Finding power needed to heat an oven through radiation and conduction

In summary, the oven has several cylinders that fit inside of one another. The innermost cylinder is a Molybdenum oven that will hold a sample of metal. A ceramic cylinder fits over this. A tungsten wire heating element is wrapped around this cylinder. Two more ceramic cylinders fit around this, and then lastly a Molybdenum shield. The oven will be raised to 900 degrees Celsius with current supplied by a PID temperature controller. Without any numbers, it is hard to tell how much current is needed. It is likely that the current required to keep the whole system warm will be small compared to the current required to heat it up quickly. The ceramic cylinders are made of Alumina, so the conduct
  • #1
swilly
4
0
I was given an oven that comprises of several cylinders that fit inside one another. The innermost cylinder is a Molybdenum oven that will hold a sample of metal. A ceramic cylinder fits over this. A tungsten wire heating element is wrapped around this cylinder. Two more ceramic cylinders fit around this, and then lastly a Molybdenum shield. I am going to be raising the temperature of the Tungsten wire to 900°C. My question is this: how can I estimate how much current to run through the Tungsten wire to reach 900°C?

I know that P=I^2R. I know the resistance of the Tungsten wire. The total power needed is going to equal the sum of the heat transfers (I think?). There is heat transfer by thermal radiation and thermal conduction. I have included a picture of the oven for reference. (Note that in the picture, the wire is not wrapped around the ceramic with threads). Please help me!
 

Attachments

  • 20120808_151901.jpg
    20120808_151901.jpg
    32.7 KB · Views: 402
Science news on Phys.org
  • #2
If you know heat conductivity and capacity of all of your components, it is possible to evaluate that. The current will not be constant, as heat loss depends on the temperature of the surrounding material.

Another idea: The resistance of the tungsten wire depends on the temperature. Assuming that the temperature is the same in the whole wire: if you measure voltage and current, you can calculate the resistance and use this as thermometer.
 
  • #3
You might need a feedback control. That sort of thing isn't very easy to get accurate. The folks in the mechanical engineering forum might know more about how to solve the thermal resistances.
 
  • #4
So, as it heats up, I will need less and less current?
Basically, I'm just trying to estimate the current required to keep the sample of metal at the center at 900 deg C. I'm confused on how I calculate thermal radiation and conductivity. I realize that every part of the system is going emit thermal radiation, and that there's going to be conduction through several layers...

I believe we will be purchasing a PID temperature controller that can control the current, but I wanted an idea of what kind of current supply we would need.
 
  • #5
Without any numbers, it is hard to tell. I would guess that conductivity of the ceramic cylinders is the most important part.

So, as it heats up, I will need less and less current?
Right.

but I wanted an idea of what kind of current supply we would need.
Depends on the time you have to heat the whole setup. The current required to keep the whole system warm should be small compared to the current required to heat it up quickly (i.e. with tungsten at constant 900°C).
 
  • #6
The ceramic cylinders are made of Alumina, so I can find the conductivity. I have a lot of time to heat it up. Can anyone help me with the math to estimate the current?
 
  • #7
A sheet of material with thermal conductivity [itex]\sigma[/itex], area A, thickness x and temperature difference [itex]\Delta T[/itex] between both sides will have an internal flow of [itex]P=\frac{\sigmaA\Delta T}{x}[/itex]. For cylinders, you need an integration to get an exact formula, but if the radius is large compared to x the difference is negligible.
Multiple materials can be treated with an equation system, or by adding their "heat resistance" (inverse value of the conductivity).

You could try to find the thermal conductivity of your ceramic cylinders and their thickness, this would help to get a rough estimate.
 
  • #8
Okay, so I treated it as a system and added the heat resistances, or R-values:

[itex]\dot{Q}[/itex] = [itex]\frac{1173K-Tb}{Rtotal}[/itex]

I calculated Rtotal by adding the R-values for the conductive layers with the R-value for radiation (radiation from the outside of the oven to the walls of the vacuum).

I used Mathematica to solve the Temperature of the outside of the oven (which came out as 798°C), which I then plugged into the original equation to find [itex]\dot{Q}[/itex] . My end result was 120 Watts of energy transfer by heat.

How can I use this result to find the current I need to run through the Tungsten wire?
 
  • #9
The power in the Tungsten wire is P = V I = R I2 = V2/R
You need the resistance to calculate required current and voltage.
 

What is the difference between radiation and conduction in terms of heating an oven?

Radiation is the transfer of heat through electromagnetic waves, while conduction is the transfer of heat through direct contact between objects. In the context of heating an oven, radiation is responsible for heating the air and objects inside the oven, while conduction is responsible for transferring heat from the walls and heating elements to the food being cooked.

How do you calculate the power needed to heat an oven through radiation?

The power needed to heat an oven through radiation can be calculated using the Stefan-Boltzmann Law, which states that the power radiated by an object is proportional to the fourth power of its absolute temperature. This means that as the temperature of the oven increases, the power needed to heat it through radiation also increases.

What factors affect the power needed to heat an oven through conduction?

The power needed to heat an oven through conduction is affected by several factors, including the surface area of the oven walls, the material they are made of, and the temperature difference between the heating elements and the food being cooked. These factors determine the rate at which heat is transferred from the walls to the food.

Can convection also play a role in heating an oven?

Yes, convection can also play a role in heating an oven. Convection is the transfer of heat through the movement of fluids, such as air. In an oven, convection helps to evenly distribute the heat from the heating elements, ensuring that all parts of the oven and the food inside are heated evenly.

Is there a way to increase the efficiency of heating an oven through radiation and conduction?

Yes, there are several ways to increase the efficiency of heating an oven through radiation and conduction. One way is to use reflective materials on the walls of the oven to reflect heat back into the oven, reducing heat loss. Another way is to use a convection fan to circulate the heated air, ensuring that all parts of the oven and the food are heated evenly. Additionally, using high-quality insulation can also help to reduce heat loss and increase efficiency.

Similar threads

  • Thermodynamics
Replies
5
Views
984
  • Thermodynamics
Replies
2
Views
1K
Replies
13
Views
3K
  • Thermodynamics
Replies
20
Views
9K
Replies
10
Views
2K
Replies
16
Views
12K
  • Electrical Engineering
Replies
23
Views
6K
  • Thermodynamics
Replies
4
Views
1K
  • General Engineering
Replies
10
Views
3K
  • Thermodynamics
Replies
6
Views
2K
Back
Top