Heat transfer theory

[RyanS]

Hi, I'm new to the forum, and I'm a beginner into electronics. I'm trying to design a small fan heater using an 80mm PC fan and a nichrome wire heating element. It will be used as a hand warmer for bad circulation.

I have a similar device which uses a 40mm fan, a commercial product that is very expensive (read: overpriced). but I want to build a second one that is a little larger.  http://www.hmc-products.com/fotos/image/VARIA/Varia/0021-7000a/MANUAL%20USER/0021-8001a-0102a.pdf  its 24V and 33 watts

So far I'm thinking of this design:
- Arduino Duemillnove or Nano (AT Mega328) to generate PWM, and make it PC controllable via USB
- power transistors or MOSFETS to handle the heating element and fan currents
- the 40mm fan uses resistors as the heat source, but I think using nichrome wire would allow more even coverage in front of the face or the 80mm fan.
- 12V as the power source (Arduino is separate and USB powered), because the fan is 12V then I don't need to convert from 24-12V
-it should be able to produce 55 degrees Celcius air temperature, 20mm away from the element

Heres a PDF of the hardware layout:

http://clients.rasvisual.com/temp/80mm_heater.pdf

QUESTIONS:
- is the distance of the nichrome element of 15mm away from the fan at the temperature I require likely to cause any problems for the fan?  although I imagine all heat is directed away from the fan.

- I will have an enclosure around the whole device, with air inlet holes around the top and side of the PCB mounting area. Is this sufficient to draw cool air over the heatsunk transistors to keep them from overheating?

- FINALLY; and in relation to my topic of Heat transfer theory, I'm sure there is a formula to work out the required wattage of heating element to produce the desired temperature at 20mm (55degC), but I'm having trouble locating it or what to search for. Best I can do is that a fan heater is technically a forced convection heat transfer device, I'm looking at laminar flow across the element and forced air has a heat transfer coefficient or btw 10 - 100(W/m²K  I just have no idea how to derive the required wattage.  If anyone is familiar with these formulas I would greatly appreciate their advice. Then I can move on and choose the appropriate transistors, etc.

[Hero999]

The amount of power required is determined by the flow rate and desired temperature rise.

According to Wikipedia, air  has a volumetric heat capacity of 0.00121J/cm³ under standard conditions. This means, if the flow rate is 1cm³/s the amount of power required to raise the temperature by 1^oC is 0.00121W or 1.21mW.
http://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
 
You need to know the flow rate of the air from the fan, the minimum room temperature and design a heater which provides a little more power than the minimum power required to heat the air. If you want to regulate the temperature, you need a temperature sensor and some negative feedback in the PWM controller.

To avoid overheating the fan it should ideally be before the heating element, i,e. it should suck cool air in and blow it over the element. There shouldn't be a problem as a typical computer fan should be able to operate up to 60^oC anyway.

For safety reasons there should be a thermal fuse and bimetal strip to cut power to the heating element in case the temperature controller fails and the air heats to a dangerous temperature, causing burns and fire.

Have you considered modifying a hair-dryer? It may be the cheapest option but there are obviously more safety hazards: mains voltage and higher power.

[RyanS]

Thanks. I'm not sure if I'm applying this formula correctly but using this fan as an example:
http://www.gelidsolutions.com/products/index.php?lid=2&cid=5&id=28&tab=2

Flow rate is 27 CFM == 12,740 cm³/s 

minimum room temperature is usually 20⁰C

I want to raise by 35⁰C to get 55⁰C

So 12,740 cm³/s   X  0.00121J/cm³  = 15.4W per 1⁰C  X 35⁰C  = 540 watts!!   

so I need 0.27 ohm heating element for 12V. that's not going to work.

The only sensible result I can get is drive the fan at a very low speed for 1000cm³/s to get 42 watts, but I don't even know if you can get the fan that slow. (900 RPM is the specified minimum, but flow rate at that speed, who knows).

I was basically looking only to heat a small area around my computer mouse, at the moment I use a 25 watt halogen lamp which is a pain because bulbs keep  blowing. Ideally I was hoping to design for 40 watts, maximum. similar to the 40mm fan heater I linked in my OP, just 80mm for a wider area.

[Hero999]

I think it's worse than that.

1ft = 30.48cm
1ft³ = 30.48³ = 28316.85cm³ which works out at around 1.2kW.

This makes sense when you think about it. Look at the power rating of a typical hair dryer and you'll find it's in the region of 1 to 2kW.

A halogen lamp will be more efficient than a fan heater because it only has to heat objects immediately in-front of it, rather than the air which is then used to heat the object. With a radiant heater the air can be at a much lower temperature than the objects being heated, for example on a hot day the air may be 35^oC but the road temperature could be 65^oC.

[RyanS]

Interesting. So the heater I linked must be relying on a really low air flow rate?  http://www.hmc-products.com/fotos/image/VARIA/Varia/0021-7000a/MANUAL%20USER/0021-8001a-0102a.pdf  being a 40mm fan at low speed. I actually have it running at the moment and about 8cm away you can barely feel the flow. it does generate a bit of heat though. Accross the face of the fan are about 6 power resistors.

Could it be possible that low flow combined with power resistors (rather than nichrome wire), allowed them to keep the power consumption as low as 34 watts?   

although I can't see whether the source is resistors or resistance wire is going to make a difference. Is one more efficient?

[Hero999]

I don't think it'll make a difference whether you use wire or resistors.

A lower flow rate would certainly allow a higher temperature rise.

It would be also more efficient if the air intake is non the other side of the hand so the air is recycled.

[Silent Jack]

Would a small fluid based radiator plus a low speed fan be more efficient.  Our house growing up was hot water heated and quite efficient.  Also a friend of mine heats his small home with an electric oil filled radiator.  Certainly the wattage for a room heater is around the 900-1500W range, but I would think for the size of this gentleman's application it could be lower.  Though admittedly I've not yet run the numbers.