How do I calculate thermal conductance for a system with multiple materials?

[ruzfactor]

I am working on a project involving this setup (please refer to the pic). Basically compressed air at a constant flow rate flows through a 1/4" tube to the tube shown and gets heated by the star-wound heater and, this hot air heats the small inner vessel and then leaves the system. Now I am stuck with doing a heat transfer estimation of the system. I know the ratings of my heater. The temp of the air should reach at least 300C. But I want to estimate whether the heater is capable of heating the air to 300C. Also, the heat transfer between the inner vessel (containing powdered material) and the hot air. This looks like a transient problem but I want to make a simple approximation to check whether the system is capable of generating heat and effective heat transfer is taking place.

Need some expert help here to initiate the approximation. thanks in advance.

 

[edgepflow]

An simple energy balance across the heater yields:

Q-Heater = mdot * cp * (Tair_out - Tair_in)

Where,

Q-Heater = heater rated power X 0.9 - heat loss
mdot = mass flow rate of air
cp = specific heat of air
Tair_out, Tair_in = air outlet and inlet temperatures.

Solve for T_air_out.

Notice in Q-heater I included a 0.9 tolerance on power and the heat escaping the system.

 

[ruzfactor]

@edgepflow

Thank you vry much. How do I approximate a heat loss for the heater?

 

[ruzfactor]

My heater specs: 420 Watt
Watt density: 16 W/in^2
max temp. 650C [temp. controllable]
I have calculated what mass flow of air is needed to heat the air to 300C with the air at initial temperature of 20C. And the answer was around 1.5 g/s. I'm still confused with my heaters ability. Whether it will be able to heat the air to a desired temp. If it ain't I'm in big big trouble with my project. :(

 

[ruzfactor]

Should I use the transient heat transfer method such as lumped capacitance model to estimate heat transfer between metal powder bed and the hot air?? or It could be estimated using a simple steady-state method.

 

[edgepflow]

ruzfactor,

I will try to answer your questions in order:

Post #3: The heat loss will depend on the surface area of the can surrounding your inner vessel and any insulation. Do you have the can diameter and insulation thickness? What insulation material are you using?

Post #4: you basically have to limit your air flow to 1.5 g/sec for the heater size you have. Are you controlling or regulating this air flow?

Post #5: You could perform a transient heat conduction model to figure out how long to reach 300 degC. Do you have a maximum allowed heatup time?

 

[ruzfactor]

@edgepflow:


I don't have any insulation for tube surrounding the heater. (the heater looks like the pic and directly fitted inside the tube without any insulation. There is a very small clearance between the heater and inner of the tube. sorry for my poor schematic). For the time being I can neglect the heat loss.

I am flowing compressed air through a pressure regulator and a valve. So I have control over the flow rate. As I know the heater specs, how can I find the optimum flow rate at which the heater would be able to heat the air to 300C. I can control the heater temp.

For the heat transfer between the metal bed and the hot air, I want determine how much time it takes to heat the bed to say 300C.

I am really getting confused. I seek your help. :(

 

[edgepflow]

ruzfactor,

First I would recommend insulation around the assembly. For safety purposes, you should put enough insulation to reduce surface temperature to under 60 degC. This is so people do not burn themselves if they touch it. It will also improve your heatup time.

As for the flow rate, if your flow rises over 1.5 g/sec, your outlet temperature will drop below 300C. Thus, consider installing a simple and inexpensive variable area flow meter with a control valve on your air inlet. You can adjust it to make your 1.5 g/sec. Make sure your heater has a high temperature shutoff mechanism.

For the heatup time, start with a lumped capacity model (let me know if you are not familiar with this). Check that your Biot number is greater than 0.1.

 

[ruzfactor]

thank you for the reply.

I would try to put some insulation around the tube. Also, I had ordered a cheap flow meter (0.4-5 LPM) which I'll get it next week. But, if I convert the mass flow to volume flow the value is much bigger. So, I think there could be some error in my calculation.

As for lumped capacitance method, I don't have much familiarity with this model. So for modelling purpose, do I need to consider only a cross-section of the top of the vessel (metalbed>copper tube>steel shell>hot air)?

My heater is a watlow starwound heater which can be controlled. During energy balance I used the heater rated wattage. But If I set the heater temp to say 400C, how can I calculate whether the heater will be able to heat the incoming air to 300C which is at say 20C? Is it possible to have an approximation.

 

[edgepflow]

For your lumped capacity model, include all surface area of the object of interest in contact with the hot air flow.

Even if you set the heater to 400C, the temperature increase is limited by the heater capacity.

 

[ruzfactor]

Please look at the attachment. I have included the calculation done by a previous group. I am working on the same project. The calculations are vague. Please comment. This previous group has made my life a living hell. :(

 

[edgepflow]

It looks like they set up a finite difference model. I did not see any numerical results. It is usually a good idea to check the output of detailed computer simulations with simple hand calculations.

 

[ruzfactor]

It looks FDM. It is also mentioned that they have used lumped capacitance method. Did they use lumped-capctnc for each node to set the equation and then used FDM to solve? I'm interested in simple estimation of the time required to attain 300C for the powder bed. Can I do that with lumped capacitance without any simulation?

 

[ruzfactor]

If is start with a steady state assumption to determine the temperature required for the hot air to heat up the metal bed>copper tube>steel shell assembly to 300C (because of thermal resistance of the metals), then use this temperature to determine the flow rate required to heat the air with the heater using a energy balance equation. Finally, using the hot air temp, a lumped capacitance approach to determine the time required for the metal powder bed to achieve that temp. Will it be a good approach?? please comment... Also, can please you refer some material for the lumpd-cap method??

 

[edgepflow]

If is start with a steady state assumption to determine the temperature required for the hot air to heat up the metal bed>copper tube>steel shell assembly to 300C (because of thermal resistance of the metals), then use this temperature to determine the flow rate required to heat the air with the heater using a energy balance equation. Finally, using the hot air temp, a lumped capacitance approach to determine the time required for the metal powder bed to achieve that temp. Will it be a good approach?? please comment... Also, can please you refer some material for the lumpd-cap method??

Here is a link for the lumped capacity method. See Equation 6.9 in:

http://ec.pathways-news.com/Text-PDF/Part B-6.pdf

Check your Biot number is within limits (Equation 6.15), or your result will not be very accurate.

Input to the lumped capacity method will be, amoung other things, the external temperature and the heat transfer coefficient (function of flow).

So I would take the external temperature to be 300C and the flow to be the 1.5 gm/sec you figured earlier. It will take a few minutes for your heater elements to get hot (the manufacturer should be able to give you this number). Add this to the time from your lumped capacity model.

 

[ruzfactor]

@edgeflow:

I am trying to model the heat transfer using the FDM. But stuck with the thermal conductance value. Please see the pic attached. I'm confused about which K value to be used for node 5, 6 and 7. Because at these nodes, there are two different materials conducting heat. Should I take an average of the two? Please comment...