A small and inexpensive kiln for melting metals and firing clay
RepKiln_Heat_Transfer_Calculations.odsspreadsheet containing simple heat transfer model of kilnspreadsheet  42.31 kB  05/08/2017 at 06:18 


RepKiln_Heat_Transfer_Calculations.xlsspreadsheet containing simple heat transfer model of kilnmsexcel  34.50 kB  05/08/2017 at 06:17 

The kiln has two heating elements, each about 33 inches (84 cm) long  this is determined by the physical construction of the kiln. We are looking for a heater power of 1500W at about 110AC, so this gives us a heater resistance of about 8 ohms and heater current of about 13.6 amps. The resistance of the heater will increase slightly as it heats up, but for sizing purposes we'll use the cold resistance so we don't trip the (15 amp) breaker when the kiln starts up. There are two options: two 16 ohm heater elements in parallel, or two 4 ohm heater elements in series.
It is likely that the heater will be wound into a coil, so we need to know how to calculate the length of a helical path. Referring to the figure below, we have the length of one turn of a helix as
where r is the helix radius and p is the pitch (distance traveled along axis for one turn). L_helix is the length of the red trace shown in the image below. The total length of the heater wire is
and the total length of the coil is
where N is the number of turns.
The next step is to size some candidate heater elements using parameters for some common nichrome heating wire. According to this table on the Wikipedia Nichrome page the recommended wire gauge for a 1500W heater operating at 110120V is B&S No./AWG 1216.
As an initial check, let's pick the Nichrome 80 alloy (this appears to be the same as "Nichrome V" in some sources). According to Wikipedia, this alloy has a composition of 80% nickel and 20% chromium, and a resistivity of 1.09E06 ohm meters. With these numbers, a 16 ohm wire would be 19 meters (63 ft) long. That's a little long. A 4 ohm wire would be 4.8 meter (16 ft) long. So let's go with two 4 ohm heaters in series.
OK, on to the next step. Let's stick with 16AWG Nichrome 80 for the moment. We'll need about 5 meters of wire (16 ft) for each 4 ohm heater.
At this point, we have several constraints on the heater coil:
16AWG, Nichrome 80
L_coil = 0.84 m (33 inches)
L_wire = 5 m (197 inches)
r = 3mm (0.12 inches)  this is set by the desire to have a winding mandrel of 3/16 inch diameter
These constraints completely determine the shape of the coil, and we can solve the above equations for the pitch p. First let's write down this relation
and then we can plug this into the very first equation up top and rearrange to get
Finally! Now we can get the pitch of the coil and figure out if this is something we can wind by hand using the little Sherline lathe. There is a spreadsheet to perform these calculations on the Repkiln Github repo called heater_coil_calculations. Here is a screen capture,
So the pitch is 3.4mm (0.134 inches). It should work out fine to wind this by hand on the lathe. Stay tuned for that in a later update!
SUMMARY: There will be two heater elements, each 4 ohms, in series, for a total heater resistance of 8 ohms. Each heater will be made of 5 meters (16ft) of 16AWG Nichrome 80 wire. Each heater will be wound in 250 turns on a 3/16 inch diameter mandrel, with a pitch of 3.4mm (0.134 inches), for a coil length of about 33 inches (84 cm).
In an earlier log we looked at the steadystate conditions to get an idea for how hot the inside of the kiln would get. This helped us get an idea for what thermal conductivity, wall thickness, and heater wattage were acceptable for getting the kiln to the desired temperature. But the steady state analysis does not tell us anything about the rate of heating. It is useful to have an estimate for how long will it take the kiln to warm up and cool down. In this project log we estimate this timedependent behavior by numerically solving an approximate solution to the transient heat conduction equation.
As we did in the steadystate analysis, we use a 1D model  the entire kiln is considered to be just one chunk of "wall". We want to model the temperature of the wall material as we move from inside to outside.
Other assumptions: material properties are constant across x, t, and T. In other words: density, thermal conductivity, specific heat capacity are constant for the entire wall, for all time, for all temperatures.
The partial differential equation that describes heat flow in the wall is
where T is temperature, t is time, k is thermal conductivity, c is specific heat, rho is density, and x is distance through the wall, from inside the kiln to outside. We also need to specify the boundary conditions (heat flow at inside and outside surfaces) and the initial conditions (initial temperature profile of wall) in order to find a solution to this differential equation.
There are many ways to solve this equation analytically. However, we have kind of funny boundary conditions that make an analytical solution somewhat mathematically involved. An alternative way to solve this is to approximate the system as a finite difference equation, and then numerically integrate it using a simple python script.
The first step is to convert the partial differential equation into a recurrence relation with finite differences. The first derivative in time, evaluated at location x, becomes
The second derivative in space, evaluated at time t, becomes
Now we can plug these approximations into the original equation to get the recurrence relation that gives us an approximate solution
The above relation holds for the internal pieces of the wall, but not for the boundaries. At the inside surface of the wall, we need to look at the heat transfer from the heater. At the outside surface, we need to look at the convective and radiative heat transfer to the surroundings.
For the volume element on the inside boundary, where x = 0, we have
For the volume element on the outside boundary, where x = L, we have
where
and
where T_inf is the temperature of the surroundings, sigma is the StefanBoltzmann constant, and h is the convective heat transfer coefficient.
Now we have all we need to write a little script to iterate the recurrence relation. You can find a python script that does this called kiln_heatup.py on the RepKiln GitHub repo.
The two plots below show the output of the python script. In the first plot, showing warmup, the initial condition has the wall at a uniform temperature of 300K. Heater power is 1500 W. It takes about 14 hours for the temperature inside to rise to 1100K (830C or 1520F). The x coordinate is distance through the wall from inside (x = 0 cm) to outside (x = 10 cm). A minor note: x actually defines the location of the center of each discrete volume element, so the actual inside and outside wall surfaces are located at dx/2 and L+dx/2 respectively. But since dx is pretty small, this error is negligible, or at least negligible compared to all the other errors in the model!
We can solve for the temperature during cooldown. We set the initial condition to the wall temperature profile after warmup, set the heater power to 0W, and iterate again.
The take home message from this analysis is that the kiln is going to be slow. Fourteen hours is a long time to wait to get up to 1100K. We can hope that perhaps the model is conservative...
Read more »The finished kiln will need about 70 bricks. So, since the last update almost two months ago, I have been making bricks. Lots of bricks. The stackup so far looks like this:
The bricks are made from a roughly onetoone mix of natural clay and expanded perlite. The perlite is purchased from the hardware store (Home Depot, also where all the orange buckets came from). Raw perlite is a naturally occurring mineral. Upon heating, it expands into the popcornlike substance that is sold in stores. The purpose of the perlite is to make the bricks better insulators, and also to some extent to reduce the thermal mass of the bricks. As a future project, it would be interesting to try to use homemade Lightweight Expanded Clay Aggregate (LECA) as a substitute for perlite. In theory, the kiln itself could be used to make LECA from natural clay, which would then be used to make more firebricks.
All the natural clay I have processed is stored wet in buckets. The first step in making bricks is to mix the wet clay with damp perlite:
It is a good idea to wear a respirator or mask when handling the perlite, as it is very dusty. Spraying it down with water also helps mitigate the dust. But why the goggles? Well, if you've never been scooping glops of wet clay into a bucket and then had a blob of it splash up and hit you square in the eye, let me tell you, it hurts.
The next step is to set the mix out on a piece of cloth (an old pair of pants here) and let it dry for a while. It can dry for several hours, up to a full 24 hours. The goal is to get an acceptable consistency for making bricks. Too much water and the bricks just turn into piles of gloop when removed from the mold. Too dry and the mix is hard to form and does not stick together well.
When the clay mix has dried to the right consistency, it gets pounded into the brick mold (see previous log for info on the brick mold). A putty knife is used to carefully go around the edges of the brick within the mold, to help release it. Then the mold is pulled up and you have a brick! The bricks are dried on a piece of cloth (in this case an old bed sheet) so that they do not stick to the underlying substrate and crack as they dry. The picture below shows a dried brick (top) compared with a fresh brick. The shrinkage is visible in this picture  dry brick is about 1/2 inch shorter than fresh brick. During drying, the bricks are also covered with a cloth to help keep the drying process slow and uniform. If they dry too fast they crack. After about a week of slow drying, the bricks are dry and warm (or rather not cold) to the touch, and they can be handled easily.
The next image shows how the grooves for one of the heating elements were carved in the somewhatwet bricks (these have dried for about a day before carving). This was done using a simple loop tool made by taping a slice of aluminum can to a stick. The plan is to have two heating elements, probably wired in series.
Two of the dry bricks spent a week or so in the bottom of a back yard fire pit, as sort of an improvised test for their high temperature performance. They turned sort of a pleasing redbrickish color, so that is somewhat encouraging.
One of the bricks broke in half, but this might be because a log fell on it, who knows. At any rate, you can see in the closeup image that the crack went through the middle of the perlite grains, rather than around them, which suggests there is a good strong bond between the clay and perlite.
To review the big idea:
This project log deals with step 2, making bricks out of clay. There are a lot of great videos on youtube of people making bricks by hand. Here are a few that I drew inspiration from:
I built three brick molds so far before getting one that even kind of works.
Brick Mold Version 1
The first version is shown in the image below. This is a two part mold. The dowels and angle brackets are attached to
the base plate, while the frame lifts off. The idea is that you fill it
from the top, flip it over, remove the back plate, and then lift up the
frame. The problem was that the bricks did not release cleanly during
this process, and the result was just multiple blobs of gooey clay stuck
hither and yon. It was a mess.
Brick Mold Version 2
I had high hopes for this version, but it didn't work either. The metal angle brackets on the large plate made it difficult to slide the plate off the bricks. Trying to lift the large plate off didn't work either, because the bricks would tear into pieces and portions of brick would stay stuck to the plate.
Brick Mold Version 3
The third version simplifies the design and has space for only one brick. The back plate (the thing with the holes in it) is completely smooth so it can be slid off the bricks, instead of lifted. There are two extra pegs on the pegboard to perform alignment. The frame is one piece, but it has a slight draft angle built in to aid with removing the bricks.
Wedges drawn on the blocks show the acute angles of the bevels, for creating the draft angle in the frame when assembled.
It is important to have the pegs aligned as accurately as possible. The pegs were cut square with a chop saw and then drilled with a lathe to get the holes on center.
Dirt is really complicated stuff. Check out the Wikipedia article on soil to get an idea. There are six processing steps to go from the large pile of rocks and dirt dug out of the ground to a semiusable natural clay that can be formed into crude pottery. The steps I used are shown in the drawing below. There are many variants of this process (people have been doing this for thousands of years after all) and youtube has a lot of interesting tutorials like this one and this one.
Step 1. Trommel Screen. This is a cylindrical screen made of chicken wire, mounted on old bicycle rims. The cylinder spins on caster wheels. The raw dirt goes in the cylinder, rocks embedded in chunks of clay go out the end after spinning. I got the idea for this from this youtube video. When I searched youtube for trommels I was amazed at how many people have made DIY trommels.
Step 2. Bucket Sieve. The "bucket sieve" is a bucket with holes drilled in it. I used a piece of pegboard as a template and a step drill (shown in the image).
The bucket with holes in it nests inside a normal bucket. Three scoops of rocks embedded in chunks of clay go into the top bucket, and then a bucket of water is poured in on top. When the water goes in, it makes an immensely satisfying bubbling and frothing noise as the air underneath escapes upward. Here is what a loaded bucket sieve nested into a normal bucket looks like:
After lifting the bucket sieve up and down for a while, the clay, gravel, and sand sink into the bottom bucket. Clean (well mostly clean) rocks are left in the top bucket. The clean rocks are reserved for later use in landscaping projects. The next steps continue to process the clay+gravel+sand+water mixture in the bottom bucket.
Step 3. Kitchen Strainer. Just a normal kitchen strainer from Target or Walmart. Stir up the stuff in the bucket, poor it through, and then we have separated out the gravel. It's that simple!
Step 4. Paint Strainer. You can find these strainers at Home Depot near the paint spraying equipment. These ones came in packs of three. They are meant to strain out tiny clumps in house paint so the spraying devices don't get clogged up. They worked really well for this application.
A muddy sand blob is left in the filter after the clay mixture is poured through. After further cleaning, this sand might be useful as foundry sand for making castings.
Step 5. Gravity settling and siphoning. After filtering through the paint strainer, the water+clay mixture is left to settle for several hours (12 to 24). A layer of thick clay sludge settles out on the bottom, and the water on top is siphoned off for reuse.
Step 6. Cloth bag. The thick clay sludge from Step 5 is scooped out with a plastic cup, and either placed in a bucket for long term storage, or dumped into a cloth bag. Yes, the cloth bag seen in the picture is the leg of an old pair of blue jeans that is tied off at each end. The clay stays in the cloth bag for a day or two or three as it dries out. When it is an acceptable consistency, the bag is opened, balls of clay are rolled into form and stored in sealed plastic bags for later use.
Filter Sizes. Just for fun, the last three pictures compare the size of holes in the three filter materials. The three pictures are at the same scale. Bucket sieve holes = 0.31 inch (7.8 mm) diameter; kitchen strainer holes = 0.08 inch (2.0 mm); paint strainer holes = 0.02 inch (0.5 mm).
The most important requirements for the kiln are that it
Being a modest man in a modest house in the United States, "mains electricity" means about 15 amps at about 115 volts AC. To be conservative we'll assume that by the time all the current makes its way through the wiring, we'll get about 1500 watts of power at the kiln's heating element.
Pure aluminum melts at 1220 °F (660 °C). A common aluminum alloy called 6061 melts at 1085 °F (585 °C). So to be safe let's just say we need to get to 1220 °F (660 °C) to melt whichever aluminum scrap we may be dealing with.
Firing (and especially glazing) pottery can get somewhat complicated. If you consult a kiln firing chart you will find a bewildering array of different effects that take place at a range of temperatures from about 750 to 2550 °F (400 to 1400 °C). An acceptable midrange temperature to aim for seems to be about 1800 °F (1000 °C). This should be adequate to fire simple objects made from the natural clay used in this project. As a point of reference, the heat color of an object at 1800 °F is orange.
At this point we have several important design parameters tentatively chosen:
The next step is to run some heat transfer calculations and see if we can arrive at a practical kiln design that is consistent with these parameters. We could go crazy with finite element analysis software, but (see above) I am a modest man in a modest house so instead we will make some crude assumptions, simplify the problem to the fullest extent possible, put some equations into a spreadsheet, and twiddle the numbers until it works.
Here is a drawing showing how the heat transfer problem is set up:
Basically we assume the kiln is a just a box with six walls, and use 1D heat conduction to model the wall, and convection and radiation transfer from the outside of the wall to ambient. This model assumes the outside temperature is uniform across the entire kiln, and the inside temperature is uniform as well. Heat conduction through the wall is just
where Q_dot is the rate of heat transfer in watts, k is thermal conductivity in W/(m*K), T_in and T_out are inside and outside wall temperatures respectively (in Kelvin), L is wall thickness (in meters), and A is the heat conduction area (m^2), which in the case of our box kiln is
The outside temperature of the kiln T_out is found by making a wild guess about the convective heat transfer coefficient h and then using the relation
where T_inf is the "temperature at infinity" or basically just the room temperature (in Kelvin), and sigma is the StefanBoltzmann constant in W/(m^2 K^4). The convective heat transfer coefficient in air typically varies between 10 and 100 W/(m^2 K) (source). For no particular reason we use a value of h = 30 W/(m^2 K) because that's close to the geometric mean of 10 and 100.
We could solve the fourth order polynomial analytically for T_out, but instead we can hack together a solution with a spreadsheet, by plotting Q_dot as a function of T_out and then manually picking off the plot the T_out corresponding to Q_dot = 1500 W. Once we determine T_out, we plug it into the conduction equation above to get T_in.
The spreadsheet was created in Gnumeric  .ods and .xls versions have been uploaded to the files section. After a bit of fiddling we get the following plot and associated parameters:
The inside kiln dimensions are H = 10.5 inches, D = 9 inches, W = 9 inches (or 26 X 22 X 22 centimeters). This doesn't quite get us to 1800 °F (1000 °C) but it's close enough to go for it and hope we pick up a few extra degrees here and...
Standard firebricks have dimensions of 9 X 4.5 X 2.5 inches. Initially I wanted to use bricks that were 7 X 3.5 X 1.5 so it would be easy to make brick molds using standard 2X4 lumber. However, a backoftheenvelope thermal calculation indicated that 3.5 inches would not be sufficient wall thickness to provide adequate insulation. So, back to 9 X 4.5. I decided to keep the thickness the same as a standard 2X4 to simplify mold construction, resulting in an overall brick size of 9 X 4.5 X 1.5 inches.
The three holes in the brick are 5/8 inch. This should give plenty of clearance when assembling the kiln  the plan is to hold the bricks in place via threaded rod going through stacks of bricks. The holes also are intended to help the clay dry uniformly and prevent cracks.
For the heat transfer calculations (in an upcoming log) it is important to have an estimate of the thermal conductivity of the bricks. This site lists red brick as k = 0.6 W/(m*K) and insulating firebrick as k = 0.15 W/(m*K). Other sources list a wider range. If I use the crude natural clay from my backyard, I expect roughly k = 1 W/(m*K). If Perlite is added to the mix, as suggested in several online recipes, the thermal conductivity can probably be brought down to perhaps (I'm guessing) k = 0.4 W/(m*K).
As a point of comparison, these firebricks available from McMasterCarr have k = 0.25 to 0.32 W/(m*K).
How do we convert McMaster's KFactor to thermal conductivity in W/(m*K)? According to McMaster: "To calculate the Rvalue of additional thicknesses, divide the material's thickness [in inches] by its Kfactor." Let's take the KFactor = 1.7, and calculate the Rvalue for a 1 inch thickness:
The rate of heat transfer is in units of Btu per hour. The heat flux density through a given area is in units of (Btu per hour) per (square foot). The Rvalue is how much temperature drop there is across a material for a given heat flux density, so it has units of degrees per ((Btu per hour) per (square foot)). This is commonly simplified to (hour * square foot * degrees) / Btu, which is more compact but less intuitively clear. To convert to sensible metric units, multiply by 0.1761101838.
Finally we can recover thermal conductivity by dividing an inch (in meters) by RSI
and that's where we get our k = 0.25 W/(m*K) number reported up above for the McMaster bricks.
The RepKiln project aims to create a small, simple, inexpensive, and relatively safe and clean kiln/furnace/oven for melting aluminum and firing basic pottery. It will be made by assembling homemade firebricks. It should be able to produce more bricks of the type from which it is made, hence the "Rep" (for replication) in the name.
RepKiln got started as a spinoff of a completely different project: a backyard chicken coop. As shown in the before/after pictures, a good chunk of dirt had to be excavated to make a giant sandbox for the chickens to poop in. I live in a densely populated subdivision where the backyards are small and not all the neighbors are thrilled about chickens. Hence chicken poop management is important.
After building the chickens their fantastic sandbox, there was a lot of soil leftover. Due to the small yards (see above) this soil couldn't just be dumped off in a corner and forgotten about. So I hatched a ridiculous scheme to "process" the soil and return/disperse it back into the yard. This process will be described in detail in a later log, but one part of it  the trommel  is shown in the images.
The soil is primarily very thick clay interspersed with rocks. So I ended up with a lot of natural clay that I wasn't sure what to do with. After watching Primitive Technology on Youtube build a kiln out of dirt with his bare hands, I thought it might be fun to try something similar, although not quite so primitive.
The idea is to process the soil into clay, process the clay into bricks, put the bricks together into an (electric) kiln, and use the kiln to do something useful  like fire pottery made from some of the rest of the clay (there's tons of it) or melt aluminum for casting.
Chicken coop before  lacking a giant sandbox in which for chickens to poop.
Sandbox ready for poop.
This is a trommel screen for separating dirt, clay, rocks. I got the idea for this from this youtube video. This particular design uses bicycle rims, chicken wire, leftover landscaping logs, and swivel casters. There are tons of designs for DIY trommels on youtube.
A initial prototype brick mold. This one didn't work so well because it was difficult to release the bricks.
I love the effort to do the thermal transfer calculations.
I didn't see where you've done the clay body testing. Not all clay bodies are equal. Some will vitrify and some will never completely vitrify but just become very brittle. I'd recommend you test your clay body before going forward.
Here's a link with more information:
https://digitalfire.com/4sight/troubleshooting/ceramic_troubleshooting_over_firing.html
Thanks for the info. I had not considered that at all. I can only hope the clay I am using is acceptable  most of the bricks have already been made. It's too late to turn back now!
I just did a quick Google search, and this showed up. Hope it helps!
Refractory Engineering: Materials  Design  Construction