# Homework Help: Air Flow through a hair dryer

1. Sep 6, 2014

### Maylis

1. The problem statement, all variables and given/known data
A hair dryer is basically a duct in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it to flow over the resistors where it is heated. Air enters a 900-W hair dryer at 100 kPa and 25° C, and leaves at 50° C. The cross-sectional area of the hair dryer at the exit is 60 cm^2. Neglecting the power consumed by the fan and the heat losses through the walls of the hair dryer, determine (a) the volume flow rate of air at the inlet, and (b) the velocity of the air at the exit.

Answers: (a) 0.0306 m/s, (b) 5.52 m/s

2. Relevant equations

3. The attempt at a solution
I already have solved this problem, but I stepped it up a notch and am now playing with MATLAB. I am varying the inlet and outlet temperatures to see how the behavior of the flow rate and velocity of air at the exit will change when I change the parameters.

One preliminary question I want to ask is why is it that the outlet pressure is assumed to be the same as the inlet pressure?

The first thing I did was vary the outlet temperature to see the effect of the velocity of air. I see in the plot that I have a ''1/x'' behavior, which is intriguing to me. I wonder, how can it be that as I increase the outlet temperature, the velocity in the exit is actually decreasing, and then plateaus?

Same thing for inlet volumetric flow rate, why the negative exponential behavior? Shouldn't hotter air travel faster??

Then I played with the inlet temperature vs. outlet velocity, and got extremely weird behavior. I suspect the reason for this is because I was varying the temperature without varying the pressure, and that would go against the degrees of freedom. Anytime I messed with the inlet temperature, it is clearly something going wrong.

Basically I'm just wondering what the physical reason is for the behavior I am getting as shown by my plots.

Lastly, are there any other suggestions for parameters to play with and see the effect for the purpose of understanding the physics of this problem?

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2. Sep 6, 2014

### Maylis

I just did a similar problem and plotted the mass flow rate vs. outlet temperature for a given $\dot{Q}$, and I think I can explain it. So if the air was flowing through the hair dryer very slowly, it will have more residence time inside the dryer and hence absorb more heat, and exit at a higher temperature.

When it is at a faster flow rate, it has less time to absorb heat, and hence leaves at a lower temperature. That is why the mass flow rate is very slow for a high outlet temperature, as seen in this graph. I think it is probably easier to conceptualize what would happen if you slowed down the flow rate, rather than try to think how the flow rate would be affected if you increased the temperature.

I think what I was hypothesizing was the fact that somehow increasing the outlet temperature has an effect on the mass flow rate intrinsically, but they are both variables that can be controlled. I am having some trouble exactly articulating this point though, so maybe someone can chime in.

3. Sep 6, 2014

### Staff: Mentor

There was discussion on hairdriers a year or two back. IIRC I observed that increasing the heating while maintaining fan speed setting fixed resulted in no discernible change in output volumetric flow. This was a surprising finding.