From a pure energetic point of view on the heat transfer objective it is sufficient to regard the energy balance only: You completely dissipate your electric energy into heat, and if the gross balance requires this, the wall temperatures will go way up automaticallly beyond your 500 °C limit in order to satisfy your balance and deliver the energy to its destination.

If you take a 2nd order look on your device you may want to scrutinize the heat transfer a bit more closely, though: You will always have a certain heat drain to the environment, and minimizing the temperature gap between your electric heater and your air stream by means of a better heat transfer coefficient will minimize losses to the ambient as well.

Cheers,

Petra

Hello Hakeem,

you have to get a set of equations, which can (fortunately) be solved segregately. The first one is the energy balance: fixed the temperatures of the air at inlet and outlet and the flow rates you know the power, but you do not know nothing about the size. Even if neglecting losses to the environment (you could refine your calculation in a second step), you need the heat transfer equation: Q = h A (Tw-Tf), where Q is the power in watt, h the heat transfer coefficient (W/m2K), A the surface in m2, Tw the average wall temperature and Tf the average fluid temperature (being the average done along the path of the fluid). With this equation, if your heater is an electric heater as I think, you could image, as a first step, the heat flux constant. So q= Q/A=heat flux=constant and hence h (Tw-Tf) = constant.

With a correlation based on the Nusselt number in forced convection of air you can calculate the heat transfer coefficient h, that depends mainly on the velocity of the fluid and on the diameter (that you have fixed).

Now  you see that if you vary the lenght, you vary A and so the heat flux and hence the average temperature difference that is important as a limiting condition for your material.

For example, if you double the lenght you divide by 2 the heat flux and so the difference between the wall and the fluid (Tw-Tf). 

I suggest you to: calculate the power A, calculate the velocity from the flow rate and the diameter and the heat transfer coefficient h by a correlation (almost constant along the tube). Fix the maximum temperature of the external material, so at the exit you can image that twall is the maximum and the Tf is the temperature of the fluid at the exit. In this way you know the power Q, and the maximum h * (Twall,max-Tf,exit). The area A=Q/h/(Twall,max-Tf,exit). 

This could be the first attempt. Then you refine you calculation with a correction on the power Q to account for heat losses, a correct on h to account for the variation of termodynamic properties of air along the heater. After 2/3 turns you should get a good solution.

Also pressure drop calculations is important for the fan sizing

Best regards,

Alfonso William MAURO

Well for steady state condition energy balance is enough...only during the transient period you may face some problem. If use can spare some time visit a thermal power station ..Pre heaters are use to heat air before the air is forced into the burners...

Look also the entropy aspects for efficient design and also an optimization exercise would improve the design.

Dear Hakeem,

The flow rate 150m3/h=41.7L/sec is high, from my experience the energy balance is not sufficient.

1- the conductivity of air is too much small.

2- the (h) overall heat transfer coefficient will play a crucial roll, which will be small for gases, without enhancement.

3-using tube with 10cm will be problematic, other wise it will be too long!!!

4- try to use fins to inhance the Heat Transfer.

Cheers!

Azd.

Well you can based your design on water tube boilers..except now your working fluid will be both air

In designing a heater, the energy required to heat the air, plus some allowance for heat losses is only the first step.

The limiting factor easily becomes the tube wall temperature or the heater wire temperature, and here's where heat transfer calculations come in. Depending on how the heating elements are designed, a limiting electrical resistance wire temperature may be as low as 1200C. If you use a steel tube (and not ceramic) the maximum materialtemperature may also be low(e.g. less than ca. 650C for mild steels). It will be the material temperature at the hot end of the heater that will be limiting. If either of the material temperatures limits the applied heat flux, this will govern the actual size (length) of the heater.

from your question you will need an electric heater that dissipates about 24kW (mcDT where, m=150*1.2/3600= 0.05 kg/s; C=1.005kJ/kgK, DT=500-30=470C). you will need to use high temperature alloys materials such as stainless steel  with thermal insulation wrapped around the duct. You will need a temperature controller to control the outlet temperature and given low thermal capacity of the system frequent cycling (on-off) may result from and hence short life.

It is sufficient for steady state heating, you will find an example to calculate the length of pipe required in Incropera's text book.

CHF boundary is the correct boundary condition as air is insulating and will result in a Biot number = 0.

Energy balance is enough

@Rasool Bahrampoury

Hi Dear,

With flow rate of about 150 m3/hr, it is clear not a steady state with temperature change from 30 to 500 C.  And the heat transfer should be studied carefully.

Regards!

Hi Azd Zayoud

how flow rate implies that the process is unsteady?

ONLY IF Heat loss is neglected.

@Rasool Bahrampoury

Dear Rasool,

From the thermal point int of view, it is transient (unsteady process) with change of T from 30 to 500C, with considering the change of temperature from the starting time to the time of achieving the required temperature. even with no motion.

From the hydrodynamic point of view, it is dynamic not static. The motion of fluid (air) with 150 m3/hr, makes a necessity of heat transfer study, since the conductivity and convection in the gas case is low.

Thanks for your question.

Regards!

Dear Azd

You are talking about start up process I think. When you are talking about the load of an a system. the full load is meant. Therefore steady state converges after this stage.

There are several papers or books on heat exchanger design..just look them up

Dear All - There will be an effectiveness (may be in the range of 0.2-0.3) will be there for transferring the heat from the electric coils to the flowing air. Am I right?

This problem confirms that the problems of heating or cooling can't be dealt purely by energy balance but really heat transfer in conjunction with material (fluid, tubes, and heaters). In this case it is necessaty to determine how much energy can be transfered from heater's surface to air. Note that air properties are not constant and the heater surface temperature is not uniform. Of course the first approximation can be formulated with energy balnce, then the problem arised with transfer rate can be solved by use of high turbulence of air flow. You need to allow air velocity over surface of heater is very high. In this cse you can devide flow or make only one long heater with the pre-estimated power (add at least 50% to remove future losses even in electric wiring). The higher the turbuoence you ptovide the better your approch will be.

One missing datum is the air pressure, so I suppose it is atmospheric conditions, otherwise it would change a lot the results. You do not specify if 150 m3/h is at the inlet or at the autet: so I suppose it is a the inlet: due to termal expansion, at 500°C the volumetric flow is nearly 3 times higher. To better specify a problel, you should give the mass flow rate in kg/s instead of m3/h.

The problem you describe is for sure steady, that means no temporal variations of local values. Inlet T is always 30°, outlet is always 500°, flow is always 150 m3/h.. Who says it is not steady has not uderstood the difference between steady and static, nor the difference between Lagrangian and Eulerian descriptions. 

It is correct that with energy balance you can calculate the heater capacity (power). Energy balance tells you that you will need 24 kW for the air, plus the extra power to compensate for looses, plus the extra power for faster transient operations if you like.

To calculate heater surface you need convection equations, someone already suggested you the book by Incropera. You did not mention if you can insert your heaters inside the tube to increase the surface amplitude and tmperature, or if you need to heat throug the tube walls, in that case it will become a very long tube with strong dissipations.

When you realize it you must check all safety issues. What happens in case of electric problems (e.g. contact between the electric heater and the tube: any danger for the people working?). What happens if the air flow stops or reverses? (the electric power cuts off, or you will burn your heaters? ) . Do you need to control the heater maximum T to avoid burning it?

The other solution is to buy an air heater from leister, watlow, tutco farnam (http://www.farnam-custom.com/air_heaters/flowTorch.php)  or other suppliers, or at least use the information to get inspiations. You need to design something like two of this http://www.hotairtools.com/prod-process-heating-industrial-LE5000HT.html

In addition to calculate convective heat transfer co-efficient to find the heat exchange b/w the heater and air, you should also estimate the 'by pass factor' which defines how much % of air will leave the heater without contacting the heater surface.

By considering the 'h' & 'BF' we can move towards an accurate calculations.

You need to do heat transfer. You can not design (size) a heat equipment with energy balance only. The relation between heat transfer area and heat transfer is heat transfer  coefficient.

refer to handbook on heat exchanger design

I belive that energy balance calculation is enough to estimate heater capacity.

@Rasool Bahrampoury

Dear Rasool,

The initial problem was solar energy system simulation, the question was simplification of the phenomena. maybe my answer ,which was based on  knowing of the problem, made a misunderstanding, sorry.

Thanks for letting us involve in this kind discussion.

with a 10cm diameter tube you option are limited. in this case you may need to use a 3 phase resistor with electrical insulation complications.

Well with nelectrical heaters arranged in concentric circles at the entrance and temperature sensors along the tube and feedback to power control  and flow rate controlyou could achieved the steady state temperature

Use SFEE for the system where heat transfer terms can be included and solve the resulting equation. This may result in complications.

Hi,

For the given details The Heater Rating would be 150 M3/Hr x 1.29 Kg/m3 x ( 500-30) deg c / 3600 = 25.26KW. ( some % to be added to cover up losses & dead mass heating).

 Normally with blower induced air, Duct heating systems are used, but achieving the temperature can be a issue.

best suited solution is Electric heat exchangers or Tubular heating System with a Thyristor control Panel.