What is fin in heat transfer
Forced convection - body flowing across the body
If you want to dry your hair after a cold shower, most of the time you do it with a blow dryer. We explain how this works in this video.
- Structure and functionality of a hair dryerin the text
- Transferring the heat from the wires to the airin the text
- Difference in the calculation of bodies flowing across the bodyin the text
- Consideration of the correction factor for the directional flowin the text
- Application of the tube bundle modelin the text
- Nu number and pipe arrangement factorin the text
- Determination of the heat transferin the text
Structure and functionality of a hair dryer
First we want to explain the structure of a hair dryer to you. In addition to the fan that generates the blower, there are several heating wires in its housing. Since the wires have electricity flowing through them, they get hot.
Transferring the heat from the wires to the air
The air that is drawn in from the environment is in turn passed over the warm heating wires. The air warms up and comes out at the front as a warm blower that you use to blow dry your hair.
Now you are probably wondering why the air gets warm when it flows over the heating wires. This is due to the convection. The heat is transferred from the wire to the air. Since the air is moved with the help of a fan, it is a question of forced convection. If you now want to know exactly how much or how well the heat is transferred, you have to do it using the Nusselt number.
Difference in the calculation of bodies flowing across the body
Since the heating wires do not flow through this time or are flowed around their length, this is the case of bodies with transverse flow. Here you need the dimensionless key figures. But first we want to distinguish between two different types. On the one hand there are bodies such as cylinders, spheres and plates and on the other hand there is a whole tube bundle. You determine the heat transfer coefficient differently depending on the type.
Let's start with the bodies cylinder, sphere and plate. Here you need the Reynolds number again. This can be calculated with .
is the inflow speed, i.e. the speed at which the fan drives the air over the heating wires. L ‘is the overcurrent length, which varies depending on the body.
When the cylinder is , where d is the outside diameter. For the sphere, L ‘= d, i.e. the sphere diameter. For the plate, L ‘= L, i.e. the length of the plate.
You need your Re to be able to calculate the Nusselt number. The formula for this mean Nusselt number is .
The values for relate to the surface, i.e. to the type of body. You can find them in a table that is usually given to you in the exam.
Nu is for the cylinderO= 0.3, for the sphere is NuO= 2 and for the plate is NuO=0.
You also calculate your laminar Nusselt number .
Your ReL ‘ you have already determined and you already know from the last videos that the Prandtl number is. On the other hand, you calculate the turbulent Nusselt number with: .
Consideration of the correction factor for the directional flow
You have probably already noticed that the correction factor, which takes the influence of direction into account, has been included in the mean Nusselt number. You have to calculate this for liquids as well and for gases with .
is the Prandtl number at wall temperature .
you get off again . But since you want to determine the heat transfer, you still have to use the formula to rearrange.
The converted formula is then .
Application of the tube bundle model
So now you can determine the heat transfer for cylinders, spheres and plates.
With the hair dryer, however, it is more likely that the heating wires are lying one behind the other in a pile. This is why you have to look at the model of the tube bundle when using the hair dryer.
You can see a sketch here. In it you can see an aligned arrangement, in which the pipes are arranged in a row, one behind the other, and an offset arrangement. There every other column is slightly offset. You have to take the arrangement into account, otherwise the result will be falsified.
But let's look at the Reynolds number first. This time the Re number refers to the cavity between the individual pipes and is calculated using .
L ‘is the overflow length, which in the case of the tube bundle with is calculated.
is the cavity speed, i.e. the speed that the medium has between the individual pipes and is determined with .
is the void fraction and depends on the aspect ratio b and the transverse division ratio a.
With and results for the case that b <1, for .
For the case that b≥1, is . Now you finally have all the sizes to be able to calculate the Re number.
Nu number and pipe arrangement factor
Now we need the middle nu number. The formula for this is:
N is the number of tubes that make up your tube bundle. You calculate your laminar and turbulent Nusselt number just as you did with the simple cylinder, only with your new one . So it is:
You're probably wondering what else this fA. is in the formula. This is the so-called pipe arrangement factor, which, as the name suggests, takes the pipe arrangement into account. The following applies to the aligned arrangement:
The formula for the staggered arrangement is:
Determination of the heat transfer
So now you just need the correct correction factor and you can completely determine your Nu number. The formulas are almost the same as before with the individual bodies for liquids and for gases. Where p = 0.25 if and p = 0.11 if .
The exponent n is gas-dependent, because with nitrogen n = 0.12 and for all other gases n = 0.
You did it in a moment. Because now you know your Nu number, you can use your heat transfer determine.
So the next time you blow dry your hair, you'll be well informed about the process. Good luck with your calculations!
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