for the interior to heat up, and applying more heat at the surface would only burn the surface. (I need to check that, though.)

If the heat transfer rate is roughly proportional to the square root of the velocity, then a cheesy 1-meter-per-second airflow should heat things about half as fast as a high-end 4-meter-per-second airflow. I think I can hit that with a $10 heat gun and a $150 draft inducer for a home furnace.

That sounds pretty good to me, for the kind of low-production-volume stuff I have in mind. If it takes me 10 or 12 minutes to heat a sheet of plastic, rather than 6, I can live with it, if I can make my own portable oven for $300 instead of spending thousands. (The latter just isn't an option.) I spend more time making bucks and trimming the parts than actually vacuum-forming anyway, so a few minutes more per part is no big deal.

Now the tricky part is ensuring that I get fairly even airflow, with no "cold spots" that heat up very slowly.

 

[zekeman]

I like radiant for this problem. You could probably make your owwn heating strip plane above you workpiece on the cheap with nichrome wires or buy the heating strips. it seems a lot cleaner, more efficient and you will get more uniformity of heating to me.

 

[drcrash]

I may indeed go with radiant, using nichrome coil. That's the easiest route to something that works fairly well.

What I'm trying to figure out is whether a convection oven would give better results, and how hard it is to construct a good enough convection oven. Ideally, I'd come up with a scalable design for a telescoping and/or collapsible oven. (That seems possible, because the bulk of a convection oven is just a pair of boxes with some holes between them---a plenum and the oven proper.) I'd like to be able to give plans like that away.

A big part of the appeal of convection is that you don't get hot spots in the same sense as with IR. Assuming the air is well mixed, all parts of the plastic will converge to the same temperature---the air temperature---though at different rates if the airflow isn't very even. At least at first glance, it seems like this should make it fairly easy to build something that gets very good results, though maybe with a time cost. (Nothing will scorch or bubble, but if the airflow is very uneven, it may take much longer for some parts of the plastic to converge to the same temperature as others. If you compensate in the easy way, by turning up the heat, you reintroduce the problem of hot spots.)

I'm not sure that this actually pays off in practice.

Actually constructing a convection oven seems relatively easy; the hard part is tuning the design to get even airflow for fast heating all over.

(Unfortunately, I don't have a thermal imager or other nice test equipment. If I did, I'd think it'd be pretty straightforward, e.g., partially blocking holes that are delivering too much air. I might get by with a board with some paper thermometers on it.)

 

[IRstuff]

Uniformity is not necessarily a benefit of convection. The main attraction in commercial ovens is the the increased speed. In a natural convection, the air closest to the material is at the same temperature as the material, resulting in a htc of something like 2-4 W/m²K, while a forced convection can double or triple that value.

But, unless you get that uniform air flow, you'll get stagnant or slow-moving regions that wil have lower htcs that will cause nonuniformity.

Generally, you get speed at the expense of uniformity.



TTFN

 

[drcrash]

IRstuff, I'm not sure what you're trying to tell me.

I understand that in a pure convection oven (no direct infrared), heating rates will vary with uneven airflow. However, as long as the airflow is nonzero everywhere and the air is continuously mixed and redistributed, all temperatures should converge from the air temperature from below. Any nonuniformity is temporary, and nothing will exceed the air temperature. (Or am I mistaken about that?)

This makes me think that it should be easy to build a convection oven that heats sheet plastic very evenly in terms of final temperatures, though perhaps unevenly in terms of how long it takes all the plastic to get to those temperatures. Subsequent tuning for more even airflow would affect the time for the coolest parts of the plastic to heat up, but not the eventual temperatures obtained.

(This, in itself, still might not be good enough. If the heating is so uneven that it takes a very long time for the whole sheet to reach forming temperature, that could be a problem. Some plastics degrade significantly if held at the forming temperature too long, even if they never exceed the forming temperature. Still, this seems much easier than designing a good general-purpose convection oven, which must deal with the vagaries of airflow around various non-sheet shapes.)

My understanding is that up to a point, increased airflow increases both average heating rates and (medium-to-long-term) uniformity, not one at the expense of the other. It increases uniformity by ensuring that the air is of more uniform temperature throughout the oven.

(If the air moves too slowly, it may dump too big a fraction of its heat into the plastic it encounters first, leaving the air significantly cooler when it flows over the remaining plastic. If airflow is high enough, the air can flow all through the oven several times before most of its heat is transferred to the plastic. Similarly, if the air is cooled by insufficiently-insulated oven walls, plastic near and downwind from those walls may not be heated as much. Higher airflow should alleviate that, too, ensuring that any given bit of air can't hang out near a cool wall long enough to be cooled much. As long as the air is sucked up and redistributed frequently relative to the cooling of the air in contact with plastic or walls, air temperatures should be pretty even, even if the oven is not very thoroughly preheated.)

So far, it seems to me that the big advantage of IR is in basic tuning. If I turn out the lights, I can see how the glow is distributed, and use screening to reduce the IR at hotspots. Seeing airflow is not as easy, so turning a passable design into a good one may be harder. On the other hand, if I use IR, I still have to deal with convection issues, e.g., cold edges or corners even when the IR is entirely even, so fine tuning is similarly tricky.

 

[IRstuff]

Uniform temperature does not guarantee uniform heating. That's because the heat transfer coefficient of the air is dependent on the velocity of the air next to the object, not just the temperature:

Q=area*htc*deltatemp

TTFN

 

[drcrash]

I believe I've acknowledged that uniform heating does not follow from uniform air temperature, and that the rate of heating depends on the velocity.

I've said so myself, repeatedly.

My point is that while heating rates for different regions of the sheet will be different, depending on air flow, they will all top out at the air temperature, approaching it from below.

So, for example, if the airflow is up to 4x higher in some places than others, and the htc depends on the square root of the velocity, then some regions may heat up to 2x slower than some others due to uneven flow. But if the air temperature is uniform, say 300 degrees, they will all approach 300 degrees after a while, and none will exceed 300 degrees. If they were somehow to exceed 300 degrees, the airflow would cool them off, while continuing to warm the regions that were below 300 degrees.

(As I understand it, in mixed IR/convection ovens, this property is used to cool off hotspots that the IR distribution alone would create, as well as to speed up heating of cool spots.)

 

[magicme]

this will not address all the issues you are facing here.
however, the link below points to a page from my heat transfer course that includes a simple calculator for the forced convection over a flat plate at zero degrees angle of attack. it will run in your web browser if you allow javascripts.

http://myweb.wit.edu/leod1/MECH594/mixedflowplate.html

the equations are also shown in the spreadsheet screen capture.

i post this for my students as a guide for writing their own spreadsheets to do this calculation. possibly it is useful to you.

regards

daveleo